Hamiltonian Monte Carlo-Based Risk-Aware Motion Planning of Autonomous Robots Subject to Uncertainty

Decision making under uncertainty is a central problem for modern robot autonomy. As robots are deployed into the chaos of the wider world, they are required to make more complex decisions with imperfect knowledge. In order to cope with this disorder, and the resulting uncertainty, a panoply of techniques have been developed which minimize or otherwise regulate uncertainty. However, such techniques lack a consideration of consequences. It is this notion of consequences and uncertainty blended together that forms the conceptual backbone of risk analysis, and it is only recently that robotics has begun to embrace these techniques.

Drawing on a rich theory of coherent risk measures, originally developed in the financial sector to aid in selecting safe investments, novel approaches to autonomous decision making have been developed that allow robots to properly evaluate risk in their decision making. In order to compute their risk measures, these approaches have generally required either highly problem specific formulations for their optimization, or that the risks be describable using well behaved functions like Gaussians.

In our approach, we devise a sampling-based means of computing risk measures that admits a wide range of possible risk metrics. We develop a technique using Hamiltonian Monte Carlo to sample the stochastic reachable set of a robot, which we convert to a distribution of consequences for estimating the Conditional Value-at-Risk for a proposed action by the robot. We also develop a scheme to overcome Hamiltonian Monte Carlo's inability to sample across abrupt changes in dynamics by partitioning the problem into single-dynamic segments, and propagating uncertainty forward across the segments.

Having developed a technique to estimate risk, we also propose a scheme using estimates of the risk of collision to enable safe navigation. Using a Probabilistic Roadmap and the A* algorithm, we generate a series of waypoints directing our robot to its goal. These waypoints are fed to a pure-pursuit controller, which we use to generate controls to compute the risk of collision. Based on this risk, we can accept the path, or reject it, and use a heuristic update to find a new path. We show simulations as proof of concept for this approach.