This work addresses the problem of resolving kinematic redundancy in legged robots, with the dual goals of maintaining a large reachable workspace and of achieving fast end effector motions in task space. In particular, for robots with four or more legs, gait planning allows for considerable flexibility in the orientation of a stance limb with respect to both body orientation and the ground. By appropriately commanding pitch, roll and yaw of the end effector as it moves relative to the body coordinate frame, one can increase the volume of space the feet can reach and thus allow the robot to negotiate larger terrain obstacles. At the same time, motions of the foot in task space should be done rapidly, given the joint velocities of the limbs. In this paper, we focus on RoboSimian, a robot with four identical limbs designed for dual use in manipulation and locomotion tasks, which was designed at Jet Propulsion Labs (JPL) for the DARPA Robotics Challenge (DRC). We present both heuristic guidelines and a novel, gradient-based algorithm for developing rules to set the inverse kinematics (IK) solution for the seven joint angles of a limb, allowing us to prescribe joint solutions rapidly through the use of an IK look-up table.

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