Effective sampling and distance metrics for 3D rigid body path planning

Important implementation issues in rigid body path planning are often overlooked. In particulars sampling-based motion planning algorithms typically require a distance metric defined on the configuration space, a sampling function, and a method for interpolating sampled points. The configuration space or a 3D rigid body is identified with the Lie group SE(3). Defining proper metrics, sampling, and interpolation techniques for SE(3) is not obvious, and can become a hidden source of failure for many planning algorithm implementations. This paper examines some of these issues and presents techniques which have been found to be effective experimentally for Rigid Body path planning.