THE RELATIONSHIP BETWEEN RECURSIVE MULTIBODY DYNAMICS AND DISCRETE-TIME OPTIMAL-CONTROL

A recursive algorithm, based on a Newton-Euler formulation, is developed for the solution of the simulation dynamics problem for a chain of rigid bodies. Arbitrary joint constraints are permitted, that is, joints may allow translational and/or rotational degrees of freedom. The recursive procedure is also shown to be identical to that encountered in a discrete-time optimal control problem. For each relevant quantity in the multibody dynamics problem, there exists an analog in the context of optimal control. The performance index that is minimized in the control problem is identified as Gibbs' function for the chain of bodies.