Sampling SE(3) with a Deterministic Sequence for 3D Rigid-Body Path Planning

Sampling-based path planners are giving very good results for problems with high degrees of freedom, being the obtention of samples a crucial factor in their performance. Sampling generation is a difficult issue that entails the challenge of obtaining an incremental and uniform coverage of the configuration space. This objective is even harder when the planning of motions of 3D rigid bodies is tackled, since the corresponding configuration space is SE(3), which requires the careful handling of rotations. This paper proposes a deterministic sampling sequence that generates configurations of SE(3) for the planning of 3D rigid-body motions using sampling-based methods. The proposed sequence is able to generate samples in an incremental low-dispersion manner, giving a good uniform coverage and a lattice structure.