Variable Impedance Control for Force Tracking in Multi-Mode Robotic Back Massage

Achieving safe physical interaction on the human back is challenging due to respiratory rhythms, complex topography, and varying tissue stiffness. To enable compliant force tracking within commercial closed position-control robot architectures, this paper presents an adaptive variable damping admittance control framework driven by multi-dimensional force sensor feedback. A stiffness-free admittance model is constructed to eliminate steady-state tracking errors, integrated with a nonlinear adaptive damping law that sensitively responds to real-time force sensor measurements. This mechanism rapidly dissipates dynamic impact energy during contacts while maintaining low impedance during steady state. Validated via a high-fidelity MATLAB R2024b-CoppeliaSim co-simulation platform replicating Traditional Chinese Medicine (TCM) manipulations, the proposed sensor-driven strategy significantly improves force tracking fidelity over traditional fixed-parameter control. Quantitative results demonstrate that across all complex therapeutic waveforms, the root mean square error (RMSE) remains below 0.42 N, the mean absolute error (MAE) is within 0.32 N, and the squared correlation coefficient (r2) exceeds 0.97. These findings confirm the high efficiency and clinical potential of the proposed framework.