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Many computations in robotics can be dramatically accelerated if the robotconfiguration space is described as a collection of simple sets. For example,recently developed motion planners rely on a convex decomposition of the freespace to design collision-free trajectories using fast convex optimization. Inthis work, we present an efficient method for approximately covering complexconfiguration spaces with a small number of polytopes. The approach constructsa visibility graph using sampling and generates a clique cover of this graph tofind clusters of samples that have mutual line of sight. These clusters arethen inflated into large, full-dimensional, polytopes. We evaluate our methodon a variety of robotic systems and show that it consistently covers largerportions of free configuration space, with fewer polytopes, and in a fractionof the time compared to previous methods.

Approximating Robot Configuration Spaces with few Convex Sets using Clique Covers of Visibility Graphs