Impedance force control for industrial robot based on unified residual compensation iterative learning control and multi-directional particle swarm optimization

An impedance force control framework that enables precise contact force tracking for industrial robots subject to unknown environment dynamics is proposed in this paper. First, a position-based impedance controller is formulated and theoretical analysis reveals that perfect force tracking requires exact knowledge of the environment stiffness and contact position—quantities that are rarely available in practice. To compensate for these uncertainties, a Unified Residual Compensation Iterative Learning Control (URC-ILC) scheme is introduced. Instead of estimating each environment parameter separately, URC-ILC aggregates all modeling errors into a single residual term, which is iteratively updated and fed forward to the impedance loop, guaranteeing stable convergence of the contact force. The controller parameters are tuned off-line by Multi-Directional Particle Swarm Optimization (MDPSO) algorithm, which is developed by (i) injecting four performance-oriented velocity components—response speed, steady-state error, oscillation, and overshoot—into the swarm dynamics, (ii) modulating the inertia weight through a sigmoid schedule, and (iii) applying a mutation operator that prevents premature convergence. Simulations show that MDPSO converges faster and attains higher accuracy than the classical PSO. Experiments further demonstrate that the URC-ILC-based impedance controller, with parameters optimized by MDPSO, reduces steady-state force error by 44.38% relative to the conventional impedance strategy. These results confirm the effectiveness of the proposed approach for high-precision, compliant robotic machining under uncertain contact conditions.