C-Uniform Trajectory Sampling For Fast Motion Planning

We study the problem of sampling robot trajectories and introduce the notion of C-Uniformity. As opposed to the standard method of uniformly sampling control inputs (which lead to biased samples of the configuration space), C-Uniform trajectories are generated by control actions which lead to uniform sampling of the configuration space. After presenting an intuitive closed-form solution to generate C-Uniform trajectories for the 1D random-walker, we present a network-flow based optimization method to precompute action probabilities which lead to C-Uniform trajectories for general robot systems. We apply the notion of C-Uniformity to the design of Model Predictive Path Integral controllers. Through simulation experiments, we show that using C-Uniform trajectories significantly improvs the performance of MPPI-style controllers, achieving up to 40 % coverage performance gain compared to the best baseline. We demonstrate the practical applicability of our method with an implementation on a $1 / 10$th scale racer.