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 operational space 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 conventional approach is incompatible with kinematics of redundant serial manipulators. The inverse position kinematic mapping presented is shown to define 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 second differentiation yields an inverse acceleration mapping that is used, without ad-hoc derivation, to obtain well posed operational space ordinary differential equations of redundant manipulator dynamics that are equivalent to the equations of multibody dynamics.
Journal of Mechanisms and Robotics Open Issues