Sampling-based min-max uncertainty path planning

We propose a new sampling-based path planning algorithm, the Min-Max Rapidly Exploring Random Tree (MM-RRT*), for robot path planning under localization uncertainty. The projected growth of error in a robot's state estimate is curbed by minimizing the maximum state estimate uncertainty encountered on a path. The algorithm builds and maintains a tree that is shared in state space and belief space, with a single belief per robot state. Due to the fact that many states will share the same maximum uncertainty, resulting from a shared parent node, the algorithm uses secondary objective functions to break ties among neighboring nodes with identical maximum uncertainty. The algorithm offers a compelling alternative to sampling-based algorithms with additive cost representations of uncertainty, which will penalize high-precision navigation routes that are longer in duration.