A symplectic direct method for motion-driven optimal control of mechanical systems

摘要

For many practical actuators, laws of motion quantities are directly imposed to control the motion of mechanical systems. Motivated by this point, considering motion quantities as control inputs is more practical and applicable. Therefore, in this paper, a novel and valuable idea is to design control laws of motion quantities to drive mechanical systems which can be optimal and meet specified requirements. To find the control laws of motion quantities, we establish motion-driven optimal control problems of mechanical systems in this paper. For solving this kind of problems, nonlinear dynamical equations need to be discretized. If dynamical equations cannot be approximated well, results will be inaccurate, unreliable, and even distorted. To overcome this difficulty, in this paper, we further proposed a symplectic-preserving method to solve the motion-driven optimal control problems. In the proposed method, a symplectic-preserving discrete formula for dynamical equations with motion-driven constraints is proposed. It can provide excellent approximation quality. Three numerical examples of typical nonlinear crane systems are tested to show the performance of the proposed method. The energy deviation of the proposed method is sufficiently small even if sparse time intervals are set. Thus the energy behavior of the original mechanical systems is preserved well. If the obtained control inputs are imposed to systems, the systems can reach the given terminal state more accurately. Thus the obtained control inputs are more accurate and reliable. Besides, the proposed method can directly consider inequality constraints of velocity level and the inequality constraints can be strictly satisfied. (C) 2022 Elsevier B.V. All rights reserved.