Optimal Trajectory Planning for Manipulators with Flexible Curved Links

Trajectory planning for manipulators with flexible links is a complicated task that plays an important role in design and application of manipulators. This paper is concerned with optimal trajectory planning for a two-link manipulator consisting of a macro flexible curved link and a micro rigid link for a point-to-point motion task. Absolute nodal coordinate formulation (ANCF) is used to derive the dynamic equations of the flexible curved link, an optimal trajectory method is adopted to generate the trajectory that minimizes the vibration of the flexible curved link. The Hamiltonian function is formed and the necessary conditions for optimality are derived from the Pontryagin's minimum principle (PMP). The obtained equations form a two-point boundary value problem (TPBVP) which can be solved by numerical techniques. Finally, simulations for the two-link manipulator are carried out to demonstrate the efficiency of the presented method. The results illustrate the validity of the method to overcome the high nonlinearity nature of the whole system.