Optimal motion planning and control of a nonholonomic spherical robot using dynamic programming approach: simulation and experimental results

Optimal motion planning and control of a nonholonomic spherical mobile robot is studied. Dynamic Programming (DP) as a direct and online approach is used to navigate the robot in an environment with/without obstacles. The optimal trajectory, which corresponds to the minimum cost, is determined in the case of presence of obstacles in the environment, and the robot can move towards the target optimally, without colliding with obstacles. DP yields optimal control inputs in a closed-loop form. In fact, a traditional control system is no longer needed to track the obtained trajectory since the resulted DP table includes optimal control inputs for every state in the admissible region. The effect of different final states and alternative intervals of the allowable state and control values are also studied. Results from several simulations show that the proposed method enables the robot to find an optimal trajectory from any given state towards a predefined target. An experimental setup is designed wherein a real spherical robot is driven according to the developed algorithm. A vision system monitors the robot and outputs the location/orientation of the robot at each step via image processing. Experimental results are then compared with simulations to validate the model and evaluate the control strategy.