Robust Motion Planning in the Presence of Estimation Uncertainty

TL;DR

This paper introduces a robust motion planning method that accounts for state estimation uncertainty using a stochastic optimal control framework, balancing safety and conservatism to reduce replanning frequency.

Contribution

It proposes a novel sampling-based approach exploring Gaussian distribution reachability, providing robustness guarantees and a trade-off between safety and efficiency.

Findings

The method ensures safety despite estimation errors.

It reduces the need for frequent replanning.

The approach is validated through theoretical analysis and simulations.

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.