Humanoid Robot Motion Tracking Control Method Integrating Adaptive PID, Kalman Filtering and Feedforward Compensation

Abstract

Aims: This study developed and evaluated a humanoid joint-space motion-tracking controller integrating standard Kalman filtering, adaptive proportional-integral-derivative feedback and model-based inverse-dynamics feedforward compensation. Study Design: A twenty-trial Monte Carlo comparative numerical simulation was conducted against a fixed-gain proportional-derivative baseline under matched plant parameters, reference trajectories, measurement-noise sequences and disturbance sequences. Place and Duration of Study: The study was conducted at the School of Automation and Electrical Engineering, Tianjin University of Technology and Education, Tianjin, China, from March 2026 to July 2026. Methodology: A simplified 12-degree-of-freedom humanoid joint-space model was simulated for 500 time steps per trial at a sampling interval of 0.01 s. Each joint state was estimated using a two-state discrete Kalman filter. The PID gains were adjusted online through bounded nonlinear laws, while nominal inverse dynamics supplied inertia, velocity-dependent and gravity feedforward compensation. Tracking performance was assessed using MAE, RMSE, maximum error and 95% confidence intervals. Results: The mean trial-level MAE decreased from 0.165825 rad to 0.039224 rad, a mean reduction of 76.35% with an approximate 95% CI of [75.91%, 76.78%]. Mean trial-level RMSE decreased from 0.224126 rad to 0.067078 rad, a mean reduction of 70.07% with an approximate 95% CI of [69.81%, 70.33%]. All twelve joints showed lower MAE. Conclusion: The integrated controller improved joint-angle tracking consistently within the evaluated simplified model. Contact-rich simulation and physical-robot experiments remain necessary for external validation.