Integrable Solutions of Kinematic Redundancy via Impedance Control

Problems arising when kinematically redundant manipulators are controlled using the Jacobian pseudoinverse are related to the non-integrability of the standard pseudo-inverse. This paper presents a class of generalized inverses which have the property of being integrable within any simply connected, nonsingular region of the workspace. Integrability is obtained by deriving the equations which describe an externally-imposed motion with the hypothesis that a compliance function is associated with each degree of freedom of the manipulator. The result is a weighted pseudo-inverse containing a term which accounts for the non-linear features of the forward kinematics. The relation of this integrable weighted pseudoinverse to the standard Moore-Penrose and other weighted pseudo-inverses are discussed.