Path planning in the presence of dynamic obstacles is a challenging problem due to the added time dimension in search space. In approaches that ignore the time dimension and treat dynamic obstacles as static, frequent re-planning is unavoidable as the obstacles move, and their solutions are generally sub-optimal and can be incomplete. To achieve both optimality and completeness, it is necessary to consider the time dimension during planning. The notion of adaptive dimensionality has been successfully used in high-dimensional motion planning such as manipulation of robot arms, but has not been used in the context of path planning in dynamic environments. In this paper, we apply the idea of adaptive dimensionality to speed up path planning in dynamic environments for a robot with no assumptions on its dynamic model. Specifically, our approach considers the time dimension only in those regions of the environment where a potential collision may occur, and plans in a low-dimensional state-space elsewhere. We show that our approach is complete and is guaranteed to find a solution, if one exists, within a cost sub-optimality bound. We experimentally validate our method on the problem of 3D vehicle navigation (x, y, heading) in dynamic environments. Our results show that the presented approach achieves substantial speedups in planning time over 4D heuristic-based A*, especially when the resulting plan deviates significantly from the one suggested by the heuristic.
In this paper, we present an algorithm for generating complex dynamically feasible maneuvers for autonomous vehicles traveling at high speeds over large distances. Our approach is based on performing anytime incremental search on a multi-resolution, dynamically feasible lattice state space. The resulting planner provides real-time performance and guarantees on and control of the suboptimality of its solution. We provide theoretical properties and experimental results from an implementation on an autonomous passenger vehicle that competed in, and won, the Urban Challenge competition. In this paper we describe a novel path planning approach for mobile robots operating in indoor environments. In such scenarios, robots must be able to maneuver in crowded spaces, partially filled with static and dynamic obstacles (such as people). Our approach produces smooth, complex maneuvers over large distances through the use of an anytime graph search algorithm applied to a novel multi-resolution state lattice, where the resolution is adapted based on both environmental characteristics and task characteristics. In addition, we present a novel approach for generating fast globally optimal trajectories in constrained spaces (i.e. rooms connected via doors and hallways). This approach exploits offline precomputation to provide extremely efficient online performance and is applicable to a wide range of both indoor and outdoor navigation scenarios. By combining an anytime, multi-resolution lattice-based search algorithm with our precomputation technique, globally optimal trajectories in up to four dimensions (2D position, heading and velocity) are obtained in real-time.