A General Purpose Optimal Trajectory Planning Algorithm for Multibody Systems (1st Report, Open Loop Systems)

Abstract

The aim of this study is to develop a general purpose optimal trajectory planning algorithm for multibody systems. Multibody systems may be divided into two groups, i.e., open loop systems and closed loop systems. In this paper, a general purpose optimal trajectory planning algorithm for open loop multibody systems is proposed. Firstly, the optimal trajectory planning problem is formulated as an optimal control problem. Then, a method to compute the partial derivatives of the state equation with respect to the state or the control variables that are necessary for optimal control calculation is developed based on a recursive dynamics computational algorithm for multibody systems. After that, a general purpose optimal trajectory planning algorithm is formulated by connecting the method for computing the partial derivatives and the robust optimal control algorithm called hierarchical gradient method. An optimal trajectory planning problem of a planar space robot with two arms is shown to demonstrate the effectiveness of the proposed algorithm.