A Simple Algorithm for Complete Motion Planning of Translating Polyhedral Robots

Abstract

We present an algorithm for complete path planning for translating polyhedral robots in three dimensions. We compute a roadmap of the free space that captures its connectivity. The roadmap is constructed without computing an explicit representation of the free space. It encodes the complete connectivity of free space and allows us to perform exact path planning. We construct a roadmap by performing a sampling of the free space in a deterministic fashion. We obtain a set of deterministic samples by generating an adaptive volumetric grid. Our algorithm is simple to implement and uses two tests: a complex cell test and a star-shaped test during sample generation. These tests can be efficiently performed on polyhedral objects using max-norm distance computation and linear programming. We demonstrate the performance of our algorithm on environments with very small narrow passages or no collision-free paths.