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

TL;DR

This work tackles the sim-to-real gap in autonomous robotics by introducing a lightweight conformal-mapping framework based on Schwarz-Christoffel Mapping to transfer control inputs and motion-planning policies from a superior teacher to a degraded learner. By mapping teacher command regions to corresponding learner regions in a two-dimensional input space, the method preserves maneuver intent for both discrete motion primitives and continuous MPC-based control, without requiring explicit dynamic model identification. Key contributions include the SCM-based control transfer, convex-hull-based characterization of learner limits with adaptive boundary updates, and command-pair refinement to handle motion noise; these are validated through extensive simulations and real-world experiments on different ground vehicles. The approach enables rapid, robust sim-to-real adaptation and has practical impact for deploying learned policies on aging or heterogeneous robotic platforms, particularly in two-dimensional control spaces where conformal mapping is tractable. The framework lays groundwork for future extensions to higher dimensions and heterogeneous system transfer using geometry-based mappings.

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.

Figures (25)

• Figure 1: A pictorial representation of the proposed transfer method. A desired command is transferred from an expert teacher to a learner, which may differ from the teacher due to unmodeled dynamics, failures, disturbances and platform aging.
• Figure 2: The block diagram of the proposed mapping-based transfer learning framework
• Figure 3: (a) Command pairs are color-coded. The dashed envelope indicates the learner's limits on the teacher's command domain; (b) Selected command pairs for constructing the mapping regions are color-coded while the red cross marks the desired teacher command and the mapped learner command.
• Figure 4: (a) Mapping flow of transferring the desired teacher command to the learner; (b) Mapping of the polygon to a rectangle while using the bi-infinite strip as the intermediate plane.
• Figure 5: Examples of characterization of learner's limits on the teacher command domain. (a) the new command pair directly marks the boundary of allowable teacher command; (b) proportionally shrinks the teacher's command space to approximate the learner's limits as the learner portion of the command pair is an outlier but not on the boundary.