Force sensorless interaction wrench estimation for neural-learning impedance control of a flying parallel robot with actuator saturation

This paper proposes a sensorless adaptive neural-learning impedance controller for a flying parallel robot (FPR) to enable compliant physical interaction while explicitly accommodating actuator saturation. The dynamic model of the multi-UAV heterogeneous cooperative FPR is first established, and an external wrench observer is developed to estimate the contact-induced torque. To address system uncertainties and achieve robust disturbance rejection, a Lyapunov-based radial basis function neural network (RBFNN) impedance controller with force-tracking capability is designed. An auxiliary compensation system is further incorporated to alleviate the adverse effects of actuator input saturation. The closed-loop stability of the overall FPR system under the proposed control law is rigorously guaranteed. ADAMS-Simulink co-simulation results demonstrate the effectiveness of the approach, confirming its ability to maintain stable and compliant interaction across diverse contact conditions.