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This paper introduces a self-contained calibration framework for humanoid robots that utilizes only onboard joint encoders and a pelvis-mounted IMU during static double-support contact, eliminating the need for external motion-capture systems. By formulating the calibration as a nonlinear least-squares problem, the authors achieve significant improvements in kinematic consistency, reducing foot-height RMS residuals from 4.26 mm to 2.20 mm on one robot model and from 8.03 mm to 1.43 mm on another. The method's effectiveness is validated through simulation and real-machine tests, demonstrating that a few static stances can yield substantial corrections in joint offsets.
Calibration without external systems can cut foot-height errors in humanoid robots by over 50%, enhancing kinematic accuracy in real-world applications.
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.
