OPTIMAL TRAJECTORIES OF OPEN-CHAIN MECHANICAL SYSTEMS - AN EXPLICIT OPTIMALITY EQUATION WITH A MULTIPLE SHOOTING SOLUTION

This paper addresses the problem of finding optimal trajectories of mu ltidegree-of-freedom open-chain systems, while minimizing integral cos t functionals. The contributions of this paper are (i) explicit optima lity equations in terms of inertia matrix and potential energy of the system, (ii) compatibility conditions on the terminal conditions of th e system that are consistent with the cost functional, (iii) a robust computational procedure for solving the two-point boundary value probl em using the multiple shooting method, and (iv) integrated software fo r dynamic optimization and simulation of open-chain systems.