Gauss' principle and the dynamics of redundant and constrained manipulators

Abstract

This paper uses Gauss' principle of least constraint to derive the "natural" dynamic equations for redundant manipulators. This approach is the fastest way to the result that the operational space inertia matrix of the manipulator is the natural weighting matrix for the projection used in solving the redundancy problem. Force-controlled robots form a special case of redundant robots, such that the results can be applied straightforwardly to solve the long-standing problem of the "non-invariance" of the selection matrices in the hybrid force/position control paradigm.