Kinematic control of redundant serial manipulators has been carried out for the past half century based primarily on a generalized inverse velocity formulation that is known to have mathematical deficiencies. A recently developed inverse kinematic position mapping is extended to an operational configuration space differentiable manifold formulation for kinematic control with obstacle avoidance is employed to resolve deficiencies in the generalized inverse velocity formulation. Output trajectory tracking with obstacle avoidance for four and twenty degree of redundancy manipulators is carried out to demonstrate the effectiveness of the differentiable manifold approach and that it resolves deficiencies of the conventional generalized inverse velocity formulation.

A recently developed differential geometric representation of redundant serial robot kinematics is employed to create an 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 term of task and self-motion coordinates. This enables enforcement of desired output trajectories, in tandem with direct enforcement of self-motion dependent operational space trajectories that are subject to obstacle avoidance and performance constraints. Four examples are presented with a one degree of redundancy robot that demonstrate validity and superior performance of the new formulation, relative to traditional task space methods used for redundant serial robot control. Finally, an example with eight degrees of redundancy is presented that further illustrates superior performance of the new formulation.