DP-based path planning of a spherical mobile robot in an environment with obstacles

A direct approach to path planning of a 2-DOFs (Degrees of Freedom) spherical robot based on Bellman׳s dynamic programming (DP) is introduced. The robot moves in an environment with obstacles and employs DP to find optimal trajectory by minimizing energy and preventing obstacle collision. While other path planning schemes rely on pre-planned optimal trajectories and/or feedback control techniques, in this approach there is no need to design a control system because DP yields the optimal control inputs in a closed loop (feedback) form. In other words, after completing the DP table, the optimal control inputs are known for every state in the admissible region and the robot can move toward the final position without colliding with obstacles. This enables the robot to function well in semi- or even non-observable environments. Results from several simulated experiments show that the proposed approach is capable of finding an optimal path from any given position/orientation towards a predefined target in an environment with obstacles within the admissible region. The method is very promising compared to other path planning schemes.