Planar Uncertainty Propagation and a Probabilistic Algorithm for Interception

Many robotics applications involve motion planning with uncertainty. In this paper, we focus on path planning for planar systems by optimizing the probability of successfully arriving at a goal. We approach this problem with a modified version of the Path-of-Probability (POP) algorithm. We extend the POP algorithm to allow for a moving target and to optimize the number of steps to reach the goal. One tool that we develop in this paper to increase efficiency of the POP algorithm is a second order closed-form uncertainty propagation formula. This formula is utilized to quickly propagate the mean and covariance of nonparametrized distributions for planar systems. The modified POP algorithm is demonstrated on a simple rolling disc example with a moving goal.