Closed-loop safety assessment of uncertain roadmaps

The main contribution of this paper is a novel method for assessing the safety of trajectories by means of their collision probability in dynamic and uncertain environments. The future trajectories of the robot are represented as directed graphs and the uncertain states of the obstacles are represented by probability distributions. Instead of evaluating the safety of the graph by determining the route with the smallest collision probability, the optimal policy minimizing the collision probability is used. The policy allows one to replan the route depending on the future probability distributions of the obstacles. Since these distributions are unknown at the time point of the assessment, they are simulated and represented by compound probability distributions. These compound distributions represent all possible future distributions of the obstacles. It is shown that this novel method is always less conservative than previous approaches. Two example implementations are presented, one using Gaussian distributions and one using motion patterns for representing the uncertain states of the obstacles. Simulation scenarios are used for validating the proposed concept.