A General Purpose Algorithm for Optimal Trajectory Planning of Closed Loop Multibody Systems

This paper discusses the optimal trajectory planning problem of multibody systems. The aim of this study is to develop a general purpose optimal trajectory planning algorithm to be applied to arbitrary multibody systems. Multibody systems may be divided into two groups, i.e. open loop systems and closed loop systems [8]. In [11] an optimal trajectory planning algorithm for open loop systems was presented. In this paper, optimal trajectory planning algorithms for closed loop systems are proposed by extending the algorithm for open loop systems. Two types of methods are presented based on the dynamic analysis by computational algorithms for closed loop systems. The first method uses generalized coordinate partitioning and embedding techniques. The second method is based on an augmented formulation with Lagrange multipliers. The first method is easily applicable to non-redundant actuation systems, while the second method considers redundant actuation. The validity of these methods for optimal trajectory planning is confirmed by computational results and their features are compared.