Towards Certified Sim-to-Real Transfer via Stochastic Simulation-Gap Functions

TL;DR

This paper introduces a stochastic simulation-gap function to quantify the difference between mathematical models and high-fidelity simulators, enabling more reliable transfer of controllers from simulation to real-world systems.

Contribution

It proposes a data-driven method to estimate the stochastic simulation-gap function with formal guarantees, improving sim-to-real transfer reliability.

Findings

Effective gap quantification for stochastic simulators

Controller designed for the mathematical model satisfies specifications in high-fidelity simulator

Validated on TurtleBot and pendulum systems

Abstract

This paper introduces the notion of stochastic simulation-gap function, which formally quantifies the gap between an approximate mathematical model and a high-fidelity stochastic simulator. Since controllers designed for the mathematical model may fail in practice due to unmodeled gaps, the stochastic simulation-gap function enables the simulator to be interpreted as the nominal model with bounded state- and input-dependent disturbances. We propose a data-driven approach and establish a formal guarantee on the quantification of this gap. Leveraging the stochastic simulation-gap function, we design a controller for the mathematical model that ensures the desired specification is satisfied in the high-fidelity simulator with high confidence, taking a step toward bridging the sim-to-real gap. We demonstrate the effectiveness of the proposed method using a TurtleBot model and a pendulum system in stochastic simulators.