Dubins-RRT* motion planning algorithm considering curvature-constrained path optimization

The motion planning problem of Dubins vehicles has long been a significant challenge in the field of mobile robots. However, the randomness in the sampling of angles at waypoints often leads to unnecessary curvature in the paths. This paper improves the sampling and collision detection algorithms of the existing Dubins-RRT* by incorporating the characteristics of Dubins paths. To avoid collision during path optimization, the concept of safety radius enlargement is introduced. Subsequently, the basic solution of the 3-point Dubins problem is extended to the curvature-constrained shortest-path problem, and the necessary conditions for achieving an optimal solution are provided. Given the complexity of solving the existing 3-point Dubins problem, three fundamental forms are presented, along with a direct root-finding approach for solving the problem. Following this, a curvature-constrained path optimization algorithm (CCPOA) is designed, and the modified Dubins-RRT* (MDR) algorithm is integrated into a motion planning algorithm for Dubins vehicles. Finally, simulation results demonstrate the effectiveness of the proposed algorithm.