Motion equations in redundant coordinates with application to inverse dynamics of constrained mechanical systems

The basis for any model-based control of dynamical systems is a numerically efficient formulation of the motion equations, preferably expressed in terms of a minimal set of independent coordinates. To this end the coordinates of a constrained system are commonly split into a set of dependent and independent ones. The drawback of such coordinate partitioning is that the splitting is not globally valid since an atlas of local charts is required to globally parameterize the configuration space. Therefore different formulations in redundant coordinates have been proposed. They usually involve the inverse of the mass matrix and are computationally rather complex. In this paper an efficient formulation of the motion equations in redundant coordinates is presented for general non-holonomic systems that is valid in any regular configuration. This gives rise to a globally valid system of redundant differential equations. It is tailored for solving the inverse dynamics problem, and an explicit inverse dynamics solution is presented for general full-actuated systems. Moreover, the proposed formulation gives rise to a non-redundant system of motion equations for non-redundantly full-actuated systems that do not exhibit input singularities.