Solving kinematic redundancy with impedance control: a class of integrable pseudoinverses

Problems arising when kinematically redundant manipulators are controlled using the Jacobian pseudoinverse are related to the nonintegrability of the standard pseudoinverse. The authors present a class of pseudoinverse 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 pseudoinverse containing a term which accounts for the nonlinear features of the forward kinematics. The relation of this integrable pseudoinverse to the standard Moore-Penrose and weighted pseudoinverses are discussed