Abstract:
An apparatus and a method for robotic control that allows an unbalanced pendulum robot to raise its Center of Mass and balance on two motorized wheels. The robot includes a pair of arms that are connected to the upper body of the robot through motorized joints. The method consists of a series of movements employing the arms of the robot to raise the robot to the upright position. The method comprises a control loop in which the motorized drives are included for dynamic balance of the robot and the control of the arm apparatus. The robot is first configured as a low Center of Mass four-wheeled vehicle, then its Center of Mass is raised using a combination of its wheels and the joint located at the attachment point of the arm apparatus and the robot body, between the rear and front wheels; the method then applies accelerations to the rear wheels to dynamically pivot and further raise the Center of Mass up and over the main drive wheels bringing the robot into a balancing pendulum configuration.

Description:
CROSS-REFERENCES TO RELATED APPLICATIONS 
       [0001]    This application is a divisional application of U.S. application Ser. No. 11/591,925. The parent application was filed on Nov. 2, 2006 and it listed the same inventors. 
     
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
       [0002]    The development of the invention that is the subject of the present application was partially supported by Department of Defense&#39;s Office of Naval Research and Defense Advanced Research Projects Agency. 
     
    
     MICROFICHE APPENDIX 
       [0003]    Not Applicable 
       BACKGROUND OF THE INVENTION 
       [0004]    1. Field of the Invention 
         [0005]    The present invention pertains to methods for control of the configuration and motion of a robot, without the aid of a person or other external means. More specifically, the present invention is directed to a reconfigurable balancing combat robot and a means for dynamically transitioning from a low Center of Mass configuration to a high Center of Mass balancing configuration without external assistance. 
         [0006]    2. Description of the Related Art 
         [0007]    Robots have useful applications in many different fields. Robots are particularly useful in combat situations, where they may be deployed into dangerous environments without putting soldiers&#39; lives at risk. 
         [0008]    Various robot platforms have been developed for combat and other applications. Conventionally, robots utilize an on-board motor to power wheels, tracks, or other ground-contacting devices to move the robot from one location to another. An operator may remotely control the movement of the robot with a joystick or other input device. Wireless communication devices allow operators to be positioned a substantial distance away from the robot. 
         [0009]    The lack of maneuverability provided by current robot platforms has greatly limited the widespread use of robots in combat situations. Unlike human soldiers, current robot platforms cannot easily maneuver around rocks, trees, and holes. While circumventing these obstacles, robots may be easily targeted and destroyed. 
         [0010]    Alternative robot platforms have been developed that overcome some of the drawbacks of a typical wheeled robot. An example of an alternative platform is the Goes-Over-All-Terrain (“GOAT”) robot. This platform has four wheels mounted on the ends of articulated arms and legs which allow the robot to travel quickly over flat ground and maneuver over a range of obstacles higher than a wheel diameter. However, the GOAT needs at least three wheels on the ground at any time in order to maintain balance. This limits the height that a sensor or actuator can reach and limits the platform&#39;s maneuverability through narrow passages. 
         [0011]    Also known in the prior art are human transporter devices that balance on two wheels, allowing for zero turn radius and the ability to ride through narrow passageways. Examples of these human transporter devices are described in U.S. Pat. No. 5,701,965 and U.S. Pat. No. 6,302,230. These transporter devices would make a poor platform for combat robots, however. The balancing vehicles described in these references lack the ability to initially balance themselves when first powered on and would not be able to get back up after falling down. Such a robot would also lack a statically stable four-wheel mode. 
       BRIEF SUMMARY OF THE INVENTION 
       [0012]    The present invention comprises a robotic vehicle capable of transitioning from a low Center of Mass (“low-COM”) configuration to a high Center of Mass (‘high-COM”) configuration. The robotic vehicle comprises a rear base, a front arm, and a motorized-joint connecting the rear base and the front arm. The robotic vehicle includes a rear drive mechanism attached to the rear base, and a means of locomotion using a rear motorized ground-contacting module. The rear ground-contacting module serves to suspend the mechanism above the rear joint. A forward ground-contacting module is provided attached to the front arm. The forward ground-contacting module may also include a brake. A control module which controls the rear motorized drive is also provided. The control module includes a control loop for dynamically stabilizing the vehicle in the fore-aft plane by operation of the rear motorized drive in connection with the rear ground-contacting module. In all embodiments the ground-contacting modules may be skids, tracks or wheels, without limitation. 
         [0013]    In a further embodiment, the forward ground-contacting module is realized as a motorized ground-contacting member. 
         [0014]    In a further embodiment, the rear base is realized as a pair of ground-contacting members, laterally disposed with respect to one another. 
         [0015]    In a further embodiment, the front base is realized as a pair of ground-contacting members, laterally disposed with respect to one another. 
         [0016]    In a further embodiment, the front arms are realized as a pair of ground-contacting members, laterally disposed with respect to one another. 
         [0017]    The preferred embodiment (shown in  FIG. 1 ) has four motorized wheels for ground-contacting modules. Two motorized wheels are connected to the rear base and two motorized wheels are connected to the front base. The preferred embodiment includes independent front drive and rear drive mechanisms. The front and rear drive mechanisms may be operated in one of several modes including: (1) a combined drive mode using the front and rear drive mechanisms in combination when operating in the low Center of Mass configuration, (2) a rear-only drive mode using only the rear drive mechanism when operating in the high Center of Mass configuration, and (3) a transition mode for transitioning between the combined drive locomotion mode and the rear drive locomotion mode. 
         [0018]    Accordingly, the proposed reconfigurable robot has a low center of mass, statically stable mode and a high center of mass, balancing mode. The robot can switch between modes by use of drive wheels and actuated joints. A control system autonomously changes between the modes and also provides balance when in the balancing mode. The robot is capable of transporting various payloads, including camera and weapon systems on a turret. The four-wheel low profile mode allows the robot to move quickly and stably, much like a traditional wheeled vehicle. The two-wheel high profile mode allows the robot to place its camera or weapon system at a high perch, thereby seeing over obstacles. This mode also allows the robot to turn with a zero turning-radius. Being able to switch modes allows the robot to have a relatively narrow width. Both the narrow width and the zero turning-radius allow the robot to get through narrow corridors. 
         [0019]    According to one illustrative embodiment of the invention, there is a base, two main drive wheels attached to the base, two actuated shoulder joints connected to the base, two arm links attached at the shoulder joints, two wheels attached to the end of the arm links, and a control system that provides a control signal to the shoulder joints and/or the main drive wheels in order to transition between a mode in which all four wheels are in contact with the ground and a mode in which only the two main drive wheels are in contact with the ground. 
         [0020]    The transition mode utilizes a transitioning process comprising the steps of:
       (a) Applying power to a combination of the rear drive mechanism, the front drive mechanism, and the motorized joint to bring the vehicle into a partially upright position;   (b) Applying power to the rear drive mechanism to accelerate the vehicle backward;   (c) Applying power to the rear drive mechanism to accelerate the vehicle forward and lift the front drive mechanism off the ground; and   (d) Applying power to the rear drive mechanism in order to keep the front drive mechanism off the ground.       
 
     
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
         [0025]      FIG. 1  is a perspective view of one embodiment of the invention shown in a two-wheel high Center of Mass balance configuration. 
           [0026]      FIG. 2  is another perspective view of the embodiment of  FIG. 1 , shown in a four-wheel low Center of Mass configuration. 
           [0027]      FIG. 3  is a perspective view of the embodiment of  FIG. 1  with the addition of a camera payload mounted on an actuated turret. 
           [0028]      FIG. 4  is a perspective view of the embodiment of  FIG. 1 , with the addition of a weapon payload mounted on an actuated turret. 
           [0029]      FIG. 5  is a perspective view of another embodiment of the invention shown in a low Center of Mass Configuration (a) and a high Center of Mass Configuration (b). 
           [0030]      FIG. 6  is a perspective view of another embodiment of the invention shown in a low Center of Mass Configuration (a) and a high Center of Mass Configuration (b). 
           [0031]      FIG. 7  shows a flowchart detailing an algorithm for transitioning the device from a low Center of Mass configuration to a high Center of Mass balance configuration. 
           [0032]      FIG. 8  shows a flowchart detailing an algorithm for transitioning the device from a high Center of Mass balance configuration to a low Center of Mass configuration. 
           [0033]      FIG. 9  is a time-lapsed image sequence of the embodiment of  FIG. 4  transitioning from a four-wheel low Center of Mass configuration to a four-wheeled A-frame configuration to a two-wheeled high Center of Mass balance configuration. 
           [0034]      FIG. 10  shows a time-lapsed composite image of one embodiment of the invention transitioning from a four-wheel low Center of Mass configuration to a four-wheeled A-frame configuration. 
           [0035]      FIG. 11  shows a time-lapsed composite image of one embodiment of the invention transitioning from a four-wheeled A-frame configuration to a two-wheeled high Center of Mass balance configuration. 
           [0036]      FIG. 12  shows a time-lapsed image sequence of the embodiment of  FIG. 4  driving over a relatively small obstacle. 
           [0037]      FIG. 13  shows a time-lapsed image sequence of the embodiment of  FIG. 4  driving over a relatively large obstacle. 
           [0038]      FIG. 14  shows a model on an inverted pendulum on a wheel. This model is useful for analyzing and designing the balance controller for the robot. 
           [0039]      FIG. 15  shows a model of one embodiment of the invention useful for computing the wheel and shoulder joint torques in order to transition from a low Center of Mass configuration to an A-frame configuration. 
           [0040]      FIG. 16  shows a model of one embodiment of the invention useful for computing a sequence of actions for dynamically transitioning from an A-frame configuration to a high Center of Mass balance configuration. 
           [0041]      FIG. 17  shows a model of one embodiment of the invention with a gun turret carriage useful for computing a sequence of actions for controlling the pitch of the gun mount while transitioning from a Low Center of Mass configuration to a high Center of Mass configuration. 
           [0042]      FIG. 18  shows a control system diagram. 
           [0043]      FIG. 19  shows an exploded view of the embodiment of  FIG. 4 . 
       
    
    
     REFERENCE NUMERALS IN THE DRAWINGS 
       [0044]      
         [0000]    
       
         
               
               
               
               
             
           
               
                   
               
             
             
               
                 20 
                 Base 
                 30 
                 main drive wheel 
               
               
                 31 
                 main drive wheel 
                 32 
                 motor amplifier 
               
               
                 34 
                 electric motor 
                 36 
                 gear reduction 
               
               
                 40 
                 powered shoulder joint 
                 41 
                 powered shoulder joint 
               
               
                 50 
                 arm link 
                 51 
                 arm link 
               
               
                 60 
                 wheel 
                 61 
                 wheel 
               
               
                 70 
                 suspension system 
                 80 
                 track system 
               
               
                 90 
                 turret 
                 92 
                 embedded computer system 
               
               
                 94 
                 inertial measurement unit 
                 100 
                 weapon system 
               
               
                 110 
                 camera system 
                 200 
                 rear ground contacting member 
               
               
                 205 
                 rear drive wheel 
                 206 
                 rear track 
               
               
                 210 
                 rear base 
                 220  
                 powered joint 
               
               
                 230 
                 front base 
                 240  
                 front ground contacting member 
               
               
                 245 
                 front drive wheel 
                 246 
                 front track 
               
               
                 700 
                 obstacle 
                 1600 
                 embedded processor 
               
               
                 1601 
                 embedded processor batteries 
                 1602 
                 pitch, roll, and yaw sensors 
               
               
                 1603  
                 motor drive batteries 
                 1610 
                 left arm wheel rotation sensor 
               
               
                 1611  
                 left arm wheel motor 
                 1612  
                 left arm wheel amplifier 
               
               
                 1615  
                 right arm wheel rotation sensor 
                 1616 
                 right arm wheel amplifier 
               
               
                 1617  
                 right arm wheel motor 
                 1620 
                 GPS device 
               
               
                 1630  
                 compass 
                 1640 
                 wireless high speed data link 
               
               
                 1650  
                 left shoulder rotation sensor 
                 1651 
                 left shoulder motor 
               
               
                 1652  
                 left shoulder amplifier 
                 1655  
                 right shoulder rotation sensor 
               
               
                 1656 
                 right shoulder amplifier 
                 1657  
                 right shoulder motor 
               
               
                 1660  
                 left rear wheel rotation sensor 
                 1661 
                 left rear wheel motor 
               
               
                 1662  
                 left rear wheel amplifier 
                 1665  
                 right rear wheel rotation sensor 
               
               
                 1666  
                 right rear wheel amplifier 
                 1667  
                 right rear wheel motor 
               
               
                 7000  
                 Stand-Up command 
                 7100 
                 watchdog timer 
               
               
                 7110  
                 step 
                 7120  
                 step 
               
               
                 7130  
                 step 
                 7140 
                 comparator 
               
               
                 7150  
                 comparator 
                 7160  
                 fault code 
               
               
                 7200  
                 watchdog timer 
                 7210 
                 step 
               
               
                 7220  
                 comparator 
                 7230 
                 comparator 
               
               
                 7240  
                 fault code 
                 7300 
                 watchdog timer 
               
               
                 7310  
                 step 
                 7320  
                 comparator 
               
               
                 7330  
                 comparator 
                 7340  
                 fault code 
               
               
                 7400  
                 balancing mode 
                 8000  
                 Lie-Down command 
               
               
                 8100  
                 watchdog timer 
                 8110 
                 step 
               
               
                 8120  
                 comparator 
                 8130  
                 comparator 
               
               
                 8140  
                 fault code 
                 8200 
                 watchdog timer 
               
               
                 8210  
                 step 
                 8220  
                 comparator 
               
               
                 8230  
                 comparator 
                 8240  
                 fault code 
               
               
                 8300  
                 watchdog timer 
                 8310 
                 step 
               
               
                 8320  
                 step 
                 8330 
                 comparator 
               
               
                 8340  
                 comparator 
                 8350  
                 fault code 
               
               
                 8400  
                 four-wheel ground contact stasis 
                 9020 
                 solenoid-activated gear 
               
               
                 9030  
                 gun mount carriage 
                 9040 
                 gears 
               
               
                   
               
             
          
         
       
     
       DETAILED DESCRIPTION OF THE INVENTION 
       [0045]    The invention may be implemented in a wide range of embodiments. A characteristic of many of these embodiments is the ability to transition from a low Center of Mass configuration to a high Center of Mass balancing configuration. In the low Center of Mass configuration, a set of rear ground contacting members and a set of front ground contacting members provide a stable base of support. In the high Center of Mass configuration, only one set of ground contacting members (typically the rear ground contacting members) provide ground support while the other set (typically the front ground contacting members) are raised off the ground. An actuated joint located between the rear ground contacting members and the front ground contacting members is used to raise the Center of Mass when transitioning between the low Center of Mass configuration and the high Center of Mass configuration, and also to hold up the front ground contacting members when in the high Center of Mass configuration. A transitioning process is provided for transition to the high Center of Mass configuration. 
         [0046]      FIGS. 1 and 2  show perspective views of one embodiment of the invention. Two main drive wheels  30 ,  31  are connected to base  20 . Main drive wheels  30 ,  31  can each be powered by various means, including an electric motor with a gear reduction, a hydraulic motor, or an internal combustion engine and transmission. Suspension system  70  may also provide support between base  20  and main drive wheels  30 ,  31 . Two powered shoulder joints  40 ,  41  are connected to the base. The shoulder joints also may be powered by various means, including electric motors with gear reductions, hydraulic motors, or internal combustion engines. Two arm links  50 ,  51  are connected to the shoulder joints. Two arm wheels  60 ,  61  are connected at the end of the arm links. These wheels may be either passive or powered and may or may not have a steering mechanism. 
         [0047]      FIG. 1  shows the invention in an upright two-wheeled high Center of Mass balance configuration in which a control system provides a command to main drive wheels  30 ,  31  in order to balance the robot on the two main drive wheels. The reader will note that when the robot is in the balance configuration, the front wheels are off the ground. Accordingly, the control system sends control signals to the motors that power the rear wheels. The control signal sent by the control system is related to a measurement of the robot&#39;s Center of Mass with respect to the contact point of the wheels that are contacting the ground. Such a measurement could come from a gyroscope mounted in the base, an inertial measurement unit mounted in the base, a camera system mounted to the base or arms, or other means. 
         [0048]      FIG. 2  shows the invention in a four-wheel low Center of Mass configuration. In this configuration powered shoulder joints  40 ,  41  can be locked in order to maintain the configuration, or they can be used in conjunction with main drive wheels  30 ,  31  and arm wheels  60 ,  61  in order to raise or lower the Center of Mass. The powered shoulder joints accomplish this by supplying a torque between the base and each of the arms. 
         [0049]      FIG. 3  shows a perspective view of the embodiment of  FIG. 1  and  FIG. 2  with the addition of a camera system and track system. In this embodiment, track system  80  is attached to base  20 . Turret  90  is also attached to base  20 , and camera system  110  is attached to turret  90 . Camera system  100  may be remotely controlled and oriented through the control of turret  90 . Track system  80  can be used in order to get over rough terrain. One or more drive wheels may be powered to drive the belt or “track.” Track system  80  may operate similarly to caterpillar-type or Kegresse-type track systems. That is, the track may comprise interlocking metal segments or a flexible material. 
         [0050]      FIG. 4  shows a perspective view of the embodiment of  FIG. 1  and  FIG. 2  with the addition of a weapon system. In this embodiment, track system  80  is attached to base  20 . Turret  90  is also attached to the base  20 , and weapon system  100  is attached to turret  90 . In this embodiment the weapon system  100  may be remotely controlled and oriented through the control of turret  90 . 
         [0051]      FIGS. 5(   a ) and  5 ( b ) show a simplified embodiment of the invention in a low Center of Mass configuration and a high Center of Mass configuration, respectively. Rear drive wheel  205  is connected to rear base  210 . Rear drive wheel  205  can be powered by various means, including electric or hydraulic motors. Powered joint  220  is connected to rear base  210 . Powered joint  220  may also be powered by various means, including electric or hydraulic motors. Front base  230  is connected to powered joint  220 . Front drive wheel  245  is connected to front base  230 . The front wheel may be either passive or powered and may or may not have a steering mechanism. 
         [0052]      FIGS. 6(   a ) and  6 ( b ) show another embodiment of the invention in a low Center of Mass configuration and a high Center of Mass configuration, respectively. Rear ground contacting member  200  includes one or more rear tracks  206  connected to rear base  210 . Rear tracks  206  can be powered by various means, including electric or hydraulic motors. Powered joint  220  is connected to rear base  210 . Powered joint  220  may also be powered by various means, including electric or hydraulic motors. Front base  230  is connected to powered joint  220 . Front ground contacting member  240  includes one or more front tracks  246  connected to front base  230 . Front tracks  246  can be powered by various means, including electric or hydraulic motors. 
         [0053]      FIG. 7  shows a flowchart detailing a process for transitioning from a low Center of Mass configuration to a high Center of Mass balance configuration. When Stand-Up command  7000  is received, watchdog timer  7100  is loaded with the expected time required for the operation. Torque is then applied in the forward direction, as indicated by step  7110 , to the drive(s) of the rear ground-contacting member concurrently with the application of torque in the reverse direction to the drive(s) of the front ground-contacting member as indicated by step  7120 . Lifting torque is also applied to the drive(s) of the arm attachment joint concurrently with the application of torque to the ground-contacting members as indicated by step  7130 . 
         [0054]    Comparator  7140  determines whether the robot has attained the threshold angle (60 degrees in the present example). Comparator  7140  makes this determination by comparing input data provided by a sensor to the predefined threshold angle. If the robot has not attained the threshold angle comparator  7140  looks to comparator  7150  to determine if the timer of watchdog timer  7100  has expired. If watchdog timer  7100  has expired, fault code  7160  is generated. The process may then be repeated. 
         [0055]    When the pitch of the robot has ascended to an angle greater than a desired maximum, placing the robot in an A-frame pose, a reverse torque is applied to the rear ground-contacting members as indicated by step  7210 . This reverse torque accelerates the robot backward until a sufficient speed in the reverse direction is reached. Watchdog timer  7200  is loaded with the time expected to attain sufficient speed concurrently with the application of reverse torque. Comparator  7220  determines whether the speed of the robot has attained the threshold speed required. If the threshold speed has not been attained comparator  7220  looks to comparator  7230  to determine whether watchdog timer  7200  has expired. If watchdog timer  7200  has expired, fault code  7240  is generated. The process may then be repeated from Stand-Up command  7000 . 
         [0056]    If a sufficient speed is attained, the torque on the rear drives is changed to accelerate the robot in the forward direction as indicated by step  7310 , dynamically lifting the aspect of the robot further to the vertical. Watchdog timer  7310  is also loaded concurrently with the application of the forward torque. Watchdog timer  7310  is loaded with the expected time required to attain a vertical pose once a sufficient forward speed has been attained. Comparator  7320  is used to determine whether the vehicle has attained a pitch greater than 90 degrees. If a vertical pose has not been attained, comparator  7320  looks to comparator  7330  to determine if watchdog timer  7310  has expired. If watchdog timer  7310  has expired, fault code  7340  is generated. The process may then be repeated from Stand-Up command  7000 . 
         [0057]    When a vertical pose is attained, the control switches to balancing mode  7400  and the robot is brought into balancing stasis. 
         [0058]      FIG. 8  shows a flowchart detailing a process for transitioning from a high Center of Mass balance configuration to a low Center of Mass configuration. When Lie-Down command  8000  is received, watchdog timer  8100  is loaded with the expected time required for the operation. Backward torque is concurrently applied to the motorized drives of the rear ground-contacting member, as indicated by step  8110 . This causes the robot to begin to tilt forward. Comparator  8120  determines whether the vehicle has attained a threshold pitch (less than 85 degrees measured from the horizontal in the present example). If the vehicle has not attained the threshold pitch, comparator  8120  look to comparator  8130  to determine whether watchdog timer  8100  has expired. If watchdog timer  8100  has expired, fault code  8140  is generated. The process may then be repeated. 
         [0059]    When sufficient reduction in pitch is attained, the torque is removed from the rear ground-contacting member and the robot is allowed to settle into the A-Frame position as indicated by step  8210 . Watchdog timer  8200  is concurrently loaded with the time expected to complete the operation. Comparator  8220  determines whether the front base of the vehicle has made contact with the ground. If it has not, comparator  8220  looks to comparator  8230  to determine whether watchdog timer  8200  has expired. If watchdog timer  8200  has expired, fault code  8240  is generated. The process may then be repeated from Lie-Down command  8000 . 
         [0060]    When contact of the front ground-contacting member and the ground is confirmed by comparator  8220 , a reverse torque is applied to the motorized drives of the rear ground-contacting member as indicated by step  8310 . Forward torque is concurrently applied to the motorized drives of the forward ground-contacting member as indicated by  8320  until the aspect of the robot is brought down to a desired threshold angle. Watchdog timer  8300  is loaded with the expected time to reach the threshold angle. Comparator  8330  determines whether the vehicle has attained the threshold angle (less than 10 degrees in the present example). If the threshold angle has not been attained, comparator  8330  looks to comparator  8340  to determine whether watchdog timer  8300  has expired. If it has, fault code  8350  is generated. The process may then be repeated from Lie-Down command  8000 . Once the vehicle attains the threshold angle, the torques are removed, leaving the robot in four-wheel ground contact stasis  8400 . 
         [0061]      FIG. 9  is a time-lapsed image sequence of the embodiment shown in  FIG. 4  transitioning from a four-wheel low Center of Mass configuration (a) to a four-wheeled A-frame configuration (d) to a two-wheeled high Center of Mass balance configuration (l). In this image sequence, a combination of main drive wheels  30 ,  31 , arm wheels  60 ,  61 , and shoulder joints  40 ,  41  are used to raise the Center of Mass. 
         [0062]      FIG. 10  shows a time-lapsed composite image of a simplified embodiment of the invention transitioning from low Center of Mass configuration to an A-frame configuration. Rear ground contacting member  200  is attached to rear base  210 . The rear base is connected to powered joint  220 . The powered joint is connected to front base  230 . The front base is connected to front ground contacting member  240 . When in both the low Center of Mass configuration and in the A-frame configuration, both the rear ground contacting member and the front ground contacting member are in contact with the ground. During the transition from the low Center of Mass configuration to the A-frame configuration, power is applied to a combination of the rear ground contacting member  200 , powered joint  220 , and front ground contacting member  240 . One such method of applying power to a specific embodiment of the invention is described subsequently. 
         [0063]      FIG. 11  shows a time-lapsed composite image of one embodiment of the invention transitioning from an A-frame configuration to a high Center of Mass balance configuration. Rear ground contacting member  200  is attached to rear base  210 . The rear base is connected to powered joint  220 . The powered joint is connected to front base  230 . The front base is connected to front ground contacting member  240 . When in the A-frame configuration, both the rear ground contacting member and the front ground contacting member are in contact with the ground. When in the high Center of Mass balance configuration, the rear ground contacting member is in contact with the ground, while the front ground contacting member is not in contact with the ground. During the transition from the A-frame configuration to the high Center of Mass balance configuration, power is applied to rear ground contacting member  200  to raise the Center of Mass up and over rear ground contacting member  200 . One such method of applying power to a specific embodiment of the invention is described subsequently. 
         [0064]      FIG. 12  shows a time-lapsed image sequence of the embodiment of the invention shown in  FIG. 4  riding over a relatively small obstacle. In this image sequence, the robot slows down on the approach of the obstacle (a); drives toward the obstacle, initiating contact between the obstacle and the rear drive wheel (b); applies a torque to the rear drive wheel to lift its center of mass onto the obstacle while balancing (c); drives over the obstacle (d); drives off the obstacle (e); and drives away from the obstacle (f). Throughout this motion, the robot remains balanced using a balance control method which is described in greater detail subsequently. 
         [0065]      FIG. 13  shows a time-lapsed image sequence of the embodiment of the invention shown in  FIG. 4  riding over a relatively large obstacle. In this image sequence, the robot lifts its arm links  50 ,  51  and arm wheels  60 ,  61  while approaching obstacle  700  while balancing (a); lowers its arm wheels  60 ,  61  onto the obstacle and lowers its base  20  such that track system  80  on base  20  makes contact with obstacle  700  (b); uses track system  80  to pull itself up and onto obstacle  700  (c); makes contact between main drive wheels  30 ,  31  and the top of obstacle  700  and uses a combination of track system  80  and main drive wheels  30 ,  31  to drive over obstacle  700 , while arm wheels  60 ,  61  regain contact with the ground (d); finishes driving over obstacle  700  using main drive wheels  30 ,  31  (e); loses contact between main drive wheels  30 ,  31  and obstacle  700  and regains contact between main drive wheels  30 ,  31  and the ground (f). During this maneuver, turret  90  can be operated to orient weapon system  100  to a desired orientation with respect to the ground, independent of the configuration of the robot. Track system  80  may be remotely actuated by an operator or it may be automatically actuated when the robot detects that its forward progress is impeded by the obstacle. 
         [0066]      FIG. 14  shows a mathematical model of an inverted pendulum on a wheel. This model is useful for analyzing and designing the balance controller for the balance configuration, as described subsequently. 
         [0067]      FIG. 15  shows a mathematical model of one embodiment of the invention useful for computing the wheel and shoulder joint torques in order to transition from a low Center of Mass configuration to an A-frame configuration. Rear drive wheel  205  is connected to rear base  210 . Rear base  210  is connected to powered joint  220 . Front base  230  is also connected to powered joint  220 . Front drive wheel  245  is connected to front base  230 . In this model, the following assumptions are made: (1) the Center of Mass of the device lies at the location of powered joint  220 ; (2) the entire device has a mass of M; (3) front base  230  and rear base  210  are both of the same length, L; (4) wheels  205 ,  245  are both of the same radius, R; (5) the torque applied to the powered joint  220  is τ S ; (6) the torque applied to each wheel  205 ,  245  is τ W ; and (7) the center of mass is at a vertical height, h, above the center of the wheels, and at a horizontal distance, w, from the center of the wheels. 
         [0068]    Shown in  FIG. 15  are various symbols representing the forces and torques on the system. F X  is the horizontal force between the ground and each wheel, and also between each wheel and its associated base. F Z  is the vertical force between the ground and each wheel, and also between each wheel and its associated base. Mg is the force produced by gravitation on the mass. With this model, the relation between the quantities required to support the mass is 
         [0000]    
       
         
           
             
               
                 τ 
                 S 
               
               + 
               
                 
                   
                     ( 
                     
                       h 
                       + 
                       R 
                     
                     ) 
                   
                   R 
                 
                  
                 
                   τ 
                   W 
                 
               
             
             = 
             
               
                 1 
                 2 
               
                
               Mgw 
             
           
         
       
     
         [0069]    The derivation of this equation is explained subsequently. This relation can be used to compute the torque at wheels  205 ,  245  and powered joint  220  needed to support the mass. If larger torques are applied, then the mass will accelerate upward, raising the Center of Mass. If smaller torques are applied, then the mass will accelerate downward, lowering the Center of Mass. 
       Balancing in the High Center of Mass Configuration 
       [0070]    The reconfigurable robot balances when in the high Center of Mass configuration. Control action required to balance this configuration is generally accomplished by: (1) computing the dynamic equations of motion for the robot; (2) linearizing the dynamic equations; (3) determining a parameterized feedback control system; and (4) determining suitable and/or optimal control system parameters using one of a number of different mathematical control system tools. 
         [0071]    As a first approximation to the full dynamics of the reconfigurable robot, we can compute the equations of motion of a simplified system consisting of an inverted pendulum on a single wheel, as shown in  FIG. 14 . This system is a simplification of a balancing robot, taking into account only planar motion and locked arms. The equations of motion can be determined using either a free-body diagram approach or a Lagrangian approach. Both approaches result in the following equations of motion: 
         [0000]    
       
         
           
             
               [ 
               
                 
                   
                     
                       
                         M 
                         W 
                       
                       + 
                       
                         M 
                         P 
                       
                       + 
                       
                         
                           J 
                           W 
                         
                         
                           R 
                           W 
                         
                       
                     
                   
                   
                     
                       
                         M 
                         P 
                       
                        
                       
                         L 
                         P 
                       
                        
                       cos 
                        
                       
                           
                       
                        
                       
                         θ 
                         P 
                       
                     
                   
                 
                 
                   
                     
                       
                         M 
                         P 
                       
                        
                       
                         L 
                         P 
                       
                        
                       cos 
                        
                       
                           
                       
                        
                       
                         θ 
                         P 
                       
                     
                   
                   
                     
                       
                         J 
                         P 
                       
                       + 
                       
                         
                           M 
                           P 
                         
                          
                         
                           L 
                           P 
                           2 
                         
                       
                     
                   
                 
               
               ] 
             
              
             
                 
               
                 
                   
                     [ 
                     
                       
                         
                           
                             
                               X 
                               ¨ 
                             
                             W 
                           
                         
                       
                       
                         
                           
                             
                               θ 
                               ¨ 
                             
                             P 
                           
                         
                       
                     
                     ] 
                   
                   + 
                   
                     [ 
                     
                       
                         
                           
                             
                               - 
                               
                                 M 
                                 P 
                               
                             
                              
                             
                               L 
                               P 
                             
                              
                             sin 
                              
                             
                                 
                             
                              
                             
                               θ 
                               P 
                             
                              
                             
                               
                                 θ 
                                 . 
                               
                               P 
                               2 
                             
                           
                         
                       
                       
                         
                           0 
                         
                       
                     
                     ] 
                   
                   + 
                   
                     [ 
                     
                       
                         
                           0 
                         
                       
                       
                         
                           
                             
                               - 
                               
                                 M 
                                 P 
                               
                             
                              
                             
                               L 
                               P 
                             
                              
                             g 
                              
                             
                                 
                             
                              
                             sin 
                              
                             
                                 
                             
                              
                             
                               θ 
                               P 
                             
                           
                         
                       
                     
                     ] 
                   
                 
                 = 
                 
                   
                     [ 
                     
                       
                         
                           
                             1 
                             
                               R 
                               W 
                             
                           
                         
                       
                       
                         
                           
                             - 
                             1 
                           
                         
                       
                     
                     ] 
                   
                    
                   τ 
                 
               
             
           
         
       
     
         [0000]    where X W  is the forward position of the center of the wheels and θ P  is the angle of the platform with respect to vertical, M P  is the mass of the upper body platform and arms, L P  is the distance from the wheel pivot to the Center of Mass of the platform, J P  is the moment of inertia of the pendulum about its Center of Mass, M W  is the total mass of the main drive wheels, J W  is the moment of inertia of the main drive wheels about their Center of Mass, R W  is the radius of a main drive wheel, τ is the torque applied, and g is the gravitational acceleration constant. The various length, mass, and inertia properties can be estimated from CAD models, measured through various experimental techniques, or estimated online during operation of the robot using standard adaptive control techniques. 
         [0072]    The equations of motion can be linearized about the upright balancing configuration and solved in terms of the state variables: 
         [0000]    
       
         
           
               
             
               
                 [ 
                 
                   
                     
                       
                         
                           X 
                           ¨ 
                         
                         W 
                       
                     
                   
                   
                     
                       
                         
                           θ 
                           ¨ 
                         
                         P 
                       
                     
                   
                 
                 ] 
               
               = 
               
                 
                   
                     [ 
                     
                       
                         
                           0 
                         
                         
                           
                             M 
                             12 
                           
                         
                       
                       
                         
                           0 
                         
                         
                           
                             M 
                             22 
                           
                         
                       
                     
                     ] 
                   
                    
                   
                     [ 
                     
                       
                         
                           
                             X 
                             W 
                           
                         
                       
                       
                         
                           
                             θ 
                             P 
                           
                         
                       
                     
                     ] 
                   
                 
                 + 
                 
                   
                     [ 
                     
                       
                         
                           
                             B 
                             1 
                           
                         
                       
                       
                         
                           
                             B 
                             2 
                           
                         
                       
                     
                     ] 
                   
                    
                   τ 
                 
               
             
           
         
       
     
         [0000]    The four condensed parameters of these equations of motion are: 
         [0000]    
       
         
           
             
               
                 M 
                 12 
               
               = 
               
                 
                   
                     - 
                     
                       M 
                       P 
                       2 
                     
                   
                    
                   
                     L 
                     P 
                     2 
                   
                    
                   g 
                 
                 den 
               
             
             ; 
           
         
       
       
         
           
             
               
                 M 
                 22 
               
               = 
               
                 
                   
                     M 
                     P 
                   
                    
                   
                     L 
                     P 
                   
                    
                   
                     g 
                      
                     
                       ( 
                       
                         
                           M 
                           W 
                         
                         + 
                         
                           M 
                           P 
                         
                         + 
                         
                           
                             J 
                             W 
                           
                           
                             R 
                             W 
                             2 
                           
                         
                       
                       ) 
                     
                   
                 
                 den 
               
             
             ; 
           
         
       
       
         
           
             
               
                 B 
                 1 
               
               = 
               
                 
                   
                     
                       M 
                       P 
                     
                      
                     
                       L 
                       P 
                     
                   
                   + 
                   
                     
                       J 
                       P 
                     
                     
                       R 
                       W 
                     
                   
                   + 
                   
                     
                       
                         M 
                         P 
                       
                        
                       
                         L 
                         P 
                         2 
                       
                     
                     
                       R 
                       W 
                     
                   
                 
                 den 
               
             
             ; 
             and 
           
         
       
       
         
           
             
               
                 B 
                 2 
               
               = 
               
                 - 
                 
                   
                     
                       M 
                       W 
                     
                     + 
                     
                       M 
                       P 
                     
                     + 
                     
                       
                         J 
                         W 
                       
                       
                         R 
                         W 
                         2 
                       
                     
                     + 
                     
                       
                         
                           M 
                           P 
                         
                          
                         
                           L 
                           P 
                         
                       
                       
                         R 
                         W 
                       
                     
                   
                   den 
                 
               
             
             , 
             
               
 
             
              
             
               
                 where 
                  
                 
                     
                 
                  
                 den 
               
               = 
               
                 
                   
                     ( 
                     
                       
                         M 
                         W 
                       
                       + 
                       
                         M 
                         P 
                       
                     
                     ) 
                   
                    
                   
                     J 
                     P 
                   
                 
                 + 
                 
                   
                     M 
                     W 
                   
                    
                   
                     M 
                     P 
                   
                    
                   
                     L 
                     P 
                     2 
                   
                 
                 + 
                 
                   
                     
                       J 
                       W 
                     
                     
                       R 
                       W 
                       2 
                     
                   
                    
                   
                     
                       ( 
                       
                         
                           J 
                           P 
                         
                         + 
                         
                           
                             M 
                             P 
                           
                            
                           
                             L 
                             P 
                             2 
                           
                         
                       
                       ) 
                     
                     . 
                   
                 
               
             
           
         
       
     
         [0073]    A simple linear control law that can balance the system, is 
         [0000]      τ= K   1 ( X   W     dex     −X   W )+ K   2 ( {dot over (X)}   W     dex     −{dot over (X)}   W )+ K   3 (θ P     dex   −θ P )+ K   4 ({dot over (θ)} P     dex   −{dot over (θ)} P )
 
         [0074]    Using this control law and rewriting the resultant linearized equations of motion in the form {dot over (X)}=AX+Bu, where X is the state variables and u are the inputs, we get 
         [0000]    
       
         
           
             
               
                 
                   
                      
                     
                        
                       t 
                     
                   
                    
                   
                     [ 
                     
                       
                         
                           
                             X 
                             W 
                           
                         
                       
                       
                         
                           
                             
                               X 
                               . 
                             
                             W 
                           
                         
                       
                       
                         
                           
                             θ 
                             P 
                           
                         
                       
                       
                         
                           
                             
                               θ 
                               . 
                             
                             P 
                           
                         
                       
                     
                     ] 
                   
                 
                 = 
                 
                   
                     [ 
                     
                       
                         
                           0 
                         
                         
                           1 
                         
                         
                           0 
                         
                         
                           0 
                         
                       
                       
                         
                           
                             
                               - 
                               
                                 B 
                                 1 
                               
                             
                              
                             
                               K 
                               1 
                             
                           
                         
                         
                           
                             
                               - 
                               
                                 B 
                                 1 
                               
                             
                              
                             
                               K 
                               2 
                             
                           
                         
                         
                           
                             
                               M 
                               12 
                             
                             - 
                             
                               
                                 B 
                                 1 
                               
                                
                               
                                 K 
                                 3 
                               
                             
                           
                         
                         
                           
                             
                               - 
                               
                                 B 
                                 1 
                               
                             
                              
                             
                               K 
                               4 
                             
                           
                         
                       
                       
                         
                           0 
                         
                         
                           0 
                         
                         
                           0 
                         
                         
                           1 
                         
                       
                       
                         
                           
                             
                               - 
                               
                                 B 
                                 2 
                               
                             
                              
                             
                               K 
                               1 
                             
                           
                         
                         
                           
                             
                               - 
                               
                                 B 
                                 2 
                               
                             
                              
                             
                               K 
                               2 
                             
                           
                         
                         
                           
                             
                               M 
                               22 
                             
                             - 
                             
                               
                                 B 
                                 2 
                               
                                
                               
                                 K 
                                 3 
                               
                             
                           
                         
                         
                           
                             
                               - 
                               
                                 B 
                                 2 
                               
                             
                              
                             
                               K 
                               4 
                             
                           
                         
                       
                     
                     ] 
                   
                    
                   
                     [ 
                     
                       
                         
                           
                             X 
                             W 
                           
                         
                       
                       
                         
                           
                             
                               X 
                               . 
                             
                             W 
                           
                         
                       
                       
                         
                           
                             θ 
                             P 
                           
                         
                       
                       
                         
                           
                             
                               θ 
                               . 
                             
                             P 
                           
                         
                       
                     
                     ] 
                   
                 
               
                 
             
             + 
             
                 
               
                   
                 
                   
                     [ 
                     
                       
                         
                           0 
                         
                         
                           0 
                         
                         
                           0 
                         
                         
                           0 
                         
                       
                       
                         
                           
                             
                               B 
                               1 
                             
                              
                             
                               K 
                               1 
                             
                           
                         
                         
                           
                             
                               B 
                               1 
                             
                              
                             
                               K 
                               2 
                             
                           
                         
                         
                           
                             
                               B 
                               1 
                             
                              
                             
                               K 
                               3 
                             
                           
                         
                         
                           
                             
                               B 
                               1 
                             
                              
                             
                               K 
                               4 
                             
                           
                         
                       
                       
                         
                           0 
                         
                         
                           0 
                         
                         
                           0 
                         
                         
                           1 
                         
                       
                       
                         
                           
                             
                               B 
                               2 
                             
                              
                             
                               K 
                               1 
                             
                           
                         
                         
                           
                             
                               B 
                               2 
                             
                              
                             
                               K 
                               2 
                             
                           
                         
                         
                           
                             
                               B 
                               2 
                             
                              
                             
                               K 
                               3 
                             
                           
                         
                         
                           
                             
                               B 
                               2 
                             
                              
                             
                               K 
                               4 
                             
                           
                         
                       
                     
                     ] 
                   
                    
                   
                     [ 
                     
                       
                         
                           
                             X 
                             
                               W 
                               des 
                             
                           
                         
                       
                       
                         
                           
                             
                               X 
                               . 
                             
                             
                               W 
                               des 
                             
                           
                         
                       
                       
                         
                           
                             θ 
                             
                               P 
                               des 
                             
                           
                         
                       
                       
                         
                           
                             
                               θ 
                               . 
                             
                             
                               P 
                               des 
                             
                           
                         
                       
                     
                     ] 
                   
                 
               
             
           
         
       
     
         [0075]    The eigenvalues of the A matrix will determine the stability and the response time of the system and will depend on the feedback parameters, K 1  through K 4 . These parameters can be chosen in many ways, including pole placement, LQR techniques, and simply trial and error. 
         [0076]    This technique gives a combined applied torque of τ. This torque can be applied to typical embodiments of the invention by dividing it among the main drive mechanisms. For example, in the embodiment of  FIG. 1 , half the torque can be applied to main drive wheel  30 , and half the torque can be applied to main drive wheel  31 . 
       Turning in the High Center of Mass Configuration 
       [0077]    In a typical embodiment of the invention, such as the embodiment shown in  FIGS. 1 and 2 , the robot can turn about a vertical axis by differentially driving main drive wheels  30 ,  31 . The following control law can be used to determine the differential torque to apply to the wheels, 
         [0000]      τ Y   =K   5 (θ Y     dex   −θ Y )+ K   6 ({dot over (θ)} Y     dex   −{dot over (θ)} Y )
 
         [0000]    where τ Y  is the differential torque to apply to the main drive wheels  30 ,  31 ; θ Y     dex    is the desired yaw angle (rotation about the vertical axis); θ Y  is the measured yaw angle; {dot over (θ)} Y     dex    is the desired yaw velocity; {dot over (θ)} Y  is the measured yaw velocity; and K 5  and K 6  are control gains. The desired yaw and yaw velocity may come from a user input interface or from a higher-level controller. The measured yaw and yaw velocity may come from a gyroscope, inertial measurement unit, vision system, or other sensing means. The control gains, K 5  and K 6  can be chosen using a variety of methods known to those familiar with control system design. 
         [0078]    This technique gives a differential applied torque of τ Y . This torque can be applied to typical embodiments of the invention by distributing it among the main drive mechanisms. For example, in the embodiment of  FIG. 1 , half the torque can be applied to main drive wheel  30 , and an equal and opposite torque can be applied to main drive wheel  31 . This will provide a differential torque that results in the control of yaw and yaw velocity. The reader will note that both the control of balance and the control of turning can be achieved simultaneously by applying the above techniques simultaneously through the summation of the resultant torques at each wheel. 
       Transitioning Between Modes 
       [0079]    Various embodiments of the invention transition between several geometric configurations and their associated modes of operation, including a two-wheeled balancing configuration, a four-wheeled low Center of Mass configuration, and a four-wheeled A-frame configuration. Switching between the configurations can be initiated by a human operator when the robot is being teleoperated or automatically during autonomous or semi-autonomous operation. 
         [0080]    When in the four-wheeled low Center of Mass configuration, the robot has a low profile and operates much like a remote-controlled car, or conventional four-wheeled robot. Steering and Velocity commands can be directly interpreted into wheel velocity commands. 
         [0081]    To transition from the four wheel low Center of Mass configuration to the four-wheeled A-frame configuration, the front wheels can be commanded to drive backwards and the rear wheels can be commanded to drive forward, while the shoulder motors are commanded to be driven to make the robot form an A shape. Once in the A-frame configuration, if desirable, brakes on the shoulder motors can be applied to lock the shoulders, reducing the power consumption at those joints.  FIG. 15  shows a schematic of a specific embodiment of the invention that can be used to compute the wheel and shoulder motor torques that can be applied to transition from a low Center of Mass configuration to an A-frame configuration. Performing force balance on the wheel, we have 
         [0000]        F   x =τ W   /R  
 
         [0000]    Performing a force balance in the vertical axis, we have 
         [0000]        F   Z   =Mg/ 2 
         [0000]    Performing a torque balance about the mass, we have 
         [0000]      2 F   Z   w −2 F   X   h− 2τ W =2τ S  
 
         [0000]    Solving the above equations to eliminate F x  and F Z  we get, 
         [0000]    
       
         
           
             
               
                 τ 
                 S 
               
               + 
               
                 
                   
                     ( 
                     
                       h 
                       + 
                       R 
                     
                     ) 
                   
                   R 
                 
                  
                 
                   τ 
                   W 
                 
               
             
             = 
             
               
                 1 
                 2 
               
                
               Mgw 
             
           
         
       
     
         [0082]    We see that the Center of Mass can be lifted through multiple combinations of shoulder torque or wheel torques. For example, if only shoulder torque is provided, we get 
         [0000]    
       
         
           
             
               τ 
               S 
             
             = 
             
               
                 1 
                 2 
               
                
               Mgw 
             
           
         
       
     
         [0000]    whereas if only wheel torque is provided, we get 
         [0000]    
       
         
           
             
               τ 
               W 
             
             = 
             
               
                 R 
                 
                   2 
                    
                   
                     ( 
                     
                       h 
                       + 
                       R 
                     
                     ) 
                   
                 
               
                
               Mgw 
             
           
         
       
     
         [0083]    The reader will note that the front and rear wheels do not both necessarily need to be motorized in order to provide a wheel torque τ W . For example, the front wheels could have a brake instead of a motor and be locked in place. τ W  could then be applied to just the rear wheel, producing nearly the same effect as had the wheel torque been applied to both wheels. The only difference would be that instead of the Center of Mass transitioning straight vertically, the front wheel would stay in its position on the ground and the Center of Mass would transition both horizontally and vertically. The above equations are for the model in which the Center of Mass lies directly at the powered joint, the front and rear base lengths are the same, the wheel diameters are the same, and the wheel torques are the same. This model was chosen for simplicity of demonstration to demonstrate one specific embodiment of the invention. One skilled in the art should be able to easily compute related equations for other embodiments of the invention. 
       Dynamic Transition to the Balancing Configuration 
       [0084]    A robot dynamically transitioning to the balancing configuration is illustrated in  FIG. 16 . During transition from the low Center of Mass configuration to the high Center of Mass configuration, the robot passes through a sequence of configurations in which the projection of the Center of Mass of the robot onto the ground (the Ground Projection of the Center of Mass) lies outside the Ground Support Polygon of the robot. The Center of Mass is the weighted average location of all of the mass of the robot. The Ground Projection of the Center of Mass, P com , is the point on the ground directly below the Center of Mass location. The Ground Support Polygon is defined by the convex hull of all the points of contact between the robot and the ground. Both “Ground Projection of the Center of Mass” and “Ground Support Polygon” are terms commonly used in dynamically balanced robotic fields, for example the field of legged robots. “Convex hull” is a term commonly used in mathematics. The convex hull of a set of points, X, is the minimal convex set containing X. If all ground contacting points lie in the same plane, the convex hull may be visualized by imagining an elastic band stretched to encompass all of the ground contacting points. If a perpendicular stake (perpendicular relative to the plane) is placed at the location of each ground contacting point, the elastic band will take on the shape of the convex hull when the elastic band is released. 
         [0085]    A robot with Static Mobility is one in which the Ground Projection of the Center of Mass always lies within the Ground Support Polygon. One example would be a slow walking hexapedal robot with an alternating tripod gait. A robot with Dynamic Mobility is one in which the Ground Projection of the Center of Mass occasionally lies outside the Ground Support Polygon. One example would be a fast walking or running biped. A robot with Static Mobility can move at slow speeds without consideration for the dynamics of the robot, but only with consideration for the geometric kinematics of the robot. A robot with Dynamic Mobility must move in such a way that takes dynamics into consideration. For example, a bipedal walking robot cannot come to a stop at an arbitrary point in its gait. When the Ground Projection of the Center of Mass lies outside the Ground Support Polygon, the robot must continue moving and take a step or it will fall down. 
         [0086]    The main advantage of Static Mobility is that when the Ground Projection of the Center of Mass is inside the Ground Support Polygon, the robot is typically very stable and resistant to disturbances or tipping. A main advantage of Dynamic Mobility is high maneuverability since it is not a requirement that the Ground Projection of the Center of Mass stays inside the Ground Support Polygon. The present invention can transition between Static Mobility configurations and Dynamic Stability configurations. Depending on the situation, a configuration can be chosen based on the importance of the advantages of that configuration. 
         [0087]    Many embodiments of the present invention exhibit Dynamic Mobility when dynamically transitioning from a low Center of Mass configuration to a high Center of Mass configuration. In the following discussion, the embodiments of  FIG. 4  and  FIG. 9  are considered, although the discussion pertains to any embodiment of the present invention that exhibits dynamic mobility. 
         [0088]    To dynamically transition from the low Center of Mass configuration to the high Center of Mass two-wheeled balancing configuration, the robot provides a rotational torque with rear drive wheels  30 ,  31 . There are a number of ways to provide this, torque. In one way, the robot starts from a stationary position and applies a large torque to the rear wheels, thereby lifting the front wheels, much like a motorcycle “popping a wheelie”. However, using this technique requires a large forward displacement of the robot as the wheel torque that lifts the body of the robot also produces a large forward acceleration of the robot. The amount of forward displacement required is in relation to the amount of rear drive wheel torque that is applied. The larger the rear drive wheel torque, the less displacement required. Thus it is preferable to apply the maximum available torque. However, drive components such as electric motors have maximum torque limits and with typical components available today, a significant forward displacement occurs using this method. 
         [0089]    A preferred method is to first apply a reversing torque to the rear drive wheels when in the A-frame configuration ( FIG. 9   e,f ), thereby causing a backward velocity of the robot. Then, after a period of time has passed or the robot has achieved a predefined threshold backward velocity, a large forward torque is applied to the rear wheels. This forward torque both stops the backward translational velocity of the robot and also lifts the body of the robot ( FIG. 9  ( g ), ( h ), ( i )). After a predefined period of time, or after a threshold pitch is reached, the balancing control system is then switched on and the robot balances ( FIG. 9  ( j ), ( k ), ( l )). A flowchart illustrating an implementation of this method is provided in  FIG. 7  (and described previously). 
         [0090]    This method of first providing a backward velocity before applying a forward rear drive wheel torque is preferred because a minimal amount of body displacement is produced as a result of the transition. Both in simulation studies and prototype experimentation, it has been determined that a robot can perform this dynamic transition in less than one meter of total travel. Determining the amount of torque to apply and the conditions for transitioning from reverse torque to forward torque can be achieved in a number of ways, including manual tuning of parameters, automatic tuning through adaptive control and learning control techniques, and automatic tuning through parameter search methods such as gradient descent and genetic algorithms. 
         [0091]    The reader should note that this method can work whether the robot starts in a low Center of Mass configuration ( FIG. 9   a ) or an intermediate Center of Mass A-Frame Configuration ( FIG. 9   d ). However, starting in the A-Frame configuration is preferable, as the amount of rear drive wheel torque required to perform the maneuver is reduced, and the amount of travel required to perform the maneuver is reduced. 
         [0092]    The reader will note that in  FIG. 16 , the Ground Projection of the Center of Mass falls a substantial distance, ΔX, away from the support points of the wheels. When ΔX is large, as in  FIG. 16 , the robot dynamically transitions to the balance configuration. In order to do so, a corresponding large torque will be applied to the main wheels. Less torque is required when ΔX is small. As mentioned previously, the method of backing up and then accelerating forward may also be used to reduce the forward distance of travel required to transition to the balancing configuration. 
       Leveling the Turet During Transitions 
       [0093]    It is a further object of the present invention to provide a method for rotating a gun carriage into a level position during the transitions to the several operating positions previously described. The amount of pitch movement is not always available within the mounted gun turret assembly, so an additional mechanism known as a gun mount carriage assembly is incorporated. 
         [0094]    As illustrated in  FIG. 17 , the rate R ({dot over (α)}) that gun mount carriage  9030  needs to rotate to keep the gun mount carriage level when the robot is balanced is about 0.8 times the rate of rotation of arm  50 . This is derived from the fact that the arms will rotate through an angle of θ to the A-frame position while the gun mount carriage needs to move only θ/2 deg. The mount needs an additional α deg of forward rotation to be level when the balanced position is attained and the total rotation of the carriage is φ=θ/2+α. This determines the gear reduction or rate to be R=φ/θ or 0.5+α/θ. A solenoid-activated gear  9020  with this ratio is attached between gears on arm motor shafts  40  and corresponding gears  9040  on the gun mount carriage. The carriage rotation is capable of being locked at the three cardinal positions (cart, A-frame and balanced) using beveled solenoid operated pins. With this configuration the gun mount carriage will rotate slightly ahead of the angular position of the arms at a rate of R times the moving angle of the arms. However, during the movement to A-frame this rate needs to be only half of the arm rate to keep the gun level so the extra rate, α/θ, is automatically removed by the gun leveling feature of the turret. When the robot reaches the A-frame position the gun carriage is locked, the arms gear disengaged, and α-degrees of turret elevation have been consumed. As the robot is configured further into the balancing posture, the gun turret-leveling feature keeps the gun level, removing the extra α-degrees of pitch from the turret elevation. Once balanced the available pitch range of the gun will be the full elevation range of the turret. 
         [0095]    A control system for the control of the robot is illustrated in  FIG. 18 . Embedded processor  1600  receives input signals from wireless high speed data link  1640 . Wireless high speed data link  1640  provides directional control over the operation of the robot. In particular, wireless data link  1640  directs the robot to move forward and backward, to turn left and right, to switch between low center of mass and high center of mass operating modes, and to control the weapons or camera systems. Embedded processor  1600  also receives inputs from various sensors including pitch, roll, and yaw sensors  1602  which provide orientation feedback to embedded processor  1600 . This orientation feedback is particularly useful in holding the robot in the balancing configuration as discussed previously. Embedded processor  1600  also receives input from GPS device  1620  and compass  1630 . Embedded processor batteries  1601  provides power for controlling the various operations carried out by embedded processor  1600 . 
         [0096]    Embedded processor  1600  directs torque to left rear wheel motor  1661  and right rear wheel motor  1667  through left rear wheel amplifier  1662  and right rear wheel amplifier  1666 , respectively. Embedded processor  1600  receives data regarding the rate of rotation of the left rear wheel and the right rear wheel via left rear wheel rotation sensor  1660  and right rear wheel rotation sensor  1665 , respectively. 
         [0097]    Embedded processor  1600  directs torque to left shoulder motor  1651  and right shoulder motor  1657  through left shoulder amplifier  1652  and right shoulder amplifier  1656 , respectively. Embedded processor  1600  receives data regarding the rate of rotation of the left shoulder and right shoulder via left shoulder rotation sensor  1650  and right shoulder rotation sensor  1655 , respectively. 
         [0098]    Embedded processor  1600  directs torque to left arm wheel motor  1611  and right arm wheel motor  1617  through left arm wheel amplifier  1612  and right arm wheel amplifier  1616 , respectively. Embedded processor  1600  receives data regarding the rate of rotation of the left arm wheel and the right arm wheel via left arm wheel rotation sensor  1610  and right arm wheel rotation sensor  1615 , respectively. Power is supplied to the aforementioned amplifiers through motor drive batteries  1603 . 
         [0099]    An exploded view of the present invention is provided in  FIG. 19 . Inertial measurement unit  94  is attached to base  20 . Inertial measurement unit  94  includes sensors capable of detecting pitch, roll, and yaw of base  20 . Inertial measurement unit  94  may optionally include sensors capable of detecting linear acceleration in the X, Y, and Z directions. Embedded computer system  92  includes the aforementioned embedded processor and related circuitry. Motor amplifier  32  amplifies signals from embedded computer system  92  to drive electric motor  34 . Gear reduction  36  is provided between electric motor  34  and main drive wheel  31  to deliver optimal rotational speed and force. 
         [0100]    The preceding description contains significant detail regarding the novel aspects of the present invention. It should not be construed, however, as limiting the scope of the invention but rather as providing illustrations of the preferred embodiments of the invention. As an example, the reconfigurable may have more utilize multiple joints to provide greater range of articulation. Such variations do not alter the function of the invention. Thus, the scope of the invention should be fixed by the following claims, rather than by the examples given.