A Simple Algorithm for Complete Motion Planning of Translating Polyhedral Robots

We present a new sampling-based algorithm for complete motion planning. Our algorithm relies on computing a star-shaped roadmap of the free space. We partition the free space into star-shaped regions such that a single point, called the guard, can see every point in the star-shaped region. The resulting set of guards capture the intra-region connectivity—the connectivity between points belonging to the same star-shaped region. We capture the inter-region connectivity by computing connectors that link guards of adjacent regions. The guards and connectors are combined to obtain the star-shaped roadmap. We present an efficient algorithm to compute the roadmap in a deterministic manner without explicit computation of the free space. We show that the star-shaped roadmap captures the connectivity of the free space, thereby enabling us to perform complete motion planning. Our approach is relatively simple to implement. We apply our approach to perform motion planning of robots with translational and rotational degrees of freedom (dof). We highlight its performance in challenging scenarios with narrow passages or when there is no collision-free path for robots with low degrees of freedom.

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