Noise Analysis and Hierarchical Adaptive Body State Estimator for Biped Robot Walking With ESVC Foot

The Ellipse-based Segmental Varying Curvature (ESVC) foot, inspired by the human foot’s rollover shape, has demonstrated substantial improvements in the energy efficiency of bipedal robotic locomotion. However, the varying curved rollover shape and the contact modeling errors directly complicate the robot state estimation. This study addresses noise analysis and state estimation challenges associated with bipedal walking using the ESVC foot. Initially, physical experiments are conducted to examine the distributions of measurement and process noise influenced by the ESVC foot. Subsequently, a temporal noise regression model utilizing a weighted sliding window is introduced to predict error covariance matrices. Based on this model, a two-stage hierarchical adaptive state estimator is proposed for bipedal robots equipped with the ESVC foot. In the pre-estimation stage, a data fusion-based approach is employed to estimate the Center of Mass (CoM) state. In the post-estimation stage, CoM acceleration is estimated using a Gaussian kernel-based adaptive fusion method, and noise covariance matrices are iteratively updated using the regression model, residuals, and prior covariances. An Extended Kalman Filter (EKF) then refines the CoM state estimation and updates sensor noise variances. Experimental validation on the TT-II robot confirms that the proposed estimator not only facilitates stable bipedal walking but also enhances position and velocity estimation accuracies by 50.07% and 53.45%, respectively, compared with a standard EKF. Furthermore, the estimator demonstrates superior adaptability under dynamic walking conditions.