Bridging the Sim-to-Real Gap in Parallel-Link Leg Mechanisms via Simulator-Side Dynamics Normalization

2026-08-03

AI Summary

This work addresses the dynamics discrepancy between simulation and reality in parallel-legged mechanisms caused by missing actuator and link inertias due to coordinate transformations in serial tree-based simulators. To resolve this, the authors propose Simulation-side System Normalization (S3N), which preserves the serial tree topology while embedding actuator inertia and damping through coordinate transformations (S3N-Act) and further recovers link inertia via frequency response identification (S3N-Full), all without modifying the underlying simulator architecture. Experimental results demonstrate that S3N-Full reduces joint position and torque RMSE by 80.9% and 82.1%, respectively, in a 2-DOF task; decreases ground reaction force errors by over 62% during stationary pitching; and lowers the average simulation-to-reality gap in circular walking from 17.3% to 9.9%.

Abstract

This paper addresses the sim-to-real gap in dynamics arising when a parallel-link mechanism is represented by a serial-tree surrogate in simulation. Conventional Jacobian-based state and torque mappings preserve consistency with the kinematic and virtual-work relations but do not account for the coordinate-induced redistribution of actuator inertia and damping and the linkage inertia omitted during serial-tree reduction. To address this gap, Simulator-Side System Normalization (S3N) is proposed to normalize the serial-tree simulator's effective dynamics while preserving its tree topology. S3N-Act incorporates actuator inertia and damping into the serial-coordinate dynamics through coordinate transformation, whereas S3N-Full restores residual linkage inertia by separately identifying actuator- and leg-level frequency responses. In the 2-DoF validation, S3N-Full reduced the joint-position and torque RMSEs by 80.9% and 82.1%, respectively, relative to the Jacobian-mapping baseline. During pitch-in-place motion, S3N-Act and S3N-Full reduced the RMSE of the ground reaction force norm by 65.1% and 62.4%, respectively. During circular locomotion, S3N-Full reduced the phase-averaged, command-normalized sim-to-real gap from 17.3% to 9.9%. These results show that simulator-side normalization improves motion- and force-level sim-to-real consistency. It enables policy training in a serial-tree framework with hardware-consistent dynamics that better represent the physical parallel-link mechanism.

Problem

• sim-to-real gap
• parallel-link leg mechanisms
• serial-tree surrogate
• dynamics normalization
• actuator inertia

Innovation

• sim-to-real gap
• parallel-link mechanism
• serial-tree surrogate
• dynamics normalization
• S3N