An Improved Optimal Trajectory Planning Method of Six-axis Robotic Manipulators along Prescribed Path Constraints

Abstract

Optimal Control Problem (OCP) is a kind of classical problem with the state space equations, containing the optimal trajectory planning problem of robotic manipulators with complicated path constraints. The optimal control method (OCM) which contains direct and indirect methods is efficient to solve this kind of problems. The Pontryagin maximum principle is the core of the indirect method which includes tedious mathematical derivations, and is hard to work with the complex mechanical system. As the result, the direct methods represented by direct collocation method (DCM) are widely used in the engineering field. They transform the original optimal control problem to nonlinear programming problems (NLP), so that the general NLP solver can be used. There are mainly three different methods based on the above direct methods, including convex optimization (CO) methods, numerical integration (NI) methods and dynamic programming (DP) methods. This paper proposes a brand new idea which can streamline the problem description compared to the CO method, extend the general objective function compared to the NI method, and reduce the cost of storage compared to the DP method, and provides a feasible local optimal solution for the problem. In addition, the simulation experiment satisfies the kinodynamic constraints properly, and the validity of the proposed method is confirmed.