A New Simulation Metric to Determine Safe Environments and Controllers for Systems with Unknown Dynamics
This addresses safety verification for autonomous systems like drones and cars, but it is incremental as it builds on existing simulation metrics.
The paper tackles the problem of providing safety guarantees for systems with unknown dynamics by proposing SPEC, a specification-centric simulation metric that reduces conservatism compared to the Standard Simulation Metric, enabling safe controller synthesis for a larger set of environments in case studies with quadrotors and autonomous cars.
We consider the problem of extracting safe environments and controllers for reach-avoid objectives for systems with known state and control spaces, but unknown dynamics. In a given environment, a common approach is to synthesize a controller from an abstraction or a model of the system (potentially learned from data). However, in many situations, the relationship between the dynamics of the model and the \textit{actual system} is not known; and hence it is difficult to provide safety guarantees for the system. In such cases, the Standard Simulation Metric (SSM), defined as the worst-case norm distance between the model and the system output trajectories, can be used to modify a reach-avoid specification for the system into a more stringent specification for the abstraction. Nevertheless, the obtained distance, and hence the modified specification, can be quite conservative. This limits the set of environments for which a safe controller can be obtained. We propose SPEC, a specification-centric simulation metric, which overcomes these limitations by computing the distance using only the trajectories that violate the specification for the system. We show that modifying a reach-avoid specification with SPEC allows us to synthesize a safe controller for a larger set of environments compared to SSM. We also propose a probabilistic method to compute SPEC for a general class of systems. Case studies using simulators for quadrotors and autonomous cars illustrate the advantages of the proposed metric for determining safe environment sets and controllers.