Integrable solutions of kinematic redundancy via impedance control

Problems arising when kinematically redundant manipulators are controlled using the Jacobian pseudoinverse are related to the nonintegrability of the standard pseudoinverse. This article presents a class of generalized inverses that have the property of being integrable within any simply connected, nonsingular region of the work space. Integrability is obtained by deriving the equations that 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 that accounts for the nonlinear features of the forward kinematics. The relation of this integrable weighted pseudoinverse to the standard Moore-Penrose and other weighted pseudoinverses is discussed.