Multi-level free-space dilation for sampling narrow passages in PRM planning

Free-space dilation is an effective approach for narrow passage sampling, a well-recognized difficulty in probabilistic roadmap (PRM) planning. Key to this approach are methods for dilating the free space and for determining the amount of dilation needed. This paper presents a new method of dilation by shrinking the geometric models of robots and obstacles. Compared with existing work, the new method is more efficient in both running time and memory usage. It is also integrated with collision checking, a key operation in PRM planning. The efficiency of the dilation method enables a new PRM planner which quickly constructs a series of dilated free spaces and automatically determine the amount of dilation needed. Experiments show that both the dilation method and the planner work well in complex geometric environments. In particular, the planner reliably solved the most difficult version of the alpha puzzle, a benchmark test for PRM planners

I. Introduction

Probabilistic roadmap (PRM) planning is a successful approach for motion planning of robots with many degrees of freedom (DOFs) in complex geometric environments (see, e.g., [1], [3], [8], [10], [13], [15], [17], [24], [25]). The main idea of PRM planning is to sample at random a robot's configuration space with a suitable probability distribution and capture the connectivity of in an extremely simplified representation, called a probabilistic roadmap. A roadmap is a graph whose nodes are the collision-free configurations sampled from and whose edges are simple collision-free paths between the nodes. This way, PRM planners avoid the prohibitive cost of constructing a complete representation of .