Sampling-based Minimum Risk path planning in multiobjective configuration spaces

We propose a new sampling-based path planning algorithm, the Optimal Minimum Risk Rapidly Exploring Random Tree (MR-RRT*), that plans minimum risk paths in accordance with primary and secondary cost criteria. The primary cost criterion is a user-defined measure of accumulated risk, which may represent proximity to obstacles, exposure to threats, or similar. Risk is only penalized in areas of the configuration space where it exceeds a user-defined threshold, causing many graph nodes to achieve identical primary cost. The algorithm uses a secondary cost criterion to break ties in primary cost. The proposed method affords the user the flexibility to tune the relative importance of the alternate cost criteria, while adhering to the requirements for asymptotically optimal planning with respect to the primary cost. The algorithm's performance is compared with T-RRT*, another optimal tunable-risk planning algorithm, in a series of computational examples with different representations of risk.