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 3D. Instead of exactly computing an explicit representation of the free space, we compute a roadmap that captures its connectivity. This representation encodes the complete connectivity of free space and allows us to perform exact path planning. We construct the roadmap by computing deterministic samples in free space that lie on an adaptive volumetric grid. Our algorithm is simple to implement and uses two tests: a complex cell test and a star-shaped test. These tests can be efficiently performed on polyhedral objects using max-norm distance computation and linear programming. The complexity of our algorithm varies as a function of the size of narrow passages in the configuration space. We demonstrate the performance of our algorithm on environments with very small narrow passages or no collision-free paths.