In this paper, we present a method to initialize at a feasible point and unfailingly solve a non-convex optimization problem in which a set-point motion is planned for a multi-link manipulator under state and control constraints. We construct an initial feasible solution by analyzing the final time effect for feasibility problems of flatness based motion planning problems. More specifically, we first find a feasible time-optimal trajectory under state constraints without a control constraint by solving a linear programming problem. Then, we find a feasible trajectory under control constraints by scaling the trajectory. To evaluate the practical applicability of the proposed method, we did numerical experiments to solve a multi-link manipulator motion planning problem by combining the method with recursive inverse dynamics algorithms.
A method that deals with a state equation constraint by locating sample times in the control horizon and calculating the states by numerical integration is called a shooting method'' @cite_16 . There are many types of research that extend this family of methods and reduce their computational cost. We focus on a method that does not use numerical integration of a state equation because a state equation of a Multi-Link robot manipulator is difficult to numerically integrate both very accurately and quickly.
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Preface 1. Introduction to nonlinear programming 2. Large, sparse nonlinear programming 3. Optimal control preliminaries 4. The optimal control problem 5. Optimal control examples Appendix A. Software Bibliography, Index.