  We present new algorithms to perform fast probabilistic collision queries
between convex as well as non-convex objects. Our approach is applicable to
general shapes, where one or more objects are represented using Gaussian
probability distributions. We present a fast new algorithm for a pair of convex
objects, and extend the approach to non-convex models using hierarchical
representations. We highlight the performance of our algorithms with various
convex and non-convex shapes on complex synthetic benchmarks and trajectory
planning benchmarks for a 7-DOF Fetch robot arm.
