Planning motion in point-represented contact spaces using approximate star-shaped decomposition

Star-shaped decomposition partitions a shape into a set of star-shaped components. A shape is star shaped if and only if there exists at least one point which can see all the points in the shape. Due to this interesting property, decomposing a configuration space into star-shaped components can be beneficial, e.g., for solving motion planning problem. In this paper, we propose a simple method to decompose the contact space, represented by point set data, into approximate star-shaped components. We propose two motion planning methods, one deterministic and one probabilistic, both based on this idea.