An Alternative Formulation of Motion Equations in Redundant Coordinates for the Inverse Dynamics of Constrained Mechanical Systems Available to Purchase

The basis for any model-based control of dynamical systems is an efficient formulation of the motion equations. These are preferably expressed in terms of independent coordinates. In other words the coordinates of a constrained system are split into a set of dependent and independent ones. It is well-known that such coordinate partitioning is not globally valid. A remedy is to switch between different possible sets of minimal coordinates. This drastically increases the numerical complexity and implementation effort, however. In this paper a formulation of the motion equations in redundant coordinates is presented for general non-holonomic systems. This gives rise to a redundant system of differential equations. The formulation is valid in any regular configuration. Because of the singular mass matrix it is not directly applicable for solving the forward dynamics but is tailored for solving the inverse dynamics. An inverse dynamics solution is presented for general full-actuated systems.