BSSM: GPU-Accelerated Point-Cloud Distance Metric for Motion Planning

We propose the BSSM: Point-Cloud based (B)iased (S)igned (S)mooth (M)etric, which is used to compute a distance metric between a manipulator and its environment. Unlike many methods that requires that the environment is modeled using simple geometric primitives such as spheres, boxes, and cylinders, our proposed metric directly utilizes point clouds. The proposed metric has properties of being smooth (infinitely differentiable), signed (yielding non-zero values upon overlap), and biased. The latter is a novel feature that, as demonstrated by our simulation results, offers advantages for motion planning. This metric is suitable for GPU parallelization and simulation studies and a real experiment are offered to investigate its benefits.