Constraint-following vibration control for robot follow-up support system under force-stiffness interdependence

The robot follow-up support system provides a cost-effective and flexible support solution for machining thin-walled workpieces. In the past, however, the control design had been a challenge, mainly due to the difficulty in coping with the complex coupling and time-varying dynamic characteristics of the follow-up support system. This study proposes a novel heterogeneous hybrid stiffness model in a “parallel-serial-parallel” structure, along with a constraint-following control method for vibration suppression. First, a second-order vibration model of the follow-up support system was developed, capturing the primary stiffness characteristics of the system while simplifying the modeling through mass bundling. Second, time-varying stiffness analytical expressions are established for the main stiffness components, including the local workpiece region, gas springs at support modules, and the normal stiffness of the robot end-effector, facilitating real-time substitution in the control process. Third, the controllable air pressure term was separated from both sides of the vibration equation, yielding an equivalent underactuated system, and a constraint-following control algorithm was designed. The simulations demonstrate that the proposed control algorithm meets the servo requirements with high precision.