The critical radius in sampling-based motion planning

The Critical Radius in Sampling-Based Motion Planning

We develop a new analysis of sampling-based motion planning with uniform random sampling, which significantly improves upon the celebrated result of Karaman and Frazzoli (2011) and subsequent work. Particularly, we prove the existence of a critical connection radius proportional to Θ(n−1/d) for n samples and d dimensions: Below this value the planner is guaranteed to fail (similarly shown by th...

Sampling-Based Motion Planning

Asymptotic Optimality in Sampling-based Motion Planning

Although one of the fundamental problems in robotics, the motion planning problem is inherently hard from a computational point of view. In particular, the piano movers’ problem [1], [2] is known to be PSPACE-hard, which implies that any algorithm aimed to solve this problem (with completeness guarantees) is expected not to scale well with increasing number of dimensions of the configuration sp...

Current Issues in Sampling-Based Motion Planning

In this paper, we discuss the field of sampling-based motion planning. In contrast to methods that construct boundary representations of configuration space obstacles, sampling-based methods use only information from a collision detector as they search the configuration space. The simplicity of this approach, along with increases in computation power and the development of efficient collision d...

Sampling-based algorithms for optimal motion planning

During the last decade, sampling-based path planning algorithms, such as Probabilistic RoadMaps (PRM) and Rapidly-exploring Random Trees (RRT), have been shown to work well in practice and possess theoretical guarantees such as probabilistic completeness. However, little effort has been devoted to the formal analysis of the quality of the solution returned by such algorithms, e.g., as a functio...