Inverse Kinematics for a Point-Foot Quadruped Robot with Dynamic Redundancy Resolution

In this work we examine the control of center of mass and swing leg trajectories in LittleDog, a point-foot quadruped robot. It is not clear how to formulate a function to compute forward kinematics of the center of mass of the robot as a function of actuated joint angles because point-foot walkers have no direct actuation between the feet and the ground. Nevertheless, we show that a whole-body Jacobian exists and is well defined when at least three of the feet are on the ground. Also, the typical approach of work-space centering for redundancy resolution causes destabilizing motions when executing fast motions. An alternative redundancy resolution optimization is proposed which projects single-leg inverse kinematic solutions into the nullspace. This hybrid approach seems to minimize 1) unnecessary rotation of the body, 2) twisting of the stance legs, and 3) whole-body involvement in achieving a step leg trajectory. In simulation, this control allows the robot to perform significantly more dynamic behaviors while maintaining stability.