Inverse and direct dynamics of constrained multibody systems based on orthogonal decomposition of generalized force

This paper presents a unified approach for inverse and direct dynamics of constrained multibody systems that can be served as a basis for analysis, simulation, and control. The compactness of the dynamics formulation can result in computational efficiency. Furthermore, the acceleration is explicitly related to the generalized force by an introduced "constraint inertia matrix" which is proved to be always invertible. Thus a simulation may proceed even with the presence of redundant constraints or singular configurations. The generalized forces are decomposed onto two orthogonal subspaces which are considered as control inputs for controlling position and constraint force. The motion controller scheme, remarkably, requires no force feedback, proves to be stable, and minimizes actuation force. Finally, numerical and experimental results obtained from dynamic simulation and control of constrained mechanical systems, based on the proposed inverse and direct dynamics formulations, are documented.