Towards Mitigating Sim2Real Gaps: A Formal Quantitative Approach

In this paper, we introduce the notion of simulation-gap functions to formally quantify the potential gap between an approximate nominal mathematical model and the high-fidelity simulator representation of a real system. Given a nominal mathematical model alongside a quantified simulation gap, the system in the simulator can be conceptualized as one characterized by bounded state and input-dependent disturbances. This allows us to effectively leverage existing powerful model-based control algorithms, ensuring the enforcement of desired specifications while guaranteeing a seamless transition from simulation to real-world application. We develop a data-driven approach to provide a formal guarantee for quantifying the simulation gap. In particular, we collect data using high-fidelity simulators, leveraging recent advancements in Real-to-Sim transfer to ensure close alignment with reality. We demonstrate the effectiveness of the proposed method through experiments conducted on a nonlinear pendulum system and a nonlinear Turtlebot model in simulators.