Shortest trajectory planning of wheeled mobile robots with constraints

In this paper, we suggest a shortest trajectory planning algorithm for wheeled mobile robots with constraints; bounded curvature paths and moving forward only motion of robots; for example, aerial vehicles or moving forward car-like mobile robots. The main purpose of the paper is to find the optimal shortest path between a starting point and a goal point with constraints. Based on the Dubins´ car and the shortest path synthesis [L.E. Dubins, 1957], a geometrical approach is addressed to solve the problem. First we define patterns of existed shortest paths on the origin of the starting point and the goal point. Second, an arbitrary given configuration is compared with one of the patterns and the motion of the vehicle is determined left turn or right turn. The proposed method is suitable for rapid decisions. Simulation results are provided to demonstrate the efficacy of the approach.