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

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.