AI 中文总结
提出仅用机载关节编码器与骨盆IMU的自包含校准框架，通过非线性最小二乘求解12维偏移向量，校准后A3、A2脚高均方根残差显著降低，可实现人形机器人下肢接触约束的关节偏移校准。
AI 中文摘要
准确的关节编码器偏移对于人形机器人下肢的运动学一致性至关重要，但现有校准方法通常需要外部运动捕捉系统或基准标记物。我们提出了一种自包含的校准框架，仅利用机载关节编码器和安装在骨盆上的IMU，在静态双支撑接触期间进行校准。当双脚固定时，正运动学得到的两脚之间的变换必须保持恒定；最小化其依赖于姿态的离散度，产生了一个针对12维偏移向量的非线性最小二乘问题。海森矩阵特征结构分析表明，平行的俯仰轴会引发旋转耦合。姿态残差仅观测到俯仰偏移的总和，而平移和姿态多样性决定了其余的数值可观测性。对于A3的滚转-俯仰-偏航排序，髋部滚转和髋部偏航的激励会降低髋部俯仰的耦合。站立姿态下的膝盖先验则锚定了剩余的弱俯仰链分解。仿真和真实机器人注入测试显示了一致的恢复效果，在保留的记录数据上，该校准将A3的脚高均方根残差从4.26 mm降至2.20 mm，A2的从8.03 mm降至1.43 mm。独立的激光雷达-惯性参考对俯仰耦合通道进行了校验，移除注入的俯仰偏移后，腿里程计的垂直漂移向激光雷达轨迹回归。因此，少数静态双支撑姿态即可为充分激励的方向提供接触一致的校正，而弱俯仰链中的单个偏移仍依赖于先验。
英文摘要
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.
