Optimal trajectories of open-chain mechanical systems: Explicit optimality equation with multiple shooting solution

This paper addresses the problem of finding globally optimal trajectories of multi-degree-of-freedom open-chain systems while minimizing integral cost functionals. The contributions of this paper are: (i) explicit optimality equations in terms of inertia matrix and potential energy of the system, (ii) compatability conditions on the terminal conditions of the system consistent with the cost functional, (iii) robust computational procedure for solving the two-point boundary value problem in differential-algebraic equations using multiple shooting method, and (iv) an integrated software for dynamic optimization and simulation of open-chain systems