Barrier-Based Test Synthesis for Safety-Critical Systems Subject to Timed Reach-Avoid Specifications
Prithvi Akella, Mohamadreza Ahmadi, Richard M. Murray, Aaron D. Ames
TL;DR
The paper addresses how to generate controller-agnostic, adversarial tests for safety-critical systems operating under timed reach-avoid specifications. It introduces a minimax test-synthesis framework built on control barrier functions to produce realizable and maximally difficult tests in both continuous- and discrete-time settings, with extensions to perturbed dynamics and time-varying constraints. The authors provide theoretical guarantees of existence and optimality for the generated tests, along with illustrative unicycle and grid-world examples and hardware experiments with a quadruped. This approach enables rigorous testing and evaluation of safety-critical controllers by exposing worst-case and time-varying failure modes without requiring knowledge of the actual controller. The work has practical impact for robust test and evaluation pipelines in autonomous systems, offering a formal method to stress-test controllers and inform design improvements.
Abstract
We propose an adversarial, time-varying test-synthesis procedure for safety-critical systems without requiring specific knowledge of the underlying controller steering the system. From a broader test and evaluation context, determination of difficult tests of system behavior is important as these tests would elucidate problematic system phenomena before these mistakes can engender problematic outcomes, e.g. loss of human life in autonomous cars, costly failures for airplane systems, etc. Our approach builds on existing, simulation-based work in the test and evaluation literature by offering a controller-agnostic test-synthesis procedure that provides a series of benchmark tests with which to determine controller reliability. To achieve this, our approach codifies the system objective as a timed reach-avoid specification. Then, by coupling control barrier functions with this class of specifications, we construct an instantaneous difficulty metric whose minimizer corresponds to the most difficult test at that system state. We use this instantaneous difficulty metric in a game-theoretic fashion, to produce an adversarial, time-varying test-synthesis procedure that does not require specific knowledge of the system's controller, but can still provably identify realizable and maximally difficult tests of system behavior. Finally, we develop this test-synthesis procedure for both continuous and discrete-time systems and showcase our test-synthesis procedure on simulated and hardware examples.