Motion Control and Dynamic Load Carrying Capacity of Mobile Robot via Nonlinear Optimal Feedback

In this paper, two methods are presented for solving closed loop optimal control problem and finding dynamic load carrying capacity (DLCC) for fixed and mobile manipulators. These control laws are based on the numerical solution to nonlinear Hamilton-Jacobi-Bellman (HJB) equation. First approach is the Successive Approximation (SA) for finding solution of HJB equation in the closed loop form and second approach is based on solving state-dependent Riccati equation (SDRE) that is an extension of algebraic Riccati equation for nonlinear systems. Afterward dynamic load carrying capacity of manipulators is computed using these controllers. The DLCC is calculated by considering tracking error and limits of torque’s joints. Finally, results are presented for two cases, a two-link planar manipulator mounted on a differentially driven mobile base and a 6DOF articulated manipulator (6R). The simulation results are verified with the experimental test for the 6R manipulator. The simulation and experimental results demonstrate that these methods are convenient for finding nonlinear optimal control laws in state feedback form and finding the maximum allowable load on a given trajectory.