Adaptive realization of desired constraint stabilization dynamics in the control of multibody systems

This paper presents a novel way of stabilizing the constraint drift dynamics in the numerical simulation of multibody systems. This formulation is applicable for a large class of uncertain mechanical systems described by nonlinear differential algebraic equations that are subject to holonomic constraints. In the absence of uncertainty in the system inertia parameters, it is possible to develop stabilization relationships that suppress the accumulation of error in the constraint equations during the time integration process. In order to account for ignorance in the parameters, we propose a model reference adaptive control scheme that ensures the asymptotic realization of the desired (reference) constraint violation dynamics. Special attention is given to the case of redundantly actuated systems, as is typical for robotics. For this class of problems, we direct special attention to optimization criteria that achieve any desired manoeuvre using minimum control effort and coordination between the redundant set of actuators. An example application demonstrates the effectiveness and practicality of the proposed adaptive control formulation.