Humanoid Robot Motion Tracking Control Method Integrating Adaptive PID, Kalman Filtering and Feedforward Compensation
Li Jinhui
School of Automation and Electrical Engineering, Tianjin University of Technology and Education, Tianjin 300222, China.
Zhang Jingyu *
School of Automation and Electrical Engineering, Tianjin University of Technology and Education, Tianjin 300222, China.
Song Changhao
School of Automation and Electrical Engineering, Tianjin University of Technology and Education, Tianjin 300222, China.
Li Xiangbin
School of Automation and Electrical Engineering, Tianjin University of Technology and Education, Tianjin 300222, China.
*Author to whom correspondence should be addressed.
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.
Keywords: Humanoid robot, motion tracking, adaptive PID, Kalman filter, inverse-dynamics feedforward, Monte Carlo simulation.