Distributionally Robust Risk-Bounded Path Planning Through Exact Spatio-temporal Risk Allocation

Planning safe paths in the presence of uncertainty is considered a central challenge in enabling robots to successfully navigate in real-world environments. Assumptions about Gaussian uncertainty are rarely justifiable based on real data and can lead to serious miscalculations of risk. Lately, it has become increasingly common to consider distributionally robust uncertainty, where the exact distribution of the uncertainty is unknown. Existing motion planning algorithms that consider distributionally robust uncertainty generates more conservative paths then their Gaussian counterparts. The aim of this thesis is to mitigate this conservatism by incorporating non-uniform spatio-temporal risk allocation into existing frameworks for distributionally robust motion planning, specifically the DR-RRT algorithm. To this end, a novel motion planning algorithm called DR-RRT-ERA (DR-RRT with Exact Risk Allocation) is proposed. This is a sampling based motion planning algorithm that builds trees of state distributions while enforcing distributionally robust chance constraints. Instead of allocating the risk uniformly over time and space, the DR-RRT-ERA uses a novel concept called exact risk allocation (ERA). The principle of ERA is to allocate exactly as much risk needed to enforce the distributionally robust risk constraints. Numerical simulations illustrate that this approach leads to less conservative paths compared to when uniform risk allocation is used.