From Uncertainty Data to Robust Policies for Temporal Logic Planning

TL;DR

This paper develops a data-driven method to synthesize robust disturbance feedback policies for systems with complex temporal logic tasks, ensuring probabilistic guarantees despite unknown uncertainty distributions.

Contribution

It introduces a novel approach combining mixed-integer optimization with probabilistic guarantees for temporal logic planning under uncertainty, using separate chance constraints.

Findings

Effective in autonomous driving motion planning scenarios.

Provides probabilistic guarantees for constraint satisfaction.

Utilizes feedback to handle uncertainty more robustly.

Abstract

We consider the problem of synthesizing robust disturbance feedback policies for systems performing complex tasks. We formulate the tasks as linear temporal logic specifications and encode them into an optimization framework via mixed-integer constraints. Both the system dynamics and the specifications are known but affected by uncertainty. The distribution of the uncertainty is unknown, however realizations can be obtained. We introduce a data-driven approach where the constraints are fulfilled for a set of realizations and provide probabilistic generalization guarantees as a function of the number of considered realizations. We use separate chance constraints for the satisfaction of the specification and operational constraints. This allows us to quantify their violation probabilities independently. We compute disturbance feedback policies as solutions of mixed-integer linear or quadratic optimization problems. By using feedback we can exploit information of past realizations and provide feasibility for a wider range of situations compared to static input sequences. We demonstrate the proposed method on two robust motion-planning case studies for autonomous driving.