Risk-Aware Submodular Optimization for Multirobot Coordination

We study the problem of incorporating risk while making combinatorial decisions under uncertainty. formulate a discrete submodular maximization for selecting set using conditional value at (CVaR), metric commonly used in financial analysis. While CVaR has recently been optimization linear cost functions robotics, we take first step toward extending this to and provide several positive results. Specifically, propose sequential greedy algorithm that provides an approximation guarantee on finding maxima function matroid constraint. The shows solution produced by our is within constant factor optimal additive term depends optimal. Our analysis uses curvature proves runs polynomial time. This formulates number problems appear robotics. use two such problems, i.e., vehicle assignment uncertainty mobility demand sensor selection with failures environmental monitoring, as case studies demonstrate efficacy formulation. also adaptive risk-aware maximization. design heuristic triggers replanning only when certain conditions are satisfied, eliminate unnecessary planning. In particular, online mobility-on-demand study, triggering new it can potentially reduce waiting time locations. verify performance proposed algorithms through simulations.