Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Towards Mitigating Sim2Real Gaps: A Formal Quantitative Approach

P Sangeerth, Abolfazl Lavaei, Pushpak Jagtap

TL;DR

This paper develops a data-driven approach to provide a formal guarantee for quantifying the simulation gap and demonstrates the effectiveness of the proposed method through experiments conducted on a nonlinear pendulum system and a nonlinear Turtlebot model in simulators.

Abstract

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 can be conceptualized as one characterized by bounded states and input-dependent disturbances. This allows us to leverage the existing powerful model-based control algorithms effectively, ensuring the enforcement of desired specifications while guaranteeing a seamless transition from simulation to real-world application. To provide a formal guarantee for quantifying the simulation gap, we develop a data-driven approach. 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.

Towards Mitigating Sim2Real Gaps: A Formal Quantitative Approach

TL;DR

This paper develops a data-driven approach to provide a formal guarantee for quantifying the simulation gap and demonstrates the effectiveness of the proposed method through experiments conducted on a nonlinear pendulum system and a nonlinear Turtlebot model in simulators.

Abstract

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 can be conceptualized as one characterized by bounded states and input-dependent disturbances. This allows us to leverage the existing powerful model-based control algorithms effectively, ensuring the enforcement of desired specifications while guaranteeing a seamless transition from simulation to real-world application. To provide a formal guarantee for quantifying the simulation gap, we develop a data-driven approach. 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.

Paper Structure

This paper contains 11 sections, 2 theorems, 17 equations, 5 figures, 1 table.

Table of Contents

  1. INTRODUCTION
  2. System Description and Problem Definition
  3. System Description
  4. Problem Formulation
  5. Data-driven Framework
  6. Formal Quantification of Simulation Gap
  7. Controller Synthesis
  8. Case Studies
  9. Pendulum System
  10. Turtlebot Model
  11. Conclusions

Key Result

Lemma 3.1

Consider the nominal mathematical model ${\Sigma}$ and its unknown simulator dynamics, denoted by $\hat{\Sigma}$. If for all $i \in \{1,2,\dots, n\}$, there exists a function map $\gamma_i:X \times U \rightarrow \mathbb{R}_0^+$, for all $x \in X$, for all $u \in U$, such that $|\hat{f_i}(x,u)-{f_i}( where $\gamma(x,u)=[\gamma_1(x,u);\gamma_2(x,u);\cdots;\gamma_n(x,u)],$$f(x,u)=[f_1(x,u);f_2(x,u);\

Figures (5)

  • Figure 1: Pendulum model in the Py-Bullet simulator.
  • Figure 2: The state trajectory $x_1$ for both the mathematical system (red) and the PyBullet model (blue) is shown. The invariance specification is violated in PyBullet when the controller is synthesized without considering $\gamma(x,u)$ (top). The state-space invariance specification is satisfied in PyBullet when the controller is synthesized considering $\gamma(x,u)$ (bottom).
  • Figure 3: The red points represent the region of invariance obtained by synthesizing the controller for the mathematical model without $\gamma(x,u)$. The blue points represent the region of invariance obtained by synthesizing after incorporating $\gamma(x,u)$ into the mathematical model.
  • Figure 4: Turtlebot model in the Gazebo simulator.
  • Figure 5: State trajectories of both the mathematical model (red) and the Gazebo model (blue). The black regions represent the obstacles, while the yellow one represents the target. When the controller is synthesized for the reach-while-avoid specification without incorporating $\gamma(x,u)$, the Pybullet model hits the obstacles (left). The underlying specification is satisfied when the controller is synthesized after incorporating $\gamma(x,u)$ (right).

Theorems & Definitions (8)

  • Remark 2.1
  • Lemma 3.1
  • proof
  • Remark 3.2
  • Theorem 4.1
  • proof
  • Remark 4.2
  • Remark 4.3