A. M. Ladd and L. E. Kavraki, “Fast Tree-Based Exploration of State Space for Robots with Dynamics,” in Algorithmic Foundations of Robotics VI, Springer, STAR 17, 2005, pp. 297–312.
This paper presents a new motion planning algorithm which we call the Path-Directed Subdivision Tree exploration Planner PDST-EXPLORE. It is a sampling-based method which builds a tree and takes a substantially different approach from other exploration planners such as RRT  and EST . PDST-EXPLORE is a general purpose planner but is designed to overcome difficulties inherent in planning for robots with non-trivial dynamics. Specifically, our planner represents samples as path segments rather than individual states and uses non-uniform subdivisions of the state space to estimate coverage. This change avoids many of the problems that previous sampling-based planners have had with milestone placement, metrics and coverage estimation. We use a deterministic update schedule together with randomized path generation to adaptively strike a balance between greedy exploration and methodical search. We have obtained a proof of probabilistic completeness for the planner which assumes very little about the specific robot system that the planner operates on. Finally, we have implemented the planner for planar kinodynamic point robots, differential drive robots and blimp-like robots. The experimental results demonstrate the efficiency of the planner’s implementation as well as its robustness in covering the entire reachable free space.