Multitask Constrained Motion Control Using a Mass-Weighted Orthogonal Decomposition

This paper presents an approach to formulating task-level motion-control for holonomically constrained multibody systems based on a mass-weighted orthogonal decomposition. The basis for this approach involves the formation of a recursive null space for constraints and motion-control tasks onto which subsequent motion-control tasks are projected. The recursive null space arises out of the process of orthogonalizing individual task Jacobian matrices. This orthogonalization process is analogous to the Gram–Schmidt process used for orthogonalizing a vector basis. Based on this mass-weighted orthogonal decomposition, recursive algorithms are developed for formulating the overall motion-control equations. The natural symmetry between task-level dynamics and the dynamics of constrained systems is exploited in this approach. An example is presented to illustrate the practical application of this methodology.