Robust Motion Planning in the Presence of Estimation Uncertainty

Abstract

Motion planning is a fundamental problem and focuses on finding control inputs that enable a robot to reach a goal region while safely avoiding obstacles. However, in many situations, the state of the system may not be known but only estimated using, for instance, a Kalman filter. This results in a novel motion planning problem where safety must be ensured in the presence of state estimation uncertainty. Previous approaches to this problem are either conservative or integrate state estimates optimistically which leads to non-robust solutions. Optimistic solutions require frequent replanning to not endanger the safety of the system. We propose a new formulation to this problem with the aim to be robust to state estimation errors while not being overly conservative. In particular, we formulate a stochastic optimal control problem that contains robustified risk-aware safety constraints by incorporating robustness margins to account for state estimation errors. We propose a novel sampling-based approach that builds trees exploring the reachable space of Gaussian distributions that capture uncertainty both in state estimation and in future measurements. We provide robustness guarantees and show, both in theory and simulations, that the induced robustness margins constitute a trade-off between conservatism and robustness for planning under estimation uncertainty that allows to control the frequency of replanning.

Disturbance-Parametrized Robust Lattice-Based Motion Planning

“…The conditions in Assumption 3 imply that the closed-loop error dynamics (7) with respect to feedback controller ν(t, x) is uniformly ultimately bounded (UUB) [Chapter 4, [21]], [22]. Therefore, there exists a time instant T (x(0), ∆ p ) > 0 and a region W p such that…”

“…The strategies proposed in [6]- [11] deal with the motion-planning problems for linear systems affected by uncertainties. The results in [6], [7] propose robust RRT strategies, which extend the standard RRT algorithm to the cases of linear systems having additive noise and uncertainty in state estimation. The approaches in [8], [10] guarantee safe motion for systems with linear models, in uncertain cluttered environments.…”