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

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.