An optimal real-time motion planner for vehicles with a minimum turning radius

In this paper, an approach is proposed to determine a real-time collision-free path for an autonomous underwater vehicle (AUV) moving in an unknown underwater space. A class of trajectories is obtained by polynomial parameterization. The coefficients of the polynomial are determined at each sampling period, by satisfying boundary condition and collision avoidance criteria. Based on the class of trajectories, a performance index related to the length of the trajectories is established, and is used to find an optimal trajectory. The turning radius along the trajectories is calculated to check the feasibility of the obtained trajectory. The solution to the trajectory and its corresponding control are found in closed form, which make the algorithm computationally efficient and real-time implementable. The proposed approach is validated by computer simulations.