Contact-Constrained Lower-Limb Joint-Offset Calibration for Humanoid Robots

Abstract

Accurate joint encoder offsets are essential for kinematic consistency in humanoid lower limbs, yet existing calibration methods typically require external motion-capture systems or fiducial targets. We present a self-contained calibration framework exploiting only onboard joint encoders and a pelvis-mounted IMU during static double-support contact. The inter-foot transform from forward kinematics must stay constant when both feet are fixed; minimizing its posture-dependent dispersion yields a nonlinear least-squares problem over the 12-dimensional offset vector. A Hessian eigenstructure analysis shows that parallel pitch axes induce a rotational coupling. Orientation residuals then observe only the pitch-offset sum, while translation and posture diversity set the remaining numerical observability. For the A3 pitch-to-roll-to-yaw ordering, hip-roll and hip-yaw excitation reduce hip-pitch coupling. A standing-posture knee prior then anchors the remaining weak pitch-chain decomposition. Simulation and real-machine injection tests show consistent recovery, and on held-out recordings calibration reduces foot-height RMS residuals from 4.26 to 2.20 mm on A3 and from 8.03 to 1.43 mm on A2. An independent LiDAR-inertial reference checks the pitch-coupled channel. Removing an injected pitch offset moves the leg-odometry vertical drift back toward the LiDAR trajectory. A few static double-support stances thus provide contact-consistent corrections for well-excited directions. Individual offsets in the weak pitch chain remain prior-dependent.