Enhancing Data-Driven Reachability Analysis using Temporal Logic Side Information

TL;DR

This paper introduces algorithms that incorporate temporal logic side information into data-driven reachability analysis, reducing conservatism while maintaining safety guarantees, validated on autonomous vehicle hardware.

Contribution

It models side information using STL fragments to constrain reachability analysis, providing formal guarantees and practical validation on autonomous vehicles.

Findings

Reduced conservatism in reachable sets

Formal safety guarantees maintained

Validated on autonomous vehicle hardware

Abstract

This paper presents algorithms for performing data-driven reachability analysis under temporal logic side information. In certain scenarios, the data-driven reachable sets of a robot can be prohibitively conservative due to the inherent noise in the robot's historical measurement data. In the same scenarios, we often have side information about the robot's expected motion (e.g., limits on how much a robot can move in a one-time step) that could be useful for further specifying the reachability analysis. In this work, we show that if we can model this side information using a signal temporal logic (STL) fragment, we can constrain the data-driven reachability analysis and safely limit the conservatism of the computed reachable sets. Moreover, we provide formal guarantees that, even after incorporating side information, the computed reachable sets still properly over-approximate the robot's future states. Lastly, we empirically validate the practicality of the over-approximation by computing constrained, data-driven reachable sets for the Small-Vehicles-for-Autonomy (SVEA) hardware platform in two driving scenarios.