Hierarchical Whole-Body Control for Tendon-Cable-Driven Humanoids via Reference-Residual Policy and Offline-Learned Tendon Mapping

Tendon-cable transmission can reduce distal-limb inertia in full-size humanoids, but its elasticity, hysteresis, backlash, and multi-joint coupling introduce state-dependent joint-to-motor discrepancies. We present a hierarchical whole-body tracking framework for the 28-DoF Droid X3 that separates high-level motion learning from transmission compensation. A reference-residual policy is trained in simulation by single-stage proximal policy optimization (PPO) using a unified robot-space motion representation, globally anchored tracking rewards, hierarchical hard-example sampling, and tendon-oriented domain randomization. In simulation checkpoint evaluation, more than 90% of 12,674 tested reference motions are completed. Independently, a state-conditioned mapper is trained offline through a differentiable motor–joint forward model identified from physical motor-excitation data and connected in series between the frozen policy and the low-level motor controller. Randomized repeated Mapping-OFF/ON trials are conducted on two nominally identical Droid X3 units. Within every robot–motion block, the frozen PPO checkpoint, reference trajectory, controller settings, safety bounds, and frozen mapper weights are held fixed; complete trials are the statistical units. OFF converts desired joint positions with the robot-specific fixed static calibration, whereas ON feeds the complete policy-level desired-joint vector and measured plant state to the frozen mapper, which directly outputs the complete motor-position command. Across the complete physical trials, the aggregate action-completion rate is 68% with Mapping OFF and 79% with Mapping ON, an increase of 11 percentage points. Representative walk, squat, and dance trajectories illustrate lower tracking errors under Mapping ON, while individual frames and selected temporal fragments are used only for visualization.