Robust belief space planning under intermittent sensing via a maximum eigenvalue-based bound

Abstract

We consider the problem of computing a minimum uncertainty path for an autonomous vehicle from a start to a destination location in the presence intermittent sensing, modeled as a stochastic process, in addition to process and measurement noise. We introduce the use of a novel bound on the maximum eigenvalue of the estimation error covariance matrix as the cost function for belief space planning. Our main contributions are three-fold. We first derive an analytic bound on the performance of a state estimator under sensor misdetection (intermittency) occurring stochastically over time. Second, we use this bound as a proxy for the expected maximum eigenvalue evolution in a sample-based path planning algorithm to produce a path that trades off accuracy and robustness. This extends the recent body of work on planning under uncertainty to include the fact that sensors may not provide any measurement owing to misdetection. Computational results demonstrate the benefit of the approach and comparisons are made with the state of the art in path planning in belief space. Third, and finally, we establish theoretically that the proposed algorithm possesses the optimal substructure property, i.e. the algorithm returns an optimal path relative to the bound treated as a proxy for the expected maximum eigenvalue evolution.