Aiming at the non-linear control problem of the compliant grinding robot under the coupling action of basic vibration,flexible vibration and environmental contact force during mobile operation,a new type of robust trajectory tracking force/position hybrid control strategy was proposed.The second type of Lagrangian method was used to establish the dynamic equation of the compliant manipulator,and the above-mentioned system was divided into two time-scale fast and slow subsystems by using the singular perturbation method.In the slow-varying subsystem,a force/position hybrid control method was adopted for the rigid part of the system,PID control was used to control the force,and the robust control based on neural network was used to control the position.In the fast-change subsystem,the speed difference feedback method was used to control the flexible part of the system.The results show that by using the proposed control strategy,the trajectory tracking effect of the end of the manipulator is better and the grinding force remains stable,which has a good suppression effect on nonlinear vibration.