Systems and Methods for Controlling a Legged Robot Based on Rate of Change of Angular Momentum

Abstract

Systems and methods are presented that use the rate of change of a legged robot's centroidal angular momentum ({dot over (H)} G ) in order to maintain or improve the robot's balance. In one embodiment, a control system determines the current value of {dot over (H)} G , compares this value to a threshold value, and determines an instruction to send to the robot. Executing the instruction causes the robot to remain stable or become more stable. Systems and methods are also presented that use a value derived from {dot over (H)} G in order to maintain or improve the robot's balance. In one embodiment, a control system determines the location of the Zero Rate of change of Angular Momentum (ZRAM) point (A), determines the distance between A and the location of the center of pressure of the resultant ground force, compares this value to a threshold value, and determines an instruction to send to the robot.

1 . A computer-implemented method for determining an instruction to send to a legged robot, the method comprising:
 determining a rate of change of the robot's centroidal angular momentum ({dot over (H)} G );   determining whether the rate of change of the robot's centroidal angular momentum ({dot over (H)} G ) exceeds a threshold value, wherein the threshold value is based on one or more factors of a group containing a friction between the robot and a support surface, a torque limit of an actuator of the robot, a design parameter of the robot, and an inertial property of the robot; and   responsive to determining that the rate of change of the robot's centroidal angular momentum ({dot over (H)} G ) exceeds the threshold value, determining an instruction to send to the robot.   
     
     
         2 . The method of  claim 1 , wherein the determined instruction causes the robot to enlarge a support polygon. 
     
     
         3 . The method of  claim 1 , wherein the determined instruction causes the robot to enlarge a support polygon, and wherein the enlarged support polygon contains a Zero Rate of change of Angular Momentum point. 
     
     
         4 . The method of  claim 1 , wherein the determined instruction causes the robot to change a location of a center of mass of the robot. 
     
     
         5 . The method of  claim 1 , wherein the determined instruction causes the robot to change a resultant ground reaction force acting upon the robot. 
     
     
         6 . The method of  claim 1 , further comprising determining the threshold value. 
     
     
         7 . The method of  claim 6 , wherein determining the threshold value comprises determining a rate of change of a human's centroidal angular momentum. 
     
     
         8 . The method of  claim 1 , wherein the robot comprises a plurality of segments, and wherein determining the rate of change of the robot's centroidal angular momentum ({dot over (H)} G ) comprises calculating the rate of change of the robot's centroidal angular momentum ({dot over (H)} G ) in accordance with the equation: 
       
         
           
             
               
                 
                   H 
                   . 
                 
                 G 
               
               = 
               
                 
                   ∑ 
                   1 
                   n 
                 
                  
                 
                   
                     H 
                     . 
                   
                   Gi 
                 
               
             
           
         
       
       wherein {dot over (H)} G , represents a rate of change of centroidal angular momentum of a segment i, and n represents a number of segments contained in the robot. 
     
     
         9 . The method of  claim 8 , wherein determining the rate of change of the robot's centroidal angular momentum ({dot over (H)} G ) further comprises determining the rate of change of centroidal angular momentum of the segment i ({dot over (H)} Gi ) prior to calculating the rate of change of the robot's centroidal angular momentum ({dot over (H)} G ). 
     
     
         10 . The method of  claim 9 , wherein determining the rate of change of centroidal angular momentum of the segment i ({dot over (H)} Gi ) comprises calculating the rate of change of centroidal angular momentum of the segment i ({dot over (H)} Gi ) in accordance with the equation:
     {dot over (H)}   Gi   =OG   i ×( m   i α i )+ I   i α i  
   
       wherein m i  represents a mass of the segment i, α i  represents a linear acceleration of the segment i, O represents a location of an origin of a coordinate system, G i  represents a location of a center of mass of the segment i, I i  represents a moment of inertia of the segment i, α i  represents an angular acceleration of the segment i, OG i  represents a vector from O to G i , and x represents a vector product operation. 
     
     
         11 . The method of  claim 9 , wherein determining the rate of change of the robot's centroidal angular momentum ({dot over (H)} G ) further comprises determining the angular acceleration of the segment i (α i ) prior to calculating the rate of change of centroidal angular momentum of the segment i ({dot over (H)} Gi ). 
     
     
         12 . The method of  claim 11 , wherein determining the angular acceleration of the segment i (α i ) comprises using an accelerometer. 
     
     
         13 . The method of  claim 11 , wherein determining the angular acceleration of the segment i (α i ) comprises using a position encoder. 
     
     
         14 . A non-transitory computer-readable storage medium storing executable computer program instructions for determining an instruction to send to a legged robot, the computer program instructions performing steps comprising:
 determining a rate of change of the robot's centroidal angular momentum ({dot over (H)} G );   determining whether the rate of change of the robot's centroidal angular momentum ({dot over (H)} G ) exceeds a threshold value, wherein the threshold value is based on one or more factors of a group containing a friction between the robot and a support surface, a torque limit of an actuator of the robot, a design parameter of the robot, and an inertial property of the robot; and   responsive to determining that the rate of change of the robot's centroidal angular momentum ({dot over (H)} G ) exceeds the threshold value, determining an instruction to send to the robot.   
     
     
         15 . A computer system for determining an instruction to send to a legged robot, comprising:
 at least one non-transitory computer-readable storage medium storing executable computer program instructions comprising instructions for:
 determining a rate of change of the robot's centroidal angular momentum ({dot over (H)} G ); 
 determining whether the rate of change of the robot's centroidal angular momentum ({dot over (H)} G ) exceeds a threshold value, wherein the threshold value is based on one or more factors of a group containing a friction between the robot and a support surface, a torque limit of an actuator of the robot, a design parameter of the robot, and an inertial property of the robot; and 
 responsive to determining that the rate of change of the robot's centroidal angular momentum ({dot over (H)} G ) exceeds the threshold value, determining an instruction to send to the robot; and 
   a processor for executing the computer program instructions.