Extended Operational Space Kinematics, Dynamics, and Control of Redundant Serial Robots

Abstract

A recently developed differential geometric representation of redundant serial robot kinematics is employed to create a new extended operational space dynamics and control formulation that explicitly accounts for redundant robot degrees of freedom. This formulation corrects deficiencies in kinematics and dynamics of redundant serial robots that have relied for over half a century on error-prone generalized inverse velocity-based kinematics for redundancy resolution. New ordinary differential equations of robot operational space dynamics are obtained, without the need for ad hoc derivation, in terms of task coordinates and self-motion coordinates that represent robot redundancy. A new extended operational space control approach is presented that exploits ordinary differential equations of motion in terms of task and self-motion coordinates, enabling enforcement of desired output trajectories, obstacle avoidance, and performance constraints. Four examples are presented with a one-degree-of-redundancy robot that demonstrate the validity and superior performance of the new formulation, relative to the traditional task space method used for redundant serial robot control. Finally, an example with eight degrees of redundancy is presented that further illustrates superior performance of the new operational space formulation.