Optimal Trajectories of Open-Chain Mechanical Systems: An Explicit Optimality Equation with a Multiple Shooting Solution*

摘要

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