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

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.