Human–Robot Interaction: External Force Estimation and Variable Admittance Control Incorporating Passivity

In the context of Industry 5.0, human–robot collaboration increasingly demands intuitive, safe, and sensorless interaction for tasks such as hand-guided teaching and concurrent manipulation. However, conventional admittance control systems are prone to instability due to abrupt changes in human arm stiffness and their reliance on accurate dynamic models. To address these challenges, this paper proposes a sensorless external force estimation and variable admittance control method that models robot dynamic uncertainties and interaction forces as normally distributed stochastic quantities. An improved particle swarm optimization algorithm is introduced to calibrate the variance parameters, enhancing estimation accuracy and robustness. Furthermore, an energy-based variable admittance control strategy is developed, which preserves system passivity by adaptively adjusting inertia and damping gains based on real-time energy variations. The proposed method was validated on a redundant robot platform. Experimental results show that the external force and torque estimation errors remain below 3 N and 3 N.m, respectively, with lower detection delays and errors than those of a first-order generalized momentum observer in collision detection. Variable admittance experiments demonstrate that the system maintains passivity and stable interaction even under sudden arm stiffness changes. The approach is well-suited for industrial applications requiring safe, sensorless, and compliant human–robot collaboration.