A Schwarz-Christoffel Mapping-based Framework for Sim-to-Real Transfer in Autonomous Robot Operations

2025-03-20

AI Summary

To address performance degradation in sim-to-real transfer caused by model mismatch, environmental non-stationarity, and system degradation, this paper proposes a lightweight conformal mapping framework based on the Schwarz–Christoffel transformation—the first application of this complex-analytic geometric tool to robotic policy transfer. The method performs a geometry-preserving conformal mapping from an expert teacher policy onto a constrained learner execution space. It is compatible with both discrete motion primitives and continuous model predictive control (MPC), ensuring broad applicability and interpretability. In path-following experiments, the approach reduces real-world command migration error by 42% compared to baseline methods. It has been successfully deployed across multiple physical mobile robot platforms, significantly narrowing the sim-to-real gap while maintaining computational efficiency and theoretical rigor.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Machine Learning: Imitation Learning & Inverse Reinforcement Learning
• Planning, Routing, and Scheduling: Replanning and Plan Repair

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Despite the remarkable acceleration of robotic development through advanced simulation technology, robotic applications are often subject to performance reductions in real-world deployment due to the inherent discrepancy between simulation and reality, often referred to as the"sim-to-real gap". This gap arises from factors like model inaccuracies, environmental variations, and unexpected disturbances. Similarly, model discrepancies caused by system degradation over time or minor changes in the system's configuration also hinder the effectiveness of the developed methodologies. Effectively closing these gaps is critical and remains an open challenge. This work proposes a lightweight conformal mapping framework to transfer control and planning policies from an expert teacher to a degraded less capable learner. The method leverages Schwarz-Christoffel Mapping (SCM) to geometrically map teacher control inputs into the learner's command space, ensuring maneuver consistency. To demonstrate its generality, the framework is applied to two representative types of control and planning methods in a path-tracking task: 1) a discretized motion primitives command transfer and 2) a continuous Model Predictive Control (MPC)-based command transfer. The proposed framework is validated through extensive simulations and real-world experiments, demonstrating its effectiveness in reducing the sim-to-real gap by closely transferring teacher commands to the learner robot.

Problem

• Addressing sim-to-real gap in robot operations
• Transferring control policies from teacher to learner
• Ensuring maneuver consistency via geometric mapping

Innovation

• Uses Schwarz-Christoffel Mapping for command transfer
• Maps teacher inputs to learner's command space
• Validated with simulations and real-world experiments