Center of Mass and Zero Moment Point Computation for Balance Identification of a Humanoid Robot using an Inertial Measurement Unit and Unscented Kalman Filtering

Humanoid robots require advanced balance control systems to safely and efficiently operate in dynamic and unstructured environments. The research contribution is an IMU-only balance-detection framework introducing a quantitative Responsiveness Index (RI) to compare the responsiveness of Center of Mass (CoM) and model-based Zero Moment Point (ZMP) estimation. The proposed method integrates CoM and ZMP analyses derived exclusively from Inertial Measurement Unit (IMU) data and employs an Unscented Kalman Filter (UKF) with optimized parameters (α=0.10, β=2, process noise covariance Q = 0.10, measurement noise covariance R = 0.10) obtained through sensitivity analysis across multiple motion states. This configuration effectively suppresses IMU noise and stabilizes attitude estimation on the DARwIn-OP3 humanoid platform. Experimental validation showed that CoM estimation achieved accuracies of 85.71 % for x, 97.85 % for y, and 99.96 % for z relative to CAD-based static references, while ZMP estimation reached 71.43 % for x and 94.89 % for y, and the Support Polygon (SP) area matched the model within ± 0.5 %. The proposed RI metric revealed that ZMP detected balance transitions approximately 20 % faster than CoM during dynamic walking and kicking, confirming its superior responsiveness. These findings demonstrate that IMU-derived, model-based ZMP estimation provides an effective, real-time indicator of humanoid balance changes, enabling future development of closed-loop control strategies to maintain ZMP within the SP for improved dynamic stability.