Solving nonlinear optimal path tracking problem using a new closed loop direct–indirect optimization method: application on mechanical manipulators

摘要

The purpose of this study is to determine the dynamic load carrying capacity (DLCC) of a manipulator that moves on the specified path using a new closed loop optimal control method. Solution methods for designing nonlinear optimal controllers in a closed-loop form are usually based on indirect methods, but the proposed method is a combination of direct and indirect methods. Optimal control law is given by solving the nonlinear Hamilton-Jacobi-Bellman (HJB) partial differential equation. This equation is complex to solve exactly for complex dynamics, so it is solved numerically using the Galerkin procedure combined with a nonlinear optimization algorithm. To check the performance of the proposed algorithm, the simulation is performed for a fixed manipulator. The results represent the efficiency of the method for tracking the pre-determined path and determining the DLCC. Finally, an experimental test has been done for a two-link manipulator and compare with simulation results.