WO2003106250A2

WO2003106250A2 - Control features for a balancing transporter

Info

Publication number: WO2003106250A2
Application number: PCT/US2003/018940
Authority: WO
Inventors: Dean L. Kamen; Burl Amsbury; J. Douglas Field; John David Heinzmann; John M. Kerwin; Christopher C. Langenfield; Jeremy B. Lund; John B. Morrell; Jonathan B. Pompa; David W. Robinson; Jon M. Stevens
Original assignee: Deka Products Limited Partnership
Priority date: 2002-06-14
Filing date: 2003-06-16
Publication date: 2003-12-24
Also published as: AU2003276075A1; WO2003106250A3; AU2003276075A8

Abstract

Methods for controlling the motion of a balancing transporter while supporting a rider or under riderless conditions and for safely limiting the speed of the transporter, and, additionally, for battery load sharing in order to maintain equal charge between dual power sources. The transporter has two laterally disposed primary wheels. In accordance with the methods, an input is received via a user input a control signal corresponding to the input received is genarated. Then a torque is applied to the laterally disposed wheels so as to propel the transporter on the basis of at least the control signal, conditioned in accordance with methods described in the invention.

Description

Control Features for a Balancing Transporter

Field of the Invention The present invention pertains generally to modes for controlling a powered balancing transporter by a user either under conditions in which the user is carried by the transporter or otherwise.

Background Art "Dynamically stabilized transporters" refer, in this description, and in any appended claims, to devices for personal locomotion having a control system that actively maintains the stability of the transporter during operation of the transporter. The control system maintains the stability of the transporter by continuously sensing the orientation, and/or changes in the orientation, of the transporter, determining the corrective action to maintain stability, and commanding the wheel motors to make the corrective action. Such a transporter is described, for example, in U.S. Patent No. 5,971,091 (Kamen et al., issued October 26, 1999). Such transporters have a control system that actively maintains the stability of the transporter while the transporter is operating. The control system maintains the stability of the transporter by continuously sensing the orientation of the transporter, determining the corrective action to maintain stability, and commanding the wheel motors to make the corrective action.

If the transporter loses the ability to maintain stability, such as through the failure of a component or a lack of sufficient power, the rider may experience a sudden loss of balance. Moreover, once a rider dismounts from such a transporter, the rider cannot control the transporter's motion by leaning. It is thus desirable to prevent loss of the ability of the transporter to maintain stability, and, moreover, to provide for control of the motion of the transporter even when the user alights from the transporter. Summary of the Invention In one embodiment of the invention, a method is provided for limiting the speed of a transporter. The method includes determining the instantaneous capability of the transporter, including the capability of the drive system and the energy storage device that powers the drive system. The speed of the transporter is then limited based at least in part on the instantaneous capability of the transporter as a whole, the drive system, and /or the storage device and the potential demands on the transporter based on its present operating condition.

A method may also be provided for estimating an instantaneous capability of one or more batteries. Each battery is characterized by an open circuit voltage and an internal resistance. The method includes measuring battery parameters including a voltage value and a current value; repeating measurements to obtain successive values of the battery parameters; and filtering the successive values of the battery parameters to estimate the instantaneous capability of the battery. The estimate of instantaneous capability for the battery may be used advantageously for limiting the speed of a transporter to maintain balance.

In a specific embodiment of the preceding embodiment, filtering the successive values of the battery parameters includes performing a statistical analysis of the successive values. In a further specific embodiment, filtering the successive values of the battery parameters includes performing recursive least squares regression. In yet another specific embodiment, filtering the measured battery parameters includes performing a recursive least squares regression with exponential forgetting.

In another embodiment of the invention, a method is provided for determining a maximum operating speed for a transporter. The transporter includes a battery supplying power to a motor, which propels the transporter. The method includes calculating an open circuit voltage estimate and an internal resistance estimate for the battery; and calculating the maximum operating speed as a function of the open circuit voltage estimate and the internal resistance estimate for the battery and the average motor current.

In a further embodiment of the invention, the transporter is a balancing transporter. The stability of the transporter in a fore-aft plane is maintained by applying a net torque about a ground contact region equal to a desired acceleration. A contribution to the net torque is provided that is a function of a system pitch value multiplied by a gain. The speed of the transporter may be limited by adding a pitch modification to the desired system pitch value. The pitch modification may be calculated based at least in part on the instantaneous capability of the drive system and the energy storage device that powers the drive system.

In specific embodiments of the invention, calculating a pitch modification may include: adding a proportional term contribution, where the proportional term contribution is a function of the difference between the system speed and an intervention speed; adding a derivative term contribution to the pitch modification, where the derivative term contribution is a function of a system- acceleration; and adding an integral term contribution to the pitch modification, the integral term contribution formed by multiplying a gain by the difference between the system speed and a speed limit, and adding a previous integral term contribution.

In another embodiment of the invention, a transporter is provided for carrying a user. The transporter includes a platform which supports a payload including the user, as well as a ground-contacting module, mounted to the platform, including at least one ground-contacting member, characterized by a ground contact region, and defining a fore-aft plane. The transporter also has a motorized drive arrangement, coupled to the ground-contacting module; the drive arrangement, ground-contacting module and payload constituting a system being unstable with respect to tipping in at least the fore-aft plane when the motorized drive is not powered, the system characterized by a pitch angle offset from a specified pitch angle and a pitch rate offset from a specified pitch rate; and a control loop in which the motorized drive arrangement is included, for dynamically maintaining stability of the system in the fore-aft plane by operation of the motorized drive arrangement so that the net torque experienced by the system about the region of contact with the surface causes a specified acceleration of the system, the net torque including a contribution related to the pitch angle offset multiplied by a first gain wherein the first gain is a function of at least one of an orientation and a displacement of the device. In another embodiment of the invention, a balancing transporter is provided. The transporter is characterized by an instantaneous displacement and orientation. The transporter includes a motorized drive for propelling the transporter; and a control loop in which the motorized drive arrangement is included, for dynamically maintaining stability of the system in the fore-aft plane by operation of the motorized drive arrangement so that the net torque experienced by the system about the region of contact with the surface causes a specified acceleration of the system, the net torque including a contribution functionally related to at least one of the pitch angle, pitch rate, wheel position and wheel velocity, wherein the functional relation varies with at least one of an orientation and a displacement of the device.

In another embodiment of the invention, a method is provided for carrying a payload including a user with a transporter. The method comprises providing a transporter that has a platform which supports a payload including the user, and a ground-contacting module, mounted to the platform, including at least one ground-contacting member, characterized by a ground contact region and a fore- aft plane. A motorized drive arrangement is coupled to the ground-contacting module such that the drive arrangement, ground-contacting module and payload together constitute a system that is unstable with respect to tipping in at least the fore-aft plane when the motorized drive is not powered. The system is characterized by a pitch angle offset from a specified pitch angle and a pitch rate offset from a specified pitch rate. The motorized drive operates the ground- contacting module using a control loop in which the motorized drive arrangement is included, for dynamically ma taining stability of the system in the fore-aft plane by operation of the motorized drive arrangement so that the net torque experienced by the system about the region of contact with the surface causes a specified acceleration of the system. The net torque includes a contribution

related to the pitch angle offset multiplied by a first gain i when the pitch angle offset is greater than or equal to zero and to the pitch angle offset multiplied by a

second gain i when the pitch angle offset is less than zero; and a contribution related to the pitch rate offset multiplied by a third gain 2 _; when the pitch rate offset is greater than or equal to zero, and to the pitch rate offset multiplied by a τζ " fourth gain 2 when the pitch rate offset is less than zero, wherein at least one of a first gain pair consisting of * and 1 and a second gain pair consisting of ² τζ " and 2 are unequal.

In a specific embodiment of the preceding embodiment of the invention, the magnitude of K 1 is less than the magnitude of K ^J . In a further specific

embodiment, K ² equals K ² .

Embodiments of the invention advantageously allow the response of the transporter to be tailored to rider preferences.

In a further embodiment of the invention, a method is provided for equalizing the charge between a first battery and a second battery. The first battery provides current to a first winding of a motor and the second battery provides a current to a second winding of the motor. The motor supplies power to a mechanical device. The method comprises determining a value of a parameter of the first battery and a value of the same parameter for the second battery and then adjusting the current from the first battery and the current from the second battery to reduce the difference of the parameter value for the first battery from the value of the parameter for the second battery. In a specific embodiment of the invention, the parameter, whose difference is to be reduced, is the open circuit voltage of each battery. The method advantageously allows device performance to be maximized, if , for reasons of redundancy, the performance of the device must be limited to a level that can be powered by the weaker of the two batteries.

In a further specific embodiment of the invention, the method further includes limiting the performance of the mechanical device so that at least one of the first battery and the second battery can power the device individually. In a further specific embodiment of the invention, the mechanical device is a balancing transporter and the performance includes the speed of the transporter. In another embodiment of the invention, a device is provided for reducing a charge difference between a first battery and a second battery, the first battery providing a first current to a first winding of a motor and the second battery providing a second current to a second winding of a motor, a first amplifier controlling the first current and a second amplifier controlling the second current. The device comprises a processor which has a comparator that receives measurements of a value of a parameter of the first battery and a value of the parameter of the second battery, and logic that controls the first amplifier and the second amplifier such that the difference between the value of the parameter of the first battery and the value of the parameter of the second battery is reduced.

In a further specific embodiment of the invention, the parameter can be an open circuit voltage. Other parameters can include battery current, motor current, state of charge, available power, internal resistance or other battery characteristics that directly or indirectly can reflect energy remaining in the batteries. In another embodiment of the invention, a method is provided for maximizing the speed limit for a balancing transporter where the speed limit is set to maintain balance. The method comprises providing a transporter including: a platform which supports a payload including the user, a ground-contacting module, mounted to the platform, including at least one ground-contacting member, characterized by a ground contact region and a fore-aft plane, and a motorized drive arrangement, coupled to the ground-contacting module, the drive arrangement, ground-contacting module and payload constituting a system being unstable with respect to tipping in at least the fore-aft plane when the motorized drive is not powered. The arrangement is powered by a first battery and a second battery, the first battery providing a first current to a first winding of a motor and the second battery providing a second current to a second winding of the motor, with the motor powering the drive arrangement.

The method further includes causing the drive arrangement to operate the ground-contacting module using a control loop in which the drive arrangement is included, for dynamically maintaining stability of the system in the fore-aft plane by operation of the drive arrangement; limiting the speed of the transporter so that at least one of the first battery and the second battery can accelerate the transporter; and equalizing the charge across the first battery and the second battery.

In a specific embodiment of the invention, equalizing the charge may include determining a value of a parameter of the first battery and a value of the parameter of the second battery, as well as adjusting the first current and the second current to reduce a difference of the value of the parameter of the first battery from the value of the parameter of the second battery.

In a further embodiment of the invention, a transporter is provided for carrying a payload including a user. The transporter has a platform which supports a payload including the user, and also a ground-contacting module, mounted to the platform, that includes at least one ground-contacting member. A motorized drive arrangement is coupled to the ground-contacting module, the drive arrangement, ground-contacting module and payload constituting a system which is unstable with respect to tipping in at least the fore-aft plane when the motorized drive is not powered. The arrangement is powered by a first battery and a second battery, the first battery providing a first current to a first winding of a motor and the second battery providing a second current to a second winding of the motor, the motor powering the arrangement. The transporter also has a controller that includes a control loop in which the drive arrangement is included, for dynamically maintaining stability of the system in the fore-aft plane by operation of the drive arrangement so that the net torque experienced by the system about the region of contact with the surface causes a specified acceleration of the system. The transporter controller also includes a comparator that receives measurements of a value of a parameter of the first battery and a value of the parameter of the second battery, and logic for limiting the speed of the transporter so that at least one of the first battery and the second battery can accelerate the transporter, as well as logic for equalizing the charge across the first battery and the second battery. In accordance with preferred embodiments of the present invention, a method is provided for maintaining stability of a riderless balancing transporter having two laterally disposed wheels. The balancing transporter has a region of contact with an underlying surface and is characterized by a center of mass. The method has a first step where the absence of a user aboard the balancing transporter is detected. Next, a desired transporter pitch is determined such as to establish the center of mass directly above the region of contact between the balancing transporter and the underlying surface. Then, a torque is applied to the laterally disposed wheels so as to maintain the transporter at the desired transporter pitch. The step of applying torque to the laterally disposed wheels may include applying a torque proportional to the difference between a present transporter pitch and the target transporter pitch. It may also include applying a torque proportional to the sum of coadded terms, a first term proportional to the difference between a present transporter pitch and the target transporter pitch and a second term proportional to the pitch rate of the transporter. Two additional terms may also be coadded to obtain a motor torque command signal: one proportional to the wheel rotational velocity and a second to a time integral of the wheel rotational velocity.

In accordance with other embodiments of the present invention, a method is provided for conducting a transporter under riderless conditions. The transporter has two laterally disposed primary wheels. In accordance with the method, an input is received via a user input disposed on the transporter and a control signal corresponding to the received input is generated. Then a torque is applied to each of the laterally disposed wheels so as propel the transporter on the basis of at least the control signal.

The control signal may correspond to either a commanded torque or to a commanded transporter velocity. The torque may include coadded terms where the terms are, respectively, proportional to the control signal, to a counteracting artificial friction proportional to the common velocity of the wheels, and a term proportional to the differential rotation of the wheels to facilitate turning of the transporter. Generating the control signal based in received input may include conditioning the signal. Conditioning may entail a deadband in the vicinity of zero signal, as well as limits on the range of control signal or on the rate at which the control signal may be slewed. Brief Description of the Drawings

The foregoing features of the invention will be more readily understood by reference to the following detailed description, taken with reference to the accompanying drawings, in which:

Fig. 1 is a perspective view of a personal transporter lacking a stable static position, in accordance with a preferred embodiment of the present invention, for supporting or conveying a subject who remains in a standing position thereon;

Fig. 2 shows an illustrative diagram of an idealized balancing transporter with a rigid wheel in motion at a constant velocity across a flat surface;

Fig. 3 illustrates the control strategy for a simplified version of Fig. 1 to achieve balance using wheel torque;

Fig.4 is a block diagram of a follow-mode controller in accordance with one embodiment of the invention;

Fig. 5 is a block diagram showing generally the nature of sensors, power and control with the embodiment of Fig. 1;

Fig. 6 is a top view of the platform of the transporter of Fig. 1, showing a rider detector in accordance with an embodiment of the invention;

Fig. 7 is a block diagram providing detail of a driver interface assembly;

Fig. 8 is a schematic of the wheel motor control during balancing and normal locomotion, in accordance with an embodiment of the present invention;

Fig. 9A is a top view of a transporter maneuvered by a user accompanying the device, while Fig. 9B is a sectional view from the side through line A-A of the same transporter in two attitudes;

Fig. 10A is a perspective view of a transporter configured as a hand truck for accompanied locomotion;

Fig. 10B is perspective view of the transporter of Fig, 10A with folded components in accordance with embodiments of the present invention.

Fig. 11 illustrates the relationship among various speed limiting parameters for a typical balancing transporter; Fig. 12 is a circuit diagram of a battery in series with a load in accordance with an embodiment of the present invention;

Fig. 13 is a flow diagram illustrating a method for estimating battery parameters;

Figs. 14A-B illustrate setting a speed limit for a transporter; Fig. 15 is a flow diagram illustrating a method for Hmiting the speed of a balancing transporter;

Fig. 16 illustrates non-linear gains for a transporter.

Fig. 17 shows a block diagram of the system architecture of an embodiment of the present invention; Fig. 18 shows a top view of the power source with the top cover removed; Fig. 19 is a block diagram of the power drive module of an embodiment of the present invention;

Fig. 20 is an electrical model of a motor; 5 Fig. 21 shows an exploded view of a yaw-input device in accordance with an embodiment of the present invention;

Fig. 22 shows a battery/ control subsystem according to an embodiment of the present invention;

Fig. 23 shows a flow diagram for a method of equalizing the charge among o a plurality of batteries;

Figs. 24A and 24B are schematic side views of the balancing transporter of Fig. 1 in two distinct conditions of stasis maintained for differing relative placement of the center of gravity in accordance with an embodiment of the invention; and 5 Fig. 25 is a block diagram of an E-stand mode controller in accordance with an embodiment of the invention.

Detailed Description of Specific Embodiments Fig. 1 shows a balancing human transporter, designated generally by numeral 18, of a sort to which the present invention may advantageously be 0 applied. Transporter 18 is described in detail in U.S. patent number 6,302,230, and is related to transporters described in U.S. Patent Nos. 5,701,965, 5,971,091, and 5,791,425.

An alternative to operation of a statically stable transporter is that dynamic stability may be maintained by action of the user, as in the case of a bicycle or 5 motorcycle or scooter, or, in accordance with embodiments of the present invention, by a control loop, as in the case of the human transporter described in U.S. Patent No. 5,701,965. The invention may be implemented in a wide range of embodiments.

Referring, again, to the embodiment of Fig. 1, a subject 10 stands on a support platform 12 of transporter 18 and holds a grip 14 on a handle 16 attached to the platform 12, so that the transporter 18 of this embodiment maybe operated in a manner analogous to a scooter. It is within the scope of the present invention that the support may be other than the platform shown, by way of example in Fig, 1, and may, for an additional example, be a seat or other form of support. A control loop may be provided so that leaning of the subject results in the application of torque to wheels 20 and 21 about axle 22 thereby causing an acceleration of the transporter.

Transporter 18, however, is statically unstable, and, absent operation of the control loop to maintain dynamic stability, subject 10 will no longer be supported in a standing position. Different numbers of wheels or other ground-contacting members may advantageously be used in various embodiments of the invention as particularly suited to varying applications. Thus, as described in greater detail below, the number of ground-contacting members may be any number equal to, or greater than, one. For example, clusters of wheels may be provided on either side of the transporter thereby providing for sta -climbing or traversing other obstacles, as described in the related US patents listed above.

For many applications, the dimensions of platform 12, and indeed of the entire ground-contacting module, designated generally by numeral 6, are advantageously comparable to the dimensions of the footprint or shoulder width of user 10. Thus transporter 18 may advantageously be used as a mobile work platform or a recreational transporter such as a golf cart, or as a delivery transporter.

Transporter 18 may be operated in a station-keeping mode, wherein balance is maintained substantially at a specified position. Additionally, transporter 18, which may be referred to herein, without limitation, as a "transporter," may also maintain a fixed position and orientation when the user 10 is not on platform 12. This mode of operation, referred to as a "kickstand" mode, prevents runaway of the transporter and provides for the safety of the user and other persons. A force plate 8 or other sensor, disposed on platform 12, detects the presence of a user on the transporter, as further described below.

A characteristic of many transporter embodiments to which the present invention may be applied is the use of a pair of laterally disposed ground- contacting members 20 and 21 to suspend subject 10 over a surface with respect to which the subject is being transported. The ground or other surface, such as a floor, over which a vehicle in accordance with the invention is employed may be referred to generally herein as the "ground." The ground-contacting members 20, 21, here depicted as wheels, are typically motor-driven. In many embodiments, the configuration in which the subject is suspended during locomotion lacks inherent stability in the fore-aft plane at least a portion of the time with respect to a vertical (axis z) but is relatively stable with respect to a vertical in the lateral plane.

Some embodiments of the invention may invoke the concept of primary wheels. The term "primary wheels," as used in this description and in any appended claims, refers to a minimum set of a vehicle's wheels on which the vehicle is capable of operating stably. More generally, the term "primary ground- contacting members" allows for a more general class of members, that includes, but is not limited to, wheels. Hence, as used in this description and in any appended claims, "primary ground-contacting members" refers to a minimum set of a vehicle's ground-contacting members on which the vehicle is capable of operating stably. Other ground-contacting members may include, without limitation: arcuate sections of a wheel, clusters of wheels, treads, etc.

In various embodiments of the invention, fore-aft stability may be achieved by providing a control loop, in which one or more motors are included, for operation of a motorized drive in connection with the ground-contacting members. As described below, a pair of ground-contacting members may, for example, be a pair of wheels or a pair of wheel clusters. In the case of wheel clusters, each cluster may include a plurality of wheels. Each ground-contacting member, however, may instead be a plurality (typically a pair) of axially-adjacent, radially supported and rotatably mounted arcuate elements. In these embodiments, the ground-contacting members are driven by the motorized drive in the control loop in such a way as to maintain, when the vehicle is not in locomotion, the center of mass of the vehicle above the region of contact of the ground-contacting members with the ground, regardless of disturbances and forces operative on the vehicle.

A ground-contacting member typically has a "point" (actually, a region) of contact or tangency with the surface over which the vehicle is traveling or standing. Due to the compliance of the ground-contacting member, the "point" of contact is actually an area, where the region of contact may also be referred to as a contact patch. The weight of the vehicle is distributed over the contact region, giving rise to a distribution of pressures over the region, with the center of pressure displaced forward during forward motion. The distribution of pressures is a function both of the composition and structure of the wheel, the rotational velocity of the wheel, the torque applied to the wheel, and thus of the frictional forces acting on the wheel.

A force in the direction of motion is required to overcome rolling friction (and other frictional forces, including air resistance). Gravity may be used, in accordance with preferred embodiments of the invention, to provide a torque about the point of contact with the surface in a direction having a component in the sense of desired motion.

Referring to Fig. 2, to illustrate these principles, a diagram is shown of the forces acting on a transporter that locomotes with constant velocity v on a single wheel over a flat surface. The principles now discussed may readily be generalized to operation on a sloped surface and to accommodate any other external forces that might be present. Wheel 2160 of radius R_w rotates with respect to chassis 2162 about axle 2164 and contacts the underlying surface at point P. For purposes of illustration only, it is assumed that wheel 2160 contacts the surface at a point.

The wheel is driven with respect to the transporter by a torque T (supplied by a motor, for example) which in turn creates a reaction torque -T on the transporter. Since the torque acts about the axle 2164, the reaction torque corresponds to a force Fb acting at the center of gravity (CG) of the system, including the transporter and payload, where F = T/RCG, where RCG is the distance between the axle and the CG of the system. The line 2170 from the CG to point P is at an angle θ_s relative to the vertical 2172.

The rolling friction, f, acting on the wheel at point P, is proportional to the velocity v of the rim of the wheel, with the proportionality expressed as f=μv. For constant velocity to be maintained, this force f must be exactly canceled.

Consequently, with gravity providing the force, the condition that must be satisfied is:

Fb cos θ_s = fb , (Eqn. 1) where fb is the component of the reaction force acting transverse to axis 2174 between the CG and point P. In order to prevent the transporter from falling, a stability condition must also exist, namely that no net force acts on the CG in a direction transverse to line 2170, i.e., there is no net torque about the point of contact P during motion at constant velocity (i.e., in an inertial frame of reference where the point P is fixed). This condition may be expressed as: F_g sin θ_s = fb , (Eqn. 2) where F_g sin θ_s is the "tipping" component of gravity, and fb is the counter-tipping component of the reactive force on the transporter caused by wheel rotation (fb =Fb cos θ), and where θ is the angle shown line 2170 and line 2174. Eqns. 1 and 2 may be combined to yield F_g sin θ_s cos θ_s = f = μv, thus, in the limit of small angles (where sin θ is approximately θ),

Θ_s = (μ/F_g) v , (Eqn. 3) showing that increasing velocity requires increased lean to overcome the effects of friction. Additionally, a control loop that imposes stability on the system will respond to an increased lean by increasing velocity of the system. While the preceding discussion assumed constant velocity, additional lean beyond that required to overcome the effects of friction will result in acceleration since an additional forward-directed force acts on the CG. Conversely, in order to achieve acceleration (or deceleration) of the transporter, additional leaning (forward or backward) must be provided in a manner discussed in further detail below.

Referring further to Fig. 1, user 10 is shown standing on platform (or 'base') 12 of ground-contacting module 6. Wheels 20 and 21 are shown as coaxial about the Y axis. Steering or other control may be provided by one or more thumbwheels 32 and 34, or by other user input mechanisms such as those described in detail in U.S. Patent 6,288,505. Any user input device that provides the functions discussed below is within the scope of the present invention. Finally, a handlebar 14 is shown as may be provided on stalk 16 for gripping by the user. A simplified control algorithm for achieving balance in the embodiment of the invention according to Fig. 1, when the wheels are active for locomotion, is shown in the block diagram of Fig. 3. The plant 61 is equivalent to the equations of motion of a system with a ground contacting module driven by a single motor, before the control loop is applied. T identifies the wheel torque. The remaining portion of the figure is the control used to achieve balance. The boxes 62 and 63 indicate differentiation. To achieve dynamic control to insure stability of the system, and to keep the system in the neighborhood of a reference point on the surface, the wheel torque T in this embodiment is governed by the following simplified control equation:

T = K₁(θ -θ₀) + K₂(θ-θ₀) + K₃(x -x₀) + K₄(x -x₀) , (Eqn. 4) where:

• T denotes a torque applied to a ground-contacting element about its axis of rotation;

• θ is a quantity corresponding to the lean of the entire system about the ground contact, with Θ o representing the magnitude of a system pitch offset, all as discussed in detail below;

• x identifies the fore-aft displacement along the surface relative to a fiducial reference point, with x_o representing the magnitude of a specified fiducial reference offset ; • a dot over a character denotes a variable differentiated with respect to time; and

• a subscripted variable denotes a specified offset that may be input into the system as described below; and

• Ki, K₂, K3, and K4 are gain coefficients that may be configured, either in design of the system or in real-time, on the basis of a current operating mode and operating conditions as well as preferences of a user. The gain coefficients may be of a positive, negative, or zero magnitude, affecting thereby the mode of operation of the vehicle, as discussed below. The gains Ki, K₂, K3, and K4 are dependent upon the physical parameters of the system and other effects such as gravity. The simplified control algorithm of Fig. 3 maintains balance and also proximity to the reference point on the surface in the presence of disturbances such as changes to the system's center of mass with respect to the reference point on the surface due to body motion of the subject or contact with other persons or objects. It should be noted that the amplifier control may be configured to control motor current (in which case torque T is commanded, as shown in Fig. 3) or, alternatively, the voltage applied to the motor may be controlled, in which case the commanded parameter is velocity.

The effect of θ 0 in the above control equation (Eqn. 4) is to produce a specified offset Θ _o from the non-pitched position where θ =0. Adjustment of θ 0 will adjust the vehicle's offset from a non-pitched position. As discussed in further detail below, in various embodiments, pitch offset may be adjusted by the user, for example, by means of a thumb wheel 32, shown in Fig. 1. An adjustable pitch offset is useful under a variety of circumstances. For example, when operating the vehicle on an incline, it may be desirable for the operator to stand erect with respect to gravity when the vehicle is stationary or moving at a uniform rate. On an upward incline, a forward torque on the wheels is required in order to keep the wheels in place. This requires that the user push the handle further forward, requiring that the user assume an awkward position. Conversely, on a downward incline, the handle must be drawn back in order to remain stationary. Under these circumstances, θ o may advantageously be manually offset to allow control with respect to a stationary pitch comfortable to the user.

Alternatively, θ o can be set by the control system of the vehicle as a method of limiting the speed and/or the performance of the vehicle.

The magnitude of K3 determines the extent to which the vehicle will seek to return to a given location. With a non-zero K3, the effect of xo is to produce a specified offset xo from the fiducial reference by which x is measured. When Ks is zero, the vehicle has no bias to return to a given location. The consequence of this is that if the vehicle is caused to lean in a forward direction, the vehicle will move in a forward direction, thereby mamtaining balance. The term "lean" is often used with respect to a system balanced on a single point of a perfectly rigid member. In that case, the point (or line) of contact between the member and the underlying surface has zero theoretical width. In that case, furthermore, lean may refer to a quantity that expresses the orientation with respect to the vertical (i.e., an imaginary line passing through the center of the earth) of a line from the center of gravity (CG) of the system through the theoretical line of ground contact of the wheel. While recognizing, as discussed above, that an actual ground-contacting member is not perfectly rigid, the term "lean" is used herein in the common sense of a theoretical limit of a rigid ground- contacting member. The term "system" refers to all mass caused to move due to motion of the ground-contacting elements with respect to the surface over which the vehicle is moving.

"Stability" as used in this description and in any appended claims refers to the mechanical condition of an operating position with respect to which the system will naturally return if the system is perturbed away from the operating position in any respect.

In order to accommodate two wheels instead of the one-wheel system illustrated for simplicity in Fig. 2, separate motors may be provided for left and right wheels of the vehicle and the torque desired from the left motor and the torque to be applied by the right motor can be governed in the general manner described below in connection with Fig.4. Additionally, tracking both the left wheel motion and the right wheel motion permits adjustments to be made to prevent unwanted turning of the vehicle and to account for performance variations between the two drive motors. In cases where gain K3 is zero, a user control input such as a joystick may be used to adjust the torques of each motor. In operation of this embodiment, forward motion of the joystick is used to cause forward motion of the transporter, and reverse motion of the joystick causes backward motion of the transporter. A left turn similarly is accomplished by leftward motion of the joystick. For a right turn, the joystick is moved to the right. The transporter may be turned in place when the joystick is moved to the left or to the right, by causing rotation of left and right motors, and hence left and right wheels, at equal rates in opposite senses of rotation. With respect to forward and reverse motion an alternative to the joystick is simply leaning forward or backward (in a case where K3 is zero), since the pitch sensor (measuring Θ) would identify a pitch change that the system would respond to, leading to forward or reverse motion, depending on the direction of lean. In such instances, other types of yaw control (i.e., control to accomplish turning right or left can be used). Alternatively, control strategies based on fuzzy logic can be implemented. It can be seen that the approach of adjusting motor torques when in the balance mode permits fore-aft stability to be achieved without the necessity of additional stabilizing wheels or struts (although such aids to stability may also be provided). In other words, stability is achieved dynamically, by motion of the components of the transporter (in this case constituting the entire transporter) relative to the ground.

In the block diagram of Fig. 5 it can be seen that a control system 51 is used to control the motor drives and actuators of the embodiment of Figs. 1-3 to achieve locomotion and balance. These include motor drives 531 and 532 for left and right wheels respectively. If clusters are present as in the embodiment of Fig. 2, actuators 541 and 542 for left and right clusters respectively. The control system has data inputs including user interface 561, pitch sensor 562 for sensing fore-aft pitch, and wheel rotation sensors 563, and pitch rate sensor 564. Pitch rate and pitch may be derived through the use of gyroscopes or inclinometers, for example, alone or in combination. Control system 51 also may contain a balancing margin monitor which combines information on current battery parameters with information on motor parameters to calculate a maximum current speed of the transporter. The control system 51 may limit the speed of the transporter to ensure that adequate speed reserve is available to maintain balance. The control system 51 may further contain logic to reduce the speed of the transporter to avoid damaging the battery due to generation of over voltage. This condition can occur if the transporter is provided with capability to regenerate the battery during braking and when traveling downhill. In accordance with other embodiments of the invention, handle 16 and grip

14 may be absent altogether, and the platform 12 may be equipped with sensors, such as force plate 8, for example, to detect leaning of the subject. Indeed, as further described herein, the pitch of the transporter is sensed and may be used to govern operation of the control loop, so that if the subject leans forward, the transporter will move forward to maintain a desired velocity or to provide desired acceleration. Accordingly, a forward lean of the subject will cause the transporter to pitch forward and produce forward movement; a backward lean will cause the transporter to pitch backward and produce backward movement. Appropriate force transducers may be provided to sense leftward and rightward leaning and related controls provided to cause left and right turning as a result of the sensed leaning. Leaning may also be detected using proximity sensors. Additionally, operation of the transporter maybe governed on the basis of the orientation of the user with respect to the platform. In further embodiments, the transporter may be equipped with a foot- (or force-) actuated switch sensitive to the presence of a user on the transporter. Thus, for example, the transporter may be powered automatically upon ascent of a user onto the platform. Conversely, when the user alights from the transporter, power can be removed and the transporter disabled. Alternatively, the transporter may be programmed to enter a dynamic "kickstand" mode in which the transporter remains balanced in place when the user alights. Thus, the transporter is ready for the user to resume travel by reboarding the transporter. Furthermore, the transporter is thus safely parked while not actively operated by a user aboard the transporter. Fig. 6 shows a rider detection mechanism used in an embodiment of the present invention, as described in detail in U.S. Patent no. 6,288,505. When the absence of a rider is detected, the transporter is allowed to operate in one or more riderless modes. Fig. 6 shows a top view of the rider detector designated generally by numeral 510. Transporter 10 incorporating the rider detector includes a base 12, left wheel fender 512, right wheel fender 514, support stem 16 for handlebar 14 (shown in Fig. 1). Wheel fenders 512 and 514 cover the corresponding wheels. Support stem 16 is attached to the base 12 and provides a sealed conduit for transmission of signals from controls 32, 34 (shown in Fig. 1) that may be located on the handlebar to the control electronics sealed in the base 12. Wheel fenders 512, 514 are rigidly attached to the sides of the base.

The top of base 12 provides a substantially flat surface and is sized to comfortably support a rider standing on the base 12. A mat 521 covers the top of the base 12 and provides additional protection to the base 12 from particles and dust from the environment. In an alternate embodiment, the mat may also cover part of the fenders 512 514 and may be used to cover a charger port (not shown) that provides for external charging of the power supply. Mat 521 may be made of an elastomeric material that provides sufficient traction such that the rider does not slip off the mat 521 under expected operating conditions. A plate 522 is positioned between base 12 and mat 521. Plate 522 is made of a rigid material and evenly distributes the force acting on the plate 522 from the rider's feet such that at least one rider detection switch 523 is activated when a rider is standing on the mat.

Fig. 7 is a block diagram providing detail of a driver interface assembly 273. A peripheral microcomputer board 291 receives an input from joystick 292 as well as from inclinometer 293 or another tπt-dete- nining arrangement. The inclinometer provides information signals as to pitch and pitch rate. (The term "inclinometer" as used in this context throughout this description and in the accompanying claims means any device providing an output indicative of pitch or pitch rate, regardless of the arrangement used to achieve the output; if only one of the pitch and pitch rate variables is provided as an output, the other variable can be obtained by suitable differentiation or integration with respect to time.) To permit controlled banking into turns by the transporter (thereby to increase stability while turning) it is also feasible to utilize a second inclinometer to provide information as to roll and roll rate or, alternatively, the resultant of system weight and centrifugal force. Other inputs 294 may also be desirably provided as an input to the peripheral micro controller board 291. Such other inputs may include signals gated by switches (knobs and buttons) for platform adjustment and for determining the mode of operation. The peripheral micro controller board 291 also has inputs for receiving signals from the battery stack 271 as to battery voltage, battery current, and battery temperature. The peripheral micro controller board 291 is in communication over bus 279 with a central micro controller board that maybe used to control the wheel motors as described below in connection with Fig. 8. Fig. 8 is a block diagram showing control algorithms, suitable for use in conjunction with the control assemblies of Fig. 7 to provide stability for a transporter according to the embodiment of Fig. 1 and other embodiments in which the transporter and payload are balanced on two ground-contacting members, both during locomotion and in a fixed position. The following conventions are used in connection with the description below:

1. Variables defined in world coordinates are named using a single subscript in capital letters. World coordinates are coordinates fixed to the earth (inertial).

2. A non-subscripted r identifies a wheel radius. 3. Lower case subscripts are used to indicate other attributes, e.g., right/left, etc.: r = right; 1 = left; ref = reference; f = finish; s = start.

4. All angles are positive in the clockwise direction, where positive travel is in the positive x direction.

5. A dot over a variable indicates differentiation in time, e.g., θ . Fig. 7 shows the control arrangement for the motors of the right and left wheels. The arrangement has inputs of θ , θ , r θ_w\ (linear velocity of the left wheel relative to the world coordinate system) and r # _Wr (linear velocity of the right wheel), in addition to directional inputs 3300 determined by joystick position along X and Y axes of a reference coordinate system. Inputs θ , θ , and error signals x and x (described below), subject to gains Ki, K₂, Ks, and K₄ respectively, become inputs to summer 3319, which produces the basic balancing torque command for the wheels, in the general manner described above in connection with Fig. 3 above. The output of summer 3319 is combined with the output of yaw PID loop 3316 (described below) in summer 3320, then divided in divider 3322 and limited in saturation limiter 3324, to produce the left wheel torque command. Similarly, the output of summer 3319 is combined with the output of PID loop 3316 in summer 3321, then divided in divider 3323 and limited in saturation limiter 3325, to produce the right wheel torque command. In Fig. 8, a directional input along the X axis moves the reference coordinate system along its X axis relative to the world coordinate system (which represents the traveled surface), at a velocity proportional to the displacement of the joystick. A directional input along the Y axis rotates the reference coordinate system about its Z axis at an angular velocity proportional to the displacement of the joystick. It will be appreciated that motion of the joystick in the positive X direction is here interpreted to mean forward motion; motion of the joystick in the negative X direction means reverse motion. Similarly, motion of the joystick in the positive Y direction means leftward turning, counter-clockwise as viewed from above; motion of the joystick in the negative Y direction means rightward turning clockwise as viewed from above. Hence the directional inputs Y and X are given deadband via deadband blocks 3301 and 3302 respectively, to widen the neutral position of the joystick, then subject to gains Kll and K10, then rate-limited by limiters 3303 and 3304 respectively, which limit the angular and linear accelerations respectively of the reference coordinate system. The sum of these outputs achieved through summer 3305 becomes the reference velocity _rref whereas the difference of these outputs achieved through summer 3306 becomes the reference velocity x ι _ref. These reference velocities are subtracted in summers 3308 and 3307 from compensated linear velocity input signals r έ. _wι and r Θ_WI for left and right wheels to obtain velocity error signals x I and x _r for left and right wheels within the reference coordinate system. In turn the average of these signals, determined via summer 3317 and divider 3318, produces a linear velocity error signal . Displacement error signal x is derived by integrating r # ι and r θ_wτ in integrators 3310 and 3309, limiting the results in saturation limiters 3312 and 3311, and then averaging their outputs via summer 3313 and divider 3315. The difference between these displacements, determined via summer 3314, produces the yaw error signal Ψ.

The yaw error signal Ψ is run through a standard proportional-plus- integral-plus-derivative (PID) control loop 3316, the output of which is combined with the output of the basic balancing torque command of summer 3319, to produce the individual wheel torque commands, which cause the wheels to maintain fore-aft stability and also cause the transporter to align itself with the axes of, and follow the origin of, the reference coordinate system as directed by directional input 3300.

In order to start the transporter, directional input 3300 (which maybe a joystick) provides a positive x for forward motion. The signal is divided and summed in summers 3308 and 3307, and subtracted from the right and left wheel velocity R and providing a negative correction; this correction leads ultimately to a negative torque contribution at summer 3319, causing the wheels to move backward, so as to create a torque due to gravity that causes the transporter to lean forward. This forward lean leads to changing θ and θ , which leads to positive corrections in summer 3319, causing the transporter to move forward. Thus, moving the joystick forward or backward will cause the transporter to lean forward or backward, as the case may be, and to move in the direction of the lean. This is a property of the control of Fig. 8. An equivalent result can be achieved by leaning, where K3 is zero.

Acceleration of the transporter may be established by system lean. For example, to achieve forward acceleration of the transporter by forward system lean; the center of gravity of the system (transporter and payload) would be placed forward of the center of the pressure distribution of the contact region where the wheels contact the ground— the more the lean, the more the acceleration. Thus, furthermore, it can be seen that leaning, in conjunction with gravity and friction, determines acceleration (positive or negative) of the system. In this manner, if the transporter is moving forward, pitching the system back will achieve braking. Because the transporter must overcome friction, there is typically some system lean when the transporter is moving at constant velocity over level ground. In other words, looking at the torque on the transporter caused by gravity and the torque caused by all other external forces, the torque applied by the motorized drive is adjusted so that the net torque from all these sources produces a desired acceleration.

Guided Control Operating modes of the transporter may include modes wherein the rider is supported by the transporter but may also include modes where the rider is not supported by the transporter. For example, it may be advantageous for the rider to be able to 'drive' or to 'conduct' the transporter while walking alongside or behind it.

Referring now to Fig. 4, a schematic is shown of a control mode, referred to as 'follow mode,' wherein a user may guide operation of a two-wheeled transporter while walking alongside or behind the transporter rather than being supported by it as in ordinary operation of the transporter.

Fig. 4 depicts the manner in which command signals are derived for each of the wheel motor amplifiers, the left wheel command 402 and the right wheel command 404. Application of motor commands to govern wheel actuators to drive wheels 20 and 21 is described in U.S. Patent no. 6,288,505. Each wheel command is the result of a signal 406 described here in regard to the left wheel for purposes of illustration. Multiple terms contribute to signal 406 and they are coadded at summer 408, with the signs of the respective terms as now described. It is to be understood that various modes of motor control are within the scope of the invention. For example, the motors may be commanded in current mode, wherein the torque applied to the wheels is commanded and, as shown below, ultimate subject to user input. Thus, the user governs how much torque is applied. This is a mode of operation that users tend to be comfortable with, allowing a user to urge the transporter over an obstacle or up a curb or a stair. On the other hand, the wheel motors may be governed in voltage mode, where wheel velocity is controlled by the user input.

User input 410 is received from a user input device which may be thumbwheel 32 (shown in Fig. 1) or may be another user input device. User input 410 leads to generation of a control signal 412. User input is typically condition in one or more manners to generate control signal 412. For example, a deadband 414 may be provided such that the range of no response is extended about zero. As another example, the range of control signal in response to user input may be limited by a limiter 416. Any manner of tailoring of the response of the control signal to user input is within the scope of the present invention. A gain is provided by amplifier 418, where the gain may be constant or dependent upon various parameters. In particular, the gain scheduling may differ between the rider and riderless modes, both as to magnitude of gain, and, in the hand truck embodiment discussed below, the sense of the response to user input may also advantageously be made variable.

Moreover, the slew rate of change of the commanded control signal may be limited by slew limiter 420.

In addition to control signal 412 which is applied, via summers 408 and 422 to the respective wheel amplifiers, a counteracting contribution to wheel torque is provided that is proportional, modulo gain 424, to the common component 426 of the rotational velocity of the respective right and left wheels. Since the counteracting component is proportional to velocity, it acts as an artificially imposed friction and the user feels a resistance to pushing (or pulling) the transporter.

Finally, a differential term, proportional, above a threshold set by deadband 428, to the differential rotational velocity 430 of the two wheels. This allows the faux friction of the preceding term to be overcome in the case where the user seeks to turn the transporter. As suggested above, transporter 10 may be guided by a user walking ahead of, behind, or alongside, the transporter. When operated without a mounted user, transporter 10 may operate in either a 'power assist' mode or in the same mode of operation as when bearing the user, in which case it operates in a 'riderless balancing mode'. If the transporter is being operated in balance mode, and if the user is no longer sensed by rider detection switch 523, then limits may be placed on the distance the transporter may be moved from its position at the time a user was last onboard the transporter, as sensed by rider detect switch 523 or other means. This function, which may be referred to as an "electronic leash," may be used as an added safety feature to limit unintended travel of the transporter. Travel of the transporter may be limited such that the transporter is decelerated to a slow speed or a stop after a specified distance with respect to a fiducial reference position, set when the rider dismounts, or under other circumstances discussed below. Additionally, once the transporter is slowed or stopped, the transporter may be switched out of balance mode and/ or may be powered off until such time as a user restarts the transporter. The distance of travel before such an electronic leash is activated may be set based on the desired performance of the transporter. For example, a distance on the order two meters may be used. The distance of travel may be determined by integrating the velocity of the transporter as determined by sensing rotation of the wheels from the position of the transporter at the time a user was last onboard the transporter, as sensed by rider detect switch 523 or other means. Alternatively, distance may be determined by other means, such as an onboard GPS receiver. In another specific embodiment, if the user is no longer sensed by rider detection switch 523 or other means, then limits may be placed on the speed the transporter may attain. If the transporter attains a specified speed without a user aboard, then the transporter maybe decelerated to a slower speed or a stop.

In the case transporter 18 is actively guided by a user in balance mode, the electronic leash may be deactivated to allow travel beyond the distanced specified for the electronic leash. Alternatively, if a user repeatedly dismounts from transporter, actively guides the transporter for short distances, such as to traverse a curb or a flight of stairs, and then remounts the transporter, it may be advantageous to continue to use the electronic leash. In this case, however, the user may wish to guide the transporter further than the distance specified by the electronic leash, for example to climb a long flight of stairs. In such a case, the electronic leash may advantageously be reset, accordingly updating the fiducial reference, to allow further riderless travel in balance mode while still guarding against unintended travel of the transporter.

One method of resetting the electronic leash while still avoiding unintended travel is to slew the wheel position variable to zero whenever the velocity of the transporter reaches or falls below a specified level, such as 0.5 mi/hr. Thus, a user may guide the transporter further than the distance specified by the electronic leash, for example to climb a large flight of stairs, while still guarding against unintended travel of the transporter. Alternatively, a user input device may be used to alternatively activate and deactivate the electronic leash or to reset the electronic leash.

Embodiments of the invention advantageously employing these capabilities are described with reference to Figs. 9 and 10. In particular, Fig. 9A shows handle 1110 configured forward of platform base 12. Handle 1110 may be drawn by a user and forward motion induced by leaning the handle from position , 1112 to position 1114. Leaning the handle causes concomitant leaning of the platform from position 1116 to position 1118. Similarly, drawing handle 1110 upward causes transporter 18 to decelerate and stop. This mode of operation may be referred to as a 'guided mule' mode.

Fig. 10A shows a transporter device 18 with handle 1110 disposed aft of platform 12 for powered operation in a 'hand truck' mode. Handle 1110 may be extended at joint 1120, which may be, for example, pivotal, as shown, or may be an extensible sleeve. Moreover, a 'dead-man' switch 1122 may be provided to ensure operation of the transporter only under active control of a user. Additionally, a platform extension 1124 may provide additional support surface. Transporter 18, in the embodiment of Fig. 10A, may be collapsed for storage and conveyance as shown in Fig. 10B. Handle 1110 and platform 1124 are shown in a folded position to minimize the volume required to contain the transporter.

Speed Limiting In a further embodiment of the invention, any of the foregoing embodiments of a transporter in accordance with the present invention may be provided with speed limiting to maintain balance and control, which may otherwise be lost if the wheels (arcuate elements, or other ground-contacting members) were permitted to reach a maximum operating speed for the transporter. The term "maximum operating speed" as used in the specification and in any appended claims, unless context requires otherwise, will mean the maximum speed at which the transporter is presently capable of being propelled. This maximum operating speed will typically be a function of an instantaneous capability of the transporter, such as the capability of the drive system and/or the capability of the energy storage device provided to power drive system. For example, the energy storage device may be chemical (in which case it is referred to as a 'battery') or otherwise. The "instantaneous capability" of the energy storage device is a measure of the instantaneous power that can be delivered by the device and the "maximum capability" of the device is a measure of the greatest power that the device can supply at any time. The terms "speed intervention band," "intervention speed," and "speed limit" as used in the specification and in any appended claims, unless context requires otherwise, will mean a range or band of speeds extending from an "intervention speed" at the lower end to a "speed limit" at the upper end. The intervention speed is a threshold speed at which means may be employed to reduce the transporter's speed. A transporter will typically be operated with a margin between the maximum operating speed and the speed limit, as illustrated in Fig. 11. This margin helps ensure that the transporter will maintain balance over a range of operating conditions.

Speed reduction may be accomplished by pitching the transporter back in the direction opposite from the current direction of travel, which causes the transporter to slow down. (As discussed above, the extent and direction of system lean determine the transporter's acceleration.) In this embodiment, the transporter is pitched back by adding a pitch modification to the inclinometer pitch value. Speed reduction can occur whenever the transporter velocity of the transporter exceeds the intervention speed. The pitch modification is determined by looking at the difference between the transporter velocity and the intervention speed, integrated over time. The automatic pitch modification sequence may be maintained until the transporter slows to the desired dropout speed (some speed below the intervention speed), and the pitch angle may then be smoothly returned to its original value.

Maximum Operating Speed Estimation One method for determining the maximum operating speed of the transporter, if the energy storage device is a battery, is to monitor the battery voltage and current produced, which are then used to estimate the maximum velocity the transporter is currently capable of mamtaining. Another method is to measure the voltages of the battery and the motor and to monitor the difference between the two; the difference provides an estimate of the amount of velocity margin (or balancing margin) currently available to the transporter. In a further embodiment of the invention, a method for estimating the instantaneous capability of a battery is provided. As shown in Fig. 12, a simplified model 5000 is used for the battery, consisting of a "perfect" DC voltage source 5010 with "open circuit" voltage, V₀-. a series resistance for the battery, Rbat, a current, Ibat, and a battery voltage, Vbat. V₀- and Rbat cannot be measured but can be estimated from measurements of Vbat and Ibat. Ideally, these variables should follow a linear relationship:

Nbat = Voc - (Ibat * Rbat) (Eqn. 5).

Since this linear relationship is ideal, measured values of Vbat and Ibat will likely present a "scatter plot." Note that 'statistical' as used herein, in either adjectival or adverbial form, refers to the drawing of inferences as to the value of a parameter based on sampling the value by measurement at intervals that may be regular or irregular with respect to distribution of the samples in time or in terms of another dimension. The verb 'filter', as used herein and in any appended claims, refers to the process of extracting a value attributable to a single point in time from a plurality of data that may be obtained in successive samplings and may be subject to either random or systematic fluctuations, or both. Application of filtering techniques, as are known in the art, to the data allows estimated values of Voc and Rbat to be derived. For example, a regression analysis using a least squares technique may be employed to derive estimated values of Voc and Rbat from the measured values of Vbat and Ibat. V_o and Rbat will change, such as, for example, due to ambient temperature, battery temperature, battery age, battery usage (both the overall amount of usage and usage pattern), and over time as the battery charge is depleted (and regenerated). Accordingly, a more accurate estimate may be obtained if the more recent measured values of Vbat and Ibat are used for the regression or more recent values are weighted more heavily than older values.

In a specific embodiment of the present invention, a recursive least squares technique with exponential forgetting is employed to estimate V_o and Rbat for the battery.

In another specific embodiment of the invention, as shown in Fig. 13 (step 5200), newly measured values of Vbat and Ibat are used to correct the estimated values using a low pass filtering algorithm. First the variables are initialized (step 5210), with Voc and Rbat set to typical values. Then, Vbat and Ibat are measured periodically (step 5220). To ensure that the signal is sufficiently "rich", i.e., there is a statistically significant difference between data points, the squared distance, D, of Vbat and Ibat from the last accepted values of these variables, V_pr-v and I_prev_. is calculated (step 5230):

D= (Vprev Vbat)²+(Iprev- Ibat)² (Eqn. 6). This calculation identifies data points that may provide additional information from which to refine the estimate of current battery parameters. For example, when the transporter is at rest, little current is drawn and a series of such measurements could skew the estimated value for the battery parameters from their true values, as filtering progresses. An appropriately set threshold for D can be used to mitigate the impact of such data points on the estimate. The following calculations may then be performed:

(1) calculate update gains Kvoc and Krbat (step 5240):

K_Voc ,1 . Pa _: Pa -Pb * a Pb

lP_b -Pc *X] (Eqn. 7) where, p_a is the direct V_oc covariance matrix element, pb is the cross coupling covariance matrix element, and p_c is the direct Rbat covariance matrix element, (Note: p_a, pb, and p_c represent the uncertainty in the state estimate);

(2) calculate error between battery state estimate and the new data point (step 5250):

Err = Vbat - (Voc - Ibat * Rbat) (Eqn. 8);

(3) update battery state estimate (step 5270):

(If D is less than the threshold (step 5265), K_rbat maybe set to zero (step 5265) so that Rbat is not updated.) Voc = Voc +K_V0C* Err (Eqn. 9)

Rbat = Rbat + Krbat * Err (Eqn. 10); and

(4) update signal content variables (step 5280), if D is greater than the threshold (step 5275):

Vprev = Vbat (Eqn. 11) Ipre = Ibat. (Eqn. 12).

The process can continue with repeated measurement of Vbat and Ibat (step 5220). In a specific embodiment of the invention, V_o is initialized to the first measured value of Vbat. Rbat is set to a value higher than expected in typical operation. This approach to initializing Rbat allows the algorithm to bring the Rbat estimate down during operation. Matrix element pb in Eqn. 7 may be set to zero, in this embodiment.

In another embodiment of the invention, estimated values of battery parameters are used to calculate a maximum operating speed for a transporter based on the state of the battery and other transporter parameters, such as motor current. For example, the maximum operating speed of the transporter, Y, may be modeled by a linear equation of the form:

Y = M *I_{mot +}B _{(Eqn l3)} The values for M and B may vary over time and either M or B may be functions of current values of transporter operating parameters such as battery open circuit voltage and internal resistance and motor parameters, such as backEMF gain and motor resistance.

In an embodiment of the invention, an estimated maximum operating speed for a transporter is calculated as a linear function of the battery open circuit voltage, the battery internal resistance and a filtered average motor current, where the value of the average motor current is filtered with a low pass filter.

In a specific embodiment of the invention, dual redundant brushless DC motors are provided to drive each wheel of a transporter, which has wheels disposed as in Fig 1. Dual batteries are provided with each battery powering two motors. The motors may be paired so that the two motors driving a wheel are powered by different batteries, providing redundancy. The transporter maximum operating speed, Y, may be calculated as: _γ=_ ( - Ken) * (R_bat + (Ru , 2)) * I_mot ) + {Vo Ken) _{(Eqn M)}

where, Ken is the line-to-line backEMF constant of each motor;

R" is the measured resistance between the two phases of the DC motor; ^ra<" is an average motor current, where """ is calculated by summing the filtered currents for the two motors for each wheel and then taking the greater of the absolute values of these sums;

Voc is the estimated open circuit voltage of a battery; and

Rbat is the estimated internal resistance of a battery.

To ensure that sufficient power is available in either battery to bring the transporter to a controlled stop or maintain balance, the lesser of the estimated values of V_oc for the two batteries and the greater of the estimated values of Rbat for the two batteries may be employed in Eqn. 14, and transporter speed limited accordingly. As the batteries are discharged, the maximum operating speed for the transporter will decrease. In a further specific embodiment of the invention, values for ^^eU , the backEMF gain of each motor, and ^Ru , the measured resistance between the two phases of the DC motor, may be estimated by using measured values of transporter operating parameters such as motor temperature. Eqn. 14 may then be periodically modified accordingly. Selection of Speed Limit

The maximum operating speed can then be used to set an intervention speed and a speed limit for the transporter, ensuring that adequate balancing margin is maintained over varying terrain and operating conditions. The balancing margin can be empirically determined to produce the desired performance characteristics of the transporter. Speed limit can then set by subtracting the balancing margin from the maximum operating speed. Alternatively, for example, the speed limit may be set as a function of the filtered average motor current, ^mot , for the transporter or as a function of maximum operating speed for a given ^mo< . The speed limit may be a fixed offset from the maximum operating speed for the full range of ^mot (as depicted in Fig. 14A) or may vary as ^mo< varies. Alternatively, the speed limit can be set to an arbitrary value for a specific range of """ (as depicted in Fig. 14B). Balancing Transporter Speed Limiting In a specific embodiment of the invention, control equation 4 for a balancing transporter may be modified to allow a pitch modification Δ to be added to the system pitch value, θ :

5 T = K₁(θ-(Δ + θ₀) + K₂θ + K₃(x + x₀) + K₄x . (Eqn. 15)

Adding the pitch modification Δ allows the speed 6200 for a balancing transporter to be limited while still providing system balance in the fore-aft plane.

Referring to Fig. 15, first, a speed intervention band is determined 6210. The upper end of the band, the speed limit, may be set by subtracting a balancing o margin from the maximum operating speed for the transporter. The intervention speed may be set by subtracting the extent of the speed intervention band from the speed limit. Each of the balancing margin and the extent of the speed intervention band may be constants or may be determined adaptively. In a specific embodiment of the invention, separate speed limits and intervention 5 bands may be defined for motion of the transporter's center of mass in the forward and in the aft directions. The maximum operating speed may be estimated by a variety of methods, including the method described above. Note that the maximum operating speed for the transporter may decrease as the transporter's battery or other fuel source is depleted and the intervention speed o and the speed limit maybe adjusted accordingly. The relationship among various speed limiting parameters for a typical balancing transporter is illustrated in Fig. 11.

Again referring to Fig. 15, the speed of the transporter is then monitored 6220. When the transporter's speed exceeds the intervention speed, the 5 transporter may be slowed by increasing 6240 the pitch modification, Δ.

Inspection of Eqn. 15 shows that the transporter will respond to the modification by increasing motor torque, causing the system to accelerate. If, for example, the system is moving in the forward direction, the acceleration will cause the system to pitch backwards. The system will respond to this decrease in system pitch value by then reducing motor torque, decelerating the system. Δ may be determined 6230 by looking at the difference between the transporter speed and the intervention speed, integrated over time. The pitch modification sequence is repeated 6250 until the transporter slows to a desired dropout speed, which may be the intervention speed, and then the pitch modification may be smoothly returned 6260 to zero. This embodiment may be used advantageously to maintain a speed margin for balancing the transporter in the fore-aft plane and to govern the speed of the transporter.

In a specific embodiment of the invention, the pitch modification may be calculated as follows. When the instantaneous velocity of the transporter's center of mass exceeds the intervention speed, then let:

A = (Sint-Sact); (proportional term) Eqn. 16)

B = S'act* A, if (S'_act> 0 and A < 0), otherwise B =0 ; (derivative term) (Eqn. 17) C = Cprev + (D*(S_S1- Sad)) if Cprev <= 0,. otherwise, C = 0 (integral term) (Eqn. 18)

And set Δ= C + A* G_P+ B* Gd, (Eqn. 19) where:

Sact is the instantaneous velocity of the transporter's center of mass, Sint is the intervention speed;

Ssi is the speed limit; S'act is the acceleration of the transporter;

Cprev is the value of C from the previous calculation of the integral term (initialized to zero); D is a gain term;

G_p is a gain term for the contribution to the desired pitch modification that is proportional to transporter speed.

Gd is a gain term for the contribution to the desired pitch modification that is proportional to transporter acceleration. Once the pitch modification is calculated, this modification may be introduced to Eqn. 15 smoothly and incrementally. Note that the integral term contribution to the pitch modification is zero until the speed of the transporter exceeds the speed limit. At that point, the term can add substantially to the value of the pitch modification. Thus, the speed limiting effect on the system can become pronounced as the speed limit is exceeded.

Calculation of the pitch modification may be repeated periodically until transporter speed decreases below a drop-out value, which may be the intervention speed. When the transporter speed decreases below the drop-out speed, the pitch modification then may be calculated as:

Δ = Cprev + (D*(Ssi- Sad)) if C<0 and otherwise 0; and (Eqn. 20)

C = Δ . (Eqn. 21)

The pitch modification calculation and changes to the pitch modification may be repeated periodically. The pitch modification may be smoothly and incrementally decreased until the modification returns to zero.

Note that techniques other than adding a pitch modification to the control equation may be used to effect a deceleration of the transporter in a similar manner. For example, an offset value added to the system pitch value, θ , as reported by an inclinometer, will cause the same result. All such techniques are intended to be within the scope of the present invention.

In a further embodiment of the invention, a transporter is provided with means to regenerate batteries supplying power to the drive arrangement. Such regeneration can occur, for example, during hard braking or when the transporter is going downhill. In such a situation, damage may occur if the battery is at full capability and the battery regeneration circuitry forces additional energy into the battery. Such energy is dissipated as heat and the battery voltage may surge. Both effects can cause damage to the battery and drive electronics.

The transporter's speed limit may be modified to prevent an over voltage condition during battery regeneration. The battery voltage is monitored periodically and filtered with a low pass filter. If the filtered battery voltage exceeds an over voltage threshold, the speed limit for the transporter, or equivalently the intervention speed, may be reduced. In a specific embodiment of the invention, an over voltage range is set for the transporter, beginning at the over voltage threshold. The speed limit for the transporter is reduced linearly over this range as a function of battery voltage to a minimum speed characteristic of the transporter. The minimum speed limit maybe set equal to the range of the intervention band.

Non-Linear Gain Scheduling In a further embodiment of the present invention, any of the foregoing embodiments of a transporter in accordance with the present invention may be provided with wheel torque, T, controlled according to Eqn. 22, which is a modified version of Eqn. 4.

T = K₁(θ-θ₀) + K₂(θ-θ₀) + K₃(x+x₀) + K₄x (Eqn. 22).

where K i = K ^J ' when the pitch angle offset, θ—θ ° , is greater than or equal to zero; j ζ M β β

^Λι = ^Λι when the pitch angle offset, ° , is less than zero;

^Ά K2 = ^Λ K2 " when the pitch rate offset, θ—θ ° , is greater than or equal to zero;

2 - 2 when the pitch angle offset, ° , is less than zero; θ ⁰ represents the magnitude of a system pitch rate offset. Other definitions are as for Eqn. 4.

The gain coefficients, ^Λ TAι ' , ^Λ Jζι " , K ' , and Tζ ² " _may be configured, either in design of the system or in real-time, on the basis of a current operating mode and operating conditions as well as preferences of a user. When gains ' = 1 and

IA ' IA " θ

^Λ2 =^Λ2 and the system pitch rate offset, ° , is zero, Eqn. 22 simplifies to Eqn. 4. The separation of gains

in Eqn. 22 allows the response of the transporter to be tailored, for example, to rider preferences. For example, setting gain Jζ i " "> ζ i ' makes the transporter more responsive to changes in pitch that are aft of the pitch offset angle than pitch changes that are forward of this angle. Control of the transporter in this fashion may be advantageous, allowing a rider more (negative) acceleration with the same degree of lean in the aft direction than would be produced by a similar lean in the forward direction. Thus, this arrangement advantageously allows more responsive braking than acceleration in the forward direction. Note that Eqn. 22 allows the contributions from the θ — θ θ — θ separate gains to change smoothly since the terms ° and ° are zero when the corresponding gains switches from one value to the other. Any of Jζ i ' , Jζ ¹ " , Jζ ² ' , and Jζ ² " may vary as a function of o ^u and o ^e . This function may be non-linear. For example, if Jζ ' ' and Jζ i " are each zero for , < < -- β J

⁰ - - o _and non-zero otherwise, as illustrated in Fig. 16A, then a θ = θ "deadband" has been introduced about ° . Changes of pitch angle in this zone will not cause additional net torque to be applied to the transporter. This θ — θ arrangement will advantageously widen the "neutral" zone about ° .

Likewise, if Jζ i ' and Jζ i " are as pictured in Fig. 16B, where the magnitude of Ki is always non-zero, then a net torque will always be applied to the transporter to compensate for friction.

Eqn. 22 may be recast in terms of the voltage applied to the drive of an electric motor to produce an output torque. The drive need not be electric and some value other than torque or voltage may be used in control of the transporter, according to a control equation similar to Eqn. 22. All such embodiments are within the scope of the invention.

System Architecture Referring now to Fig. 17, a block diagram is shown of the system architecture of an embodiment of the present invention. A left motor 110 drives a left wheel 20 (shown in Fig. 1) and a right motor 120 drives a right wheel 21. Motors 110 and 120 are preferably DC brushless but may be either AC or DC motors and either brushed or brushless. Each motor is energized by a redundant set of windings 111, 112, 121, 122. Each winding is capable of energizing the motor in the event the complimentary winding is unable to energize the motor. In the discussion below, each redundant component is distinguished by a two letter group identifying either the left (L) or right (R) side of the transporter and either the A group or B group of redundant components. For example, the left motor winding energized by the A group of components is designated as the LA winding. Each of motor windings 111, 112, 121, 122 is driven by a motor amplifier

132, 133, 142, 143. The A-group amplifiers 132, 133 are supplied by the A-group power supply 131 and the B-group amplifiers 142, 143 are supplied by the B- group power supply 141. The electrical connections between the power supplies and amplifiers and between the amplifiers and motor windings are expected to carry large currents up to 20 to 40 Amperes and are identified by thick lines 105 in Fig. 17.

Each motor 110 120 has a shaft feedback device (SFD) 113 123 that measures the position or angular velocity of the motor shaft. The SFD is in signal communication with the motor amplifiers driving the motor associated with the SFD. For example, the right SFD 123 associated with the right motor 120 is in signal communication with the RA amplifier 133 and the RB amplifier 143. The SFD is preferably a Hall sensor that determines the position of the shaft, however the SFD may be selected from a variety of sensors such as encoders, resolvers, and tachometers, all listed without limitation for purposes of example. Certain sensors, such as tachometers, may also be used to measure the shaft velocity. Conversion of a signal representing instantaneous shaft velocity to or from a signal representing position is accomplished by integrating or differentiating the signal, respectively.

The A-group amplifiers 132, 133 are commanded by the A processor 135 while the B-group amplifiers 142, 143 are commanded by the B processor 145. Power is supplied to the A processor from the A power source 131 through the A- group DC-DC converter 136. Similarly, the B power source 141 supplies power to the B processor 146 through the B-group DC-DC converter 145. The A-group amplifiers 132, 133, A-group converter 136, and A processor 135 are preferably grouped together into a compartment or tray 130 that is at least partially isolated by a barrier 150 from the B-tray 140 containing the B-group amplifiers, B-group converter, and B processor. Physically separating the A tray 130 and B tray 140 reduces the probability of a common point failure. The barrier 150 acts to delay the propagation of a failure, in one tray to the other tray such that the transporter has sufficient time to put the rider in a safe condition to exit the transporter. Similarly, the A power supply 131 is physically separated from the B power supply 141. The A power supply 131 and the components in the A tray 130 are capable of driving both motors 110, 120 for a short period of time, on the order of a few seconds, in the event of a failure in any one of the B-group components. Conversely, the B power supply 141 and the components in the B tray 140 are capable of driving both motors 110, 120 for a short period of time if an A-group component fails.

Although the processors 135, 145 are physically isolated from each other, signal communication is maintained between the processors via commimication channels 137, 147. Communication channels 137, 147 are preferably electrical conductors but may also be electromagnetic such as optical, infrared, microwave, or radio. The A channel 137 transmits signals from the A processor 135 to the B processor 145 and the B channel 147 transmits signals from the B processor 145 to the A processor 135. Optical isolators 139, 149 are incorporated into channels 137, 147 to prevent over-voltages from propagating from a shorted processor to the other processor.

Each processor receives signals from a plurality of sensors that monitor the state of the transporter and the input commands of the rider. The processor uses the sensor signals to determine and transmit the appropriate command to the motor amplifiers. The information transmitted to the processors by the sensors include the spatial orientation of the transporter provided by an inertial measurement unit (IMU) 181, 182, the rider directed turn command provided by a yaw input device (YID) 132, 142, and the presence of a rider on the transporter provided by a rider detector (RD) 161, 162, 163, 164. Other inputs to the processor may include a rider operated pitch trim device (PTD) 148 for adjusting the pitch of the transporter to a more comfortable pitch and a stop button (not shown) for bringing the transporter to a stop quickly. Depending on the importance of the sensor to the operation of the transporter, the sensors may or may not be duplicated for redundancy. For example, the spatial orientation of the transporter is central to the operation of the transporter, as is described below, and therefore an A-group IMU 181 supplies transporter orientation information to the A processor 135 and a B-group IMU 182 supplies transporter orientation information to the B-processor 145. On the other hand, the transporter may still be operated in a safe manner without the PTD 148 so only one such device is typically provided. Similarly, an output device such as a display 138 does not require redundancy. A non-redundant device such as a display 138 or a PTD 148 may be connected to either processor. In the embodiment depicted in Fig. 17, display 138 is controlled by the A processor 136 and the PTD 148 is in direct signal communication with the B processor 145. The information provided by the PTD 148 is transmitted by the B processor 145 to the A processor 135 via the B channel 147.

Additionally, each processor 135, 145 communicates with one of the user interface processors (UIPs) 173, 174. Each UIP 173, 174 receives steering commands from the user through one of the yaw input devices 171, 172. A-group UIP 173 also communicates to the non-redundant UIDs such as the display 138, brake switch 175, and pitch trim control 148. Other user interface devices that are not provided redundantly in the embodiment shown in Fig. 17, such as a sound warning device, lights, and an on/ off switch, may also be connected to the A- group UIP 173. The A-group UIP 173 may also pass along information provided by the user interface devices to the B-group UIP 174.

In accordance with preferred embodiments of the invention, the A-group UIP 173 compares calculations of the A-group processor with calculations of the B-group processor and queries the A-group processor 135 with a 'watchdog' calculation to verify operation of the A-group processor. Similarly, the B-group UIP 174 queries the B-group processor 145 to verify normal operation of the B- group processor. Several further components of personal transporter 18, in accordance with various embodiments of the present invention, are now described.

Battery The transporter power required to drive the motors 110, 120 and electrical components may be supplied by any known source of electrical power known in the electrical arts. Sources of power may include, for example, both internal and external combustion engines, fuel cells, and rechargeable batteries. In preferred embodiments of the present invention, power supplies 131, 141 are rechargeable battery packs. Various battery chemistry modalities may be used, as preferred under various conditions, and may include, without limitation, lead-acid, Lithium-ion, Nickel-Cadmium (Ni-Cd), or Nickel-metal hydride (Ni-MH) chemistry. Each power supply 131, 141 is enclosed in a container that protects the battery packs and associated electronics from the environment.

Fig. 18 shows a top view of one embodiment of the power supply with the top cover removed. A tray 205 that is covered and sealed to protect the contents from the environment encloses the components of power supply 200. Tray 205 houses a plurality of battery blocks 210, each of which contains a plurality of battery cells 215. The number of cells 215 packaged in a block 210 and the total number of blocks in the power supply is determined by the expected power requirements of the transporter. In a preferred embodiment, cells 215 are "sub-C"- size cells and each block 210 contains ten cells 215. In other embodiments, block 210 may contains other numbers of cells 215. Cells 215 are preferably connected in series, as are blocks 210. In other embodiments blocks 210 may be connected in parallel with the cells 215 within each block connected in series, or, alternatively, blocks 210 may be connected in series with the cells 215 within each block 210 connected in parallel, each configuration providing advantages for particular applications.

Electrical current flowing into or out of power supply 200 is conducted through a connector 220 that provides the electrical interface between the power supply 200 and the transporter 10. In an embodiment shown in Fig. 18, connector 220 is located on the top cover (not shown) of power supply 200 but any positioning of connector 220 is within the scope of the present invention. In addition to conducting current into or out of power supply 200, connector 220 may also include a plurality of signal lines that establish signal communication between the power supply internals and any other transporter processor.

The temperature of each block 210 is monitored by the supply controller 230 through temperature sensors 235. In addition, supply controller 230 also monitors the voltage of each block 210. If supply controller 230 detects that the temperature of a block 210 is over a preset temperature limit, the supply controller 230 sends an over-temperature signal to the processor through connector 220. Similarly, if supply controller 230 detects that the voltage of a block 210 is below a preset voltage limit, the supply controller 230 sends an under-voltage signal to the processor through the connector 220.

Supply controller 230 preferably contains an ID chip 240 that stores information about the power supply such as battery type, the number of cells in the power supply 210, and optionally, a date code or serial number code. The ID chip 240 may be of any type of permanent or semi-permanent memory devices known in the electronics art. The information contained in the ID chip 240 may be used by the processor 135, 145 to set various operating parameters of the transporter. The information may also be used by a charger (not shown) to recharge the power supply.

Power supply 200 may be connected via connector 220 to a charger that is either external to the transporter or contained within the transporter. In one embodiment of the present invention, the charger is located on the transporter and is an AC switch mode charger well known in the power art. In another embodiment, the charger is contained within battery tray 205. In another embodiment of the present invention, power supply 200 is charged by an auxiliary power unit (APU). Motor Amplifier & Operating Modes

Fig. 19 shows a block schematic of a power module 300 of one embodiment of the present invention. A balancing processor 310 generates a command signal to motor amplifier 320 that, in turn, applies the appropriate power to motor 330. Balancing processor 310 receives inputs from the user and system sensors and applies a control law, as discussed in detail below, to maintain balance and to govern motion of the transporter in accordance with user commands. Motor 330, in turn, rotates a shaft 332 that supplies a torque, τ, at an angular velocity, ω, to a wheel 20, 21 (shown in Fig. 1) that is attached to shaft 332. In some embodiments, a transmission, not shown, may be used to scale the wheel speed in relation to the angular velocity of the shaft 332. In a preferred embodiment of the present invention, motor 330 is a three-coil brushless DC motor. In that embodiment, motor 330 has three sets of stator coils although any number of coils may be used. The stator coils are electrically connected to a power stage 324 by coil leads 337 capable of conducting large currents or high voltages. It is understood that the large currents and high voltages are relative to the currents and voltages normally used in signal processing and cover the range above 1 ampere or 12 volts, respectively.

Motor amplifier 320 itself contains both an amplifier processor 322 and a power amplification stage 324. Amplifier controller 322 may be configured to control either current or voltage applied to the motor 330. These control modes may be referred to as current control mode and voltage control mode, respectively. Power stage 324 switches the power source 340 into or out of connection with each coil, with the switching of the power stage 324 controlled by the amplifier controller 322. An inner loop 326 senses whether the output of power stage 324 is as commanded and feeds back an error signal to amplifier controller 322 at a closed loop bandwidth, preferably on the order of 500 Hz. Additionally, control by amplifier controller 322 is based, in part, on a feedback signal from shaft feedback sensor (SFS) 335. Shaft feedback sensor 335 is also in signal communication with the processor 310 and provides information related to the shaft position or motion to the processor. The shaft feedback sensor 335 may be any sensor known in the sensor art capable of sensing the angular position or velocity of a rotating shaft and includes tachometers, encoders, and resolvers. In a preferred embodiment, a Hall sensor is used to sense the position of the rotating shaft 332. An advantage of a Hall sensor is the low cost of the sensor. In order to obtain a measure of shaft rotation velocity from a position signal provided by shaft feedback sensor 335, the position signal is differentiated by differentiator 308. The outer feedback loop 342 operates at a bandwidth characteristic of the balance control provided by balance processor 310 and may be as low as 20-30 Hz.

While current and voltage may be equivalent in certain applications, voltage control is advantageously applied in embodiments of transporter control where the outer loop bandwidth is more than 3-4 times slower than the inner closed loop b-mdwidth, for the reasons now discussed with reference to Fig. 20. Fig. 20 shows an electrical model 410 of a motor. A motor has a pair of terminals 411, 412 across which a voltage V is applied. Motor 410 also has a rotating shaft 420 characterized by a shaft velocity, ω, and a torque, τ. Motor 410 may be modeled by resistor 430 of resistance R carrying a current i in series with an ideal motor 435 having a voltage drop Nemf. For an ideal motor, N_emf = k_v • ω and τ = k_c • - where k_v and k_c are motor constants. Series resistor 430 models the losses of the motor 410.

The differences in behavior of transporter 18 (shown in Fig. 1) due to voltage control or current control can be seen using the example of a tiansporter encountering and driving over an obstacle. When a wheel 20 of the transporter encounters an obstacle, the wheel velocity will decrease because the torque applied to the wheel is insufficient to drive the wheel over the obstacle. The drop in wheel velocity will be reflected in a decrease in the back-electromotive-force ("back-emf") voltage across the ideal motor. Considering, first, the case of voltage control: If the amplifier is in voltage control mode, the voltage applied to terminals 411, 412 remains constant and additional current will be drawn through resistance 430 and ideal motor 435. The additional current through the motor will generate the additional torque to drive the wheel over the obstacle. As the transporter drives over the top of the obstacle, the wheel will accelerate under the additional torque that was generated to drive over the obstacle but is no longer required to drive off the obstacle. As the wheel accelerates, the back-emf across the motor will increase and the current through R will decrease in order to keep the voltage across terminals 411, 412 constant. The decrease in current reduces the applied torque generated by the ideal motor thereby reducing the acceleration of the wheel. The advantage of voltage control mode is that the ideal motor naturally draws the current required to drive over the obstacle and naturally reduces the current to drive off the obstacle without any change required in the motor command. As long as the power source can supply the required current, the motor essentially acts as its own feedback sensor and the control loop delay for the motor is essentially zero.

Under current control mode, on the other hand, the amplifier will keep the current constant through resistor 430 and ideal motor 435 until the controller sends a new current command during the next processor frame. When the wheel encounters the obstacle, ω decreases and the back-emf across the ideal motor decreases. However, since the amplifier controller is keeping the current constant, the voltage across terminals 411, 412 is allowed to drop. Since the current is held constant by the amplifier controller, the torque remains constant. However, the torque is insufficient to drive over the obstacle and the inertia of the moving transporter will cause the transporter to pitch forward. As the transporter begins to pitch forward over the obstacle, the balancing controller will detect the pitching, either through a change in the pitch error or through a change in the velocity, and command an increase in current to the amplifier controller, in accordance with the control algorithm taught in U.S. Patent no. 5,971,091. The motor amplifier will respond to the increased current command by supplying additional current through R and the ideal motor. The increased current through the ideal motor increases the torque applied to the wheel until it is sufficient to drive the wheel over the obstacle. As the transporter moves over the obstacle, however, the increased torque will accelerate the wheels since the obstacle no longer resists the wheels. The wheel acceleration will cause the wheels to move ahead of the transporter's center of gravity {CG) and cause the transporter to pitch backward. The balancing controller will detect the pitching condition through either a change in pitch error or through a change in the transporter velocity and command a decrease in the current supplied to the ideal motor thereby reducing the torque applied to the wheel.

If the delay caused by the balancing controller is negligible and the accuracy of the velocity information fed back to the balancing controller is extremely high, the rider will not notice a difference whether voltage or current control is used. However, if the controller or shaft sensor selected for the transporter has a limited bandwidth, current control mode will not provide the prompt response that voltage control mode exhibits for small obstacles. In a preferred embodiment of the invention, a low-cost Hall Effect sensor is employed to detect shaft rotation. In addition, for reasons described below, limitations on the selection of the gains used in the control law for current control mode result in a softer transporter response relative to voltage control mode.

Steering Device Referring now to Fig.21, an exploded view is shown of an embodiment of a steering device for a scooter-like vehicle such as the balancing vehicle 18 of Fig. 1. A potentiometer 602, or other sensor of the position of a rotatable shaft 604, is attached to a housing 606. The housing may be part of handlebar 14 (shown in Fig. 1). A rotatable grip 608 is attached to potentiometer shaft 604 and provides a grip for the rider. A torsional spring 610 is connected at one end to the rotatable grip 608 and at the other end to the potentiometer 602 or to housing 606. As the rider rotates grip 608, the grip turns shaft 604. Potentiometer 602, with voltage suitably applied across it, as known in the art, generates a signal substantially proportional to the rotation of the shaft. If the rider releases the grip, torsional spring 610 rotates grip 608 and the shaft to their respective neutral or zero positions. Return of grip 608 to its neutral position allows the transporter to continue traveling in the same direction as when the grip was released. If the grip was not returned to the neutral position when released, the transporter would continue to turn in the direction of the residual rotation.

The direction of rotation may be used to encourage the rider to lean into the turn. For example, referring further to Fig. 21, if the rider's right hand holds grip 608, a twist in the direction of the rider's fingers corresponds to a right turn. The rotation of the rider's right wrist to the outside of the handlebar encourages the rider to shift weight to the right and into the turn. Shifting weight into the turn improves the transporter's lateral stability.

Battery Charge Equalization As has been discussed, a plurality of batteries may power the motor which propels the transporter. While unstable, at least in the fore-aft plane, when not powered, tiansporter 18 maintains balance during normal operation by sensing parameters such as the system pitch, θ and the rate of change of pitch θ and applying torque to the wheels according to a control law, as described in detail above. As explained in U. S. Patent No. 6,302,230, if the transporter is not pitched rearward when braking is desired, it is necessary to accelerate the wheels of the transporter, thereby pitching the transporter in the rearward direction, so that the transporter may slow in a controlled fashion. Thus, it is desirable to impose a speed limit on the transporter so that each of the batteries individually contains sufficient charge to accelerate the transporter, to achieve braking. This requirement helps prevent a single battery failure from impairing transporter ability to slow in a controlled fashion. Equalizing the charge among the batteries advantageously allows such a transporter to maximize the transporter's speed limit, consistent with the above requirement for controlled braking.

In an embodiment of the present invention, a method is provided for equalizing the charge among a plurality of batteries, each battery powering a winding of a motor. Each motor winding is isolated from other windings so that the batteries are coupled primarily through the mechanical action of the drive shaft, which is driven by these windings. Battery parameters, such as the battery voltage and current for example, are monitored for each battery and an estimate of the instantaneous charge state of each battery can be made. The current through each winding is adjusted by an amplifier in each winding circuit so that differences among the charge states of the batteries may be minimized. Charge equalization among the batteries advantageously allows the motor to be driven at a higher maximum load, if, for purposes of redundancy, each battery must be capable of driving the motor individually at that load. Note that the term "amplifier" in this specification and in any appended claims, unless context requires otherwise, shall mean any device that supplies power to a succeeding element of a system based on a control input, for example without limitation, a transistor, field-effect-transistor, varistor, switch mode power converter, etc.

Fig. 22 shows a schematic diagram of a battery/motor subsystem 1400 of a transporter 1310 according to an embodiment of the present invention. For purposes of illustration, a subsystem 1400 is shown that includes 2 batteries, 1410 and 1460, driving a motor 1430. It will be readily apparent to those skilled in the art that this system may be generalized to systems employing any number of batteries. Each battery may be modeled as an internal resistance in series with a voltage source. Battery 1410 is connected through an amplifier 1420 in series with a winding 1432 of the motor 1430. Likewise, battery 1460 is connected through an amplifier 1450 in series with a winding 1434 of the motor 1430. The motor 1430 drives a drive shaft 1440. Windings 1432 and 1434 are substantially isolated from each other and coupled through the mechanical action of drive shaft 1440. Processor 1470 receives measurements of battery parameters (not shown) and controls amplifiers 1420 and 1460.

Fig. 23 illustrates charge equalization for the batteries of subsystem 1400 according to an embodiment of the invention. First, processor 1470 receives 1510 measurements of battery parameters that may be used to characterize the charge of the batteries. These battery parameters include battery voltage under various load conditions, as discussed below. If the charges among the batteries are unequal 1520, the processor can then adjust 1530 the current to winding 1432 and the current to winding 1434 to draw more current from the battery with the higher charge. In systems where circuitry is provided to charge a battery from the motor, the processor may equalize the charge by charging one battery while drawing current from the other battery or charging the batteries at unequal rates. The processor periodically repeats measuring the battery parameters 1510 and adjusting 1530 the current in the winding, if needed, to equalize the charges of the batteries. In another specific embodiment of the invention, the processor 1470 adjusts the voltages across the windings to equalize the charge on each battery. The net output of the drive system, which is a function of step 1530, may advantageously be the same as if no load sharing were occurring.

In a specific embodiment of the invention, battery voltage and current may be measured and used to characterize each battery's charge. The battery's charge may be characterized by considering the battery to consist of an ideal voltage source with open circuit voltage, V_oc, and internal resistance, Rbat. Periodic measurements of battery voltage and current maybe used to estimate Voc and Rbat- The above procedure may then be used to equalize V_oc across the batteries or to equalize a combination of V_oc and Rbat- Other parameters that may be included are: battery current, motor current, state of charge, or available power.

In another specific embodiment of the invention, the motor drives a mechanical device. Each battery has a charge and the performance of the motor is limited so that each battery separately has the charge to maintain the motor performance. In a specific embodiment of the invention, a balancing transporter is provided. The transporter includes a plurality of batteries in a redundant configuration for driving a motor that propels the transporter. The transporter includes a controller that sets a speed limit such that any of the batteries contains sufficient charge to bring the transporter to a controlled stop. The controller includes logic that maximizes the speed limit for the transporter by equalizing the charge of the batteries, as illustrated in Fig. 23.

Referring now to Fig. 24A, a schematic sideview is shown of transporter 18, represented by one of its wheels 21, platform 12, handlebar 14, and stalk 16. The center of mass (CM) 40 must lie on a vertical line 42 that passes through the region of contact 44 between wheel 21 and the underlying surface if the transporter is to remain at rest. Otherwise, the pitch of the transporter will cause the wheel to rotate under the transporter to achieve balance, and motion will ensue. The condition in which the transporter is in repose will be referred to herein as 'stasis.' Two conditions of stasis are shown in Figs. 24A and 24B which differ in that the CM 40 of Fig. 24B lies aft (i.e., to the left on the page) of its position in Fig. 24A. In 'E-stand' mode, if the CM is biased forward, the transporter will pitch backward, and mutatis mutandis, a backward bias of the CM leads to a forward pitch.

Referring now to Fig. 25, a schematic is shown of a control mode, referred to as 'kickstand mode,' wherein the transporter may stationkeep in a balanced position. Fig. 25 depicts the manner in which a pitch command 50 is derived to be applied to both primary wheel amplifiers. Application of motor commands to govern wheel actuators to drive wheels 20 and 21 is described in U.S. Patent no. 6,288,505. First, the difference θ_er- between the desired pitch condition θdest-ed and the present pitch θ as determined by an on-board pitch sensor, is subject to gain 52 and supplied to summer 54. Additionally, a signal 56 proportional to a sensed pitch rate ^ is supplied to summer 54. State variables θ and θ may be provided by a sensing system such as, for example, an inertial sensing system as described in U.S. Patent no. 6,332,103, which is incorporated herein by reference.

The rate ω of wheel rotation provides another input to summer 54, subject to gain 58, while the wheel rotation is also integrated up by integrator 60 so that the cumulative wheel rotation required to bring the transporter to a pitch state of stasis is maintained. Integrator 60 may be initialized at a given value when the absence of a rider is detected by the rider detection mechanism.

It should be noted that where flow diagrams are used herein to demonstrate various aspects of the invention, and should not be construed to limit the present invention to any particular logic flow or logic implementation. The described logic may be partitioned into different logic blocks (e.g., programs, modules, functions, or subroutines) without changing the overall results or otherwise departing from the true scope of the invention. Oftentimes, logic elements may be added, modified, omitted, performed in a different order, or implemented using different logic constructs (e.g., logic gates, looping primitives, conditional logic, and other logic constructs) without changing the overall results or otherwise departing from the true scope of the invention.

The present invention may be embodied in many different forms, including, but in no way limited to, computer program logic for use with a processor {e.g., a microprocessor, microcontroller, digital signal processor, or general purpose computer), programmable logic for use with a programmable logic device {e.g., a Field Programmable Gate Array (FPGA) or other PLD), discrete components, analog circuits, integrated circuitry {e.g., an AppHcation Specific Integrated Circuit (ASIC)), or any other means including any combination thereof. Computer program logic implementing all or part of the functionality previously described herein may be embodied in various forms, including, but in no way limited to, a source code form, a computer executable form, and various intermediate forms {e.g., forms generated by an assembler, compiler, linker, or locator.) Source code may include a series of computer program instructions implemented in any of various programming languages (e.g., an object code, an assembly language, or a high-level language such as FORTRAN, C, C++, JAVA, or HTML) for use with various operating systems or operating environments. The source code may define and use various data structures and communication messages. The source code may be in a computer executable form {e.g., via an interpreter), or the source code may be converted {e.g., via a translator, assembler, or compiler) into a computer executable form.

The computer program may be fixed in any form {e.g., source code form, computer executable form, or an intermediate form) either permanently or transitorily in a tangible storage medium, such as a semiconductor memory device {e.g., a RAM, ROM, PROM, EEPROM, or Flash-Programmable RAM), a magnetic memory device (e.g., a diskette or fixed disk), an optical memory device (e.g., a CD-ROM), a PC card (e.g., PCMCIA card), or other memory device. The computer program may be fixed in any form in a signal that is transmittable to a computer using any of various communication technologies, including, but in no way limited to, analog technologies, digital technologies, optical technologies, wireless technologies, networking technologies, and internetworking technologies. The computer program may be distributed in any form as a removable storage medium with accompanying printed or electronic documentation (e.g., shrink wrapped software or a magnetic tape), preloaded with a computer system (e.g., on system ROM or fixed disk), or distributed from a server or electronic bulletin board over the communication system (e.g., the Internet or World Wide Web.)

Hardware logic (including programmable logic for use with a programmable logic device) implementing all or part of the functionality previously described herein may be designed using traditional manual methods, or may be designed, captured, simulated, or documented electronically using various tools, such as Computer Aided Design (CAD), a hardware description language (e.g., VHDL or AHDL), or a PLD programming language (e.g., PALASM, ABEL, or CUPL.) Moreover, the described embodiments of the invention are intended to be merely exemplary and numerous variations and modifications will be apparent to those skilled in the art. All such variations and modifications are intended to be within the scope of the present invention as defined in the appended claims.

Claims

What is claimed is:

1. A method for estimating an instantaneous capability of a battery, the battery characterized by an open circuit voltage and an internal resistance, the method comprising:

5 a. measuring battery parameters to obtain values of the battery parameters including a voltage value and a current value; b. repeating measurements to obtain successive values of the battery parameters; and c. filtering the successive values of the battery parameters to estimate the o instantaneous cap ability of the battery.

2. A method according to claim 1 wherein filtering the successive values of the battery parameters includes performing a statistical analysis of the successive values.

3. A method according to claim 1, wherein filtering the successive values of 5 the battery parameters includes performing recursive least squares regression.

4. A method according to claim 1, wherein filtering the measured battery parameters includes performing a recursive least squares regression with exponential forgetting.

5. A method for estimating an instantaneous capability of a battery, the o battery characterized by an open circuit voltage and an internal resistance, the method comprising: a. measuring battery parameters to obtain values including a voltage value and a current value; b. repeating measurements to obtain successive values of the battery 5 parameters; and c. statistically analyzing the successive values of the battery parameters to estimate the instantaneous capability of the battery.

6. A method for determining a maximum operating speed for a transporter, the transporter including a battery supplying power to a motor, the battery characterized by a battery voltage, an open circuit voltage and an internal resistance, the motor propelling the transporter, the motor characterized by an average motor current, the method comprising: a. calculating an open circuit voltage estimate and an internal resistance estimate for the battery; and b. calculating the maximum operating speed as a function of the open circuit voltage estimate and the internal resistance estimate for the battery and the average motor current.

7. A method according to claim 6, wherein the function is a linear function of the open circuit voltage estimate, the internal resistance estimate for the battery and the average motor current.

8. A transporter for carrying a payload including a user, the transporter comprising: a. a platform for supporting the user; b. a ground-contacting module, coupled to the platform for propelling the transporter over an underlying surface in motion characterized by a speed; c. a motorized drive arrangement, the drive arrangement, ground-contacting module and payload comprising a system being unstable with respect to tipping in a fore-aft plane when the motorized drive is not powered, the motorized drive arrangement causing, when powered, automatically balanced operation of the system; d. a power source characterized by an instantaneous capability to energize the motorized drive arrangement; and e. a governor that limits the speed of the ground-contacting module based at least on the instantaneous capability of the power source.

9. A transporter according to claim 8, wherein the motorized drive arrangement is characterized by an average motor current and wherein the maximum operating speed is a function of the average motor current.

10. A transporter according to claim 9, further comprising a monitor, coupled to the motorized drive arrangement, the monitor including logic for calculating a maximum operating speed as a function of a battery open circuit voltage estimate, a battery internal resistance estimate and the average motor current.

11. A transporter according to claim 10, wherein the function is a linear function of the battery open circuit voltage and internal resistance and the average motor current.

12. A method for limiting the speed of a transporter, the method comprising: a. providing a transporter including: i) a platform which supports a payload including the user, ii) a ground-contacting module, mounted to the platform, including at least one ground-contacting member, characterized by a ground contact region and a fore-aft plane, iii) a motorized drive arrangement, coupled to the ground-contacting module, the drive arrangement, ground-contacting module and payload constituting a system being unstable with respect to tipping in at least the fore-aft plane when the motorized drive is not powered, the system characterized by a system speed and a system pitch value, and iv) an energy storage device, characterized by a instantaneous capability, powering the drive arrangement; b. determining the instantaneous capability of the energy storage device; and c. limiting operation of the motorized drive arrangement on the basis, at least, of the instantaneous capability of the energy storage device.

13. A method according to claim 12, further including: d. dynamically maintaining stability of the system in the fore-aft plane by operation of the drive arrangement so that the net torque experienced by the system about ground contact region causes a specified acceleration of the system.

14. A method according to claim 13, wherein the step of dynamically mamtaining stability includes applying a contribution to the net torque that is a function of a system pitch value multiplied by a gain.

15. A method according to claim 14, further including: e. calculating a pitch modification value based at least on the instantaneous capability of the energy storage device; and f . adding the pitch modification value to the system pitch value in such a manner as to limit the system speed when the system speed exceeds an intervention speed.

16. A method according to claim 15, further including: g. subtracting the pitch modification value from the system pitch value when the system speed falls below a drop-out value.

17. A method according to claim 16 wherein subtracting the pitch modification includes subtracting the modification incrementally.

18. A method according to claim 15, wherein calculating a pitch modification includes adding a proportional term contribution, where the proportional term contribution is a function of the difference between the system speed and the intervention speed.

19. A method according to claim 18, wherein calculating a pitch modification includes adding a derivative term contribution to the pitch modification, where the derivative term contribution is a function of a system acceleration.

20. A method according to claim 19, wherein calculating a pitch modification includes adding an integral term contribution to the pitch modification, the integral term contribution formed by: i) multiplying a gain by the difference between the system speed and a speed limit, and ii) adding a previous integral term contribution.

21. A method according to claim 15, wherein the intervention speed is a function of the direction of system velocity.

22. A method according to claim 15, wherein the energy storage device is a battery and the transporter further includes a capability to regenerate the battery from the motorized drive arrangement, the battery further characterized by an over voltage threshold and an over voltage range, wherein the intervention speed is reduced as a function of an over voltage difference between the battery voltage and the over voltage threshold.

23. A method according to claim 22 wherein the function of the over voltage difference is a linear function of the over voltage difference when the battery voltage is within the over voltage range and a constant when the battery voltage exceeds the over voltage range.

24. A transporter for carrying a payload including a user, the transporter comprising: a. a platform which supports a payload including the user; b. a ground-contacting module, mounted to the platform, including at least one ground-contacting member, characterized by a ground contact region and a fore-aft plane; c. a motorized drive arrangement, coupled to the ground-contacting module, the drive arrangement, ground-contacting module and payload constituting a system being unstable with respect to tipping in at least the fore-aft plane when the motorized drive is not powered, the system characterized by a system speed, and a system pitch value; d. an energy storage device, characterized by a instantaneous capability, powering the drive arrangement; and e. a controller including: i) a control loop in which the drive arrangement is included, for dynamically mamtaining stability of the system in the fore-aft plane by operation of the drive arrangement so that the net torque experienced by the system about the region of contact with the ground causes a specified acceleration of the system, the net torque including a contribution that is a function of the system pitch value multiplied by a gain, and ii) logic that determines the instantaneous capability of the energy storage device; and iii) logic that limits operation of the motorized drive arrangement on the basis, at least, of the instantaneous capability of the energy storage device.

25. A transporter according to claim 24, wherein the logic that limits operation of the motorized drive arrangement includes logic that: a. calculates a pitch modification value based at least on the instantaneous capability of the energy storage device; and b. adds the pitch modification value to the system pitch value in such a manner as to limit the system speed when the system speed exceeds an intervention speed.

26. A transporter according to claim 25, wherein the energy storage device is a battery.

27. A transporter according to claim 26, wherein the transporter further includes a capability to regenerate the battery from energy derived from the motorized drive arrangement, the battery further characterized by a battery voltage, an over voltage threshold and an over voltage range, wherein the intervention speed is reduced as a function of an over voltage difference between the battery voltage and the over voltage threshold.

28. A transporter according to claim 27, wherein the function is a linear function of the over voltage difference when the battery voltage is within the over voltage range and a constant when the battery voltage exceeds the over voltage range.

29. A device for carrying a user, the device comprising: a. a platform which supports a payload including the user, b. a ground-contacting module, mounted to the platform, including at least one ground-contacting member, characterized by a ground contact region, and defining a fore-aft plane; c. a motorized drive arrangement, coupled to the ground-contacting module; the drive arrangement, ground-contacting module and payload

5 constituting a system being unstable with respect to tipping in at least the fore-aft plane when the motorized drive is not powered, the system characterized by a pitch angle offset from a specified pitch angle and a pitch rate offset from a specified pitch rate; and d. a control loop in which the motorized drive arrangement is included, 0 for dynamically mamtaining stability of the system in the fore-aft plane by operation of the motorized drive arrangement so that the net torque experienced by the system about the region of contact with the surface causes a specified acceleration of the system, the net torque including a contribution related to the pitch angle offset multiplied by a first gain 5 wherein the first gain is a function of at least one of an orientation and a displacement of the device.

30. A balancing transporter characterized by an instantaneous displacement and orientation, the transporter comprising: a. a motorized drive for propelling the transporter; o b. a control loop in which the motorized drive arrangement is included, for dynamically mamtaining stability of the system in the fore-aft plane by operation of the motorized drive arrangement so that the net torque experienced by the system about the region of contact with the surface causes a specified acceleration of the system, the net torque 5 including a contribution functionally related to at least one of the pitch angle, pitch rate, wheel position and wheel velocity, wherein the functional relation varies with at least one of an orientation and a displacement of the device.

31. A method for carrying a payload including a user with a transporter, the method comprising: a. providing a transporter including: i. a platform which supports a payload including the user, ii. a ground-contacting module, mounted to the platform, including at least one ground-contacting member, characterized by a ground contact region and a fore-aft plane; iii. a motorized drive arrangement, coupled to the ground- contacting module; the drive arrangement, ground-contacting module and payload constituting a system being unstable with respect to tipping in at least the fore-aft plane when the motorized drive is not powered, the system characterized by a pitch angle offset from a specified pitch angle and a pitch rate offset from a specified pitch rate; and b. causing the motorized drive to operate the ground-contacting module using a control loop in which the motorized drive arrangement is included, for dynamically maintaining stability of the system in the fore-aft plane by operation of the motorized drive arrangement so that the net torque experienced by the system about the region of contact with the surface causes a specified acceleration of the system, the net torque including: i) a contribution related to the pitch angle offset multiplied by a first gain K_x when the pitch angle offset is greater than or equal to zero and to the pitch angle offset multiplied by a second gain K_λ when the pitch angle offset is less than zero; and ii) a contribution related to the pitch rate offset multiplied by a third gain K_{2 .}when the pitch rate offset is greater than or equal to zero and to the pitch rate offset multiplied by a fourth gain K₂ when the pitch rate offset is less than zero, wherein at least one of a first gain pair consisting of K_λ and K_λ and a second gain pair consisting of K₂ and K₂ are unequal.

32. A method according to claim 31 wherein the magnitude of K_t is less than the magnitude of K_λ

33. A method according to clai 31 wherein K₂ equals K₂ .

5 34. A method for equahzing the charge between a first battery and a second battery, the first battery providing a first current to a first winding of a motor and the second battery providing a second current to a second winding of the motor, the motor supplying power to a mechanical device, the method comprising: a. determining a value of a parameter of the first battery and a value of the o parameter of the second battery; and b. adjusting the first current and the second current to reduce a difference of the value of the parameter of the first battery from the value of the parameter of the second battery.

35. A method according to claim 34 wherein the parameter is an open circuit 5 voltage.

36. A method according to claim 34, further comprising: c. limiting the performance of the mechanical device so that at least one of the first battery and the second battery can power the device.

37. A method according to claim 36, wherein the mechanical device is a o balancing transporter and the performance includes the speed of the transporter.

38. A device for reducing a charge difference between a first battery and a second battery, the first battery providing a first current to a first winding of a motor and the second battery providing a second current to a second winding of a motor, a first amplifier controlling the first current and a second amplifier 5 controlling the second current, the device comprising a processor including: a. a comparator that receives measurements of a value of a parameter of the first battery and a value of the parameter of the second battery; and b. logic that controls the first amplifier and the second amplifier such that the difference between the value of the parameter of the first battery and the value of the parameter of the second battery is reduced.

39. A device according to claim 38, wherein the parameter is an open circuit 5 voltage.

40. A method for maximizing the speed limit for a balancing transporter, the speed limit set to maintain balance, the method comprising: a. providing a transporter including: i. a platform which supports a payload including the user, o ii. a ground-contacting module, mounted to the platform, including at least one ground-contacting member, characterized by a ground contact region and a fore-aft plane, and iii. a motorized drive arrangement, coupled to the ground- contacting module, the drive arrangement, ground-contacting 5 module and payload constituting a system being unstable with respect to tipping in at least the fore-aft plane when the motorized drive is not powered, the arrangement powered by a first battery and a second battery, the first battery providing a first current to a first winding of a motor and the second battery providing a second o current to a second winding of the motor, the motor powering the arrangement; b. causing the drive arrangement to operate the ground-contacting module using a control loop in which the drive arrangement is included, for dynamically mamtaining stability of the system in the fore-aft plane by 5 operation of the drive arrangement; c. limiting the speed of the transporter so that at least one of the first battery and the second battery can accelerate the transporter; and d. equalizing the charge across the first battery and the second battery.

41. A method according to claim 40, wherein equalizing the charge includes: a. dete-r-nining a value of a parameter of the first battery and a value of the parameter of the second battery; and b. adjusting the first current and the second current to reduce a difference of the value of the parameter of the first battery from the value of the parameter of the second battery.

42. A transporter for carrying a payload including a user, the transporter comprising: a. a platform which supports a payload including the user; b. a ground-contacting module, mounted to the platform, including at least one ground-contacting member, characterized by a ground contact region and a fore-aft plane; c. a motorized drive arrangement, coupled to the ground-contacting module, the drive arrangement, ground-contacting module and payload constituting a system being unstable with respect to tipping in at least the fore-aft plane when the motorized drive is not powered, the arrangement powered by a first battery and a second battery, the first battery providing a first current to a first winding of a motor and the second battery providing a second current to a second winding of the motor, the motor powering the arrangement; and d. a controller including: i. a control loop in which the drive arrangement is included, for dynamically mamtairiing stability of the system in the fore-aft plane by operation of the drive arrangement so that the net torque experienced by the system about the region of contact with the surface causes a specified acceleration of the system, ii. a comparator that receives measurements of a value of a parameter of the first battery and a value of the parameter of the second battery, and ϋi. logic for limiting the speed of the transporter so that at least one of the first battery and the second battery can accelerate the transporter; and iv. logic for equalizing the charge across the first battery and the second battery.

43. A method for mamtaining stability of a riderless balancing transporter having two laterally disposed wheels, the balancing transporter having a region of contact with an underlying surface and characterized by a center of mass, the method comprising: a. detecting the absence of a user aboard a balancing transporter; b. determining a desired transporter pitch such as to establish the center of mass directly above the region of contact between the balancing transporter and the underlying surface; c. applying a torque to the laterally disposed wheels so as to maintain the transporter at the desired transporter pitch.

44. A method in accordance with claim 43, wherein the step of applying the torque includes applying a torque proportional to the difference between a present transporter pitch and the target transporter pitch.

45. A method in accordance with claim 43, wherein the step of applying the torque includes applying a torque proportional to the sum of coadded terms, a first term proportional to the difference between a present transporter pitch and the target transporter pitch and a second term proportional to the pitch rate of the transporter.

46. A transporter for transporting a load over a surface, the transporter comprising: a. a support platform for supporting the load, the support platform characterized by a fore-aft axis, a lateral axis, and an orientation with respect to the surface, the orientation referred to as an attitude; b. at least one ground-contacting element flexibly coupled to the support platform in such a manner that the attitude of the support platform is capable of variation; c. a motorized drive arrangement for driving the at least one ground- contacting elements; 5 d. a sensor module for generating a signal characterizing the attitude of the support platform; and e. a controller for commanding the motorized drive arrangement based at least on the attitude of the support platform.

47. A method for conducting a riderless balancing transporter having two o laterally disposed wheels, the balancing transporter having a user input, the method comprising: a. receiving an input via the user input; b. generating a control signal corresponding to the input received; and c. applying a torque to the laterally disposed wheels so as propel the 5 balancing transporter on the basis of at least the control signal.

48. A method in accordance with claim 47, wherein the control signal corresponds to a commanded torque.

49. A method in accordance with claim 47, wherein the control signal corresponds to a commanded velocity. 0

50. A method in accordance with claim 47, wherein the step of applying the torque includes applying a torque proportional to a sum of coadded terms, a first term proportional to the control signal and a second term proportional to additive inverse of the wheel velocity common to the two wheels.

51. A method in accordance with claim 47, wherein the step of applying the 5 torque includes applying a torque proportional to a sum of coadded terms, a first term proportional to the control signal, a second term proportional to additive inverse of the wheel velocity common to the two wheels, and a third term proportional to the differential velocity of the two wheels.

52. A method in accordance with claim 47, wherein the step of generating a control signal corresponding to the signal received includes conditioning the input received.

53. A method in accordance with claim 52, wherein conditioning the input includes providing a deadband region in the vicinity of zero input.

54. A method in accordance with claim 52, wherein conditioning the input includes limiting the effect of user input to a specified range of control signals.

55. A method in accordance with claim 52, wherein conditioning the input includes limiting the slew rate of change of control signals in response to user input.

56. A transporter for transporting a load over a surface, the transporter comprising: a. a support platform for supporting the load, the support platform characterized by a fore-aft axis, a lateral axis, and an orientation with respect to the surface, the orientation referred to as an attitude; b. at least one ground-contacting element coupled to the support platform in such a manner as to provide locomotion of the support platform with respect to an underlying surface; c. a motorized drive arrangement for driving the at least one ground- contacting element in such a manner as to propel the transporter in dynamically balanced operation; d. a controller for commanding the motorized drive arrangement based at least on the attitude of the support platform; and e. a user input for receiving a command from a user not carried by the transporter to govern operation of the motorized drive arrangement.

010Θ2/D60 O ₂S5702.1