Redundant Serial Manipulator Inverse Position Kinematics and Dynamics

Abstract A redundant serial manipulator inverse position kinematic mapping is employed to define a new manipulator operational space differentiable manifold and an associated system of well posed differential equations of manipulator dynamics. A review of deficiencies in the conventional generalized inverse velocity approach to manipulator redundancy resolution and a numerical example show that the generalized inverse velocity approach is incompatible with the kinematics of redundant serial manipulators. An inverse position kinematic mapping is presented with a differentiable manifold that is parameterized by either input or operational space coordinates. Differentiation of the inverse position mapping yields an inverse velocity mapping that is a total differential, in contrast with generalized inverse velocity mappings, hence avoiding the deficiencies identified. A sec-ond differentiation yields an inverse acceleration mapping that is used, without ad-hoc derivation, to obtain a system of well posed operational space ordinary differential equations of redundant manipulator dynamics that are equivalent to the equations of multibody dynamics.