Optimal motion planning of non-linear dynamic systems in the presence of obstacles and moving boundaries using SDRE: application on cable-suspended robot

In this paper a closed-loop non-linear optimal controller is designed via State Dependent Riccati Equation (SDRE) and employed for a spatial six-cable robot. SDRE provides a systematic and effective design of controller for non-linear systems. The power series approximation method is extended and used to solve SDRE. Trajectory tracking along with point to point movement is carried out. Moreover, two common constraints of optimal path planning, i.e., obstacles and moving boundaries are studied, and proper strategies are proposed to deal with these constraints. Obstacle avoidance technique used in this paper is based on the concept of Artificial Potential Field, while calculus of variations is applied to choose the optimal initial or end points from the moving boundaries. Capabilities of SDRE method provides an outstanding opportunity to be combined with the considered strategies. Simulations for the spatial six-cable robot are done, and Dynamic Load Carrying Capacity is computed to illustrate the efficiency of the employed procedure. Finally the results are validated by experimental tests conducted on ICaSbot which is a spatial six-cable robot manufactured in robotics research laboratory of Iran University of Science and Technology.