Robust model predictive control of sampled-data Lipschitz nonlinear systems: Application to flexible joint robots

Controlling flexible joint robots has drawn the attention of many industry professionals during the past two decades. It is a difficult task because various structural features that make the control of rigid robots easier, such as passivity of the motor torque to link velocity, full actuation, and separate control of each joint, are lost when we consider joint flexibility in the control design of these robots. However, we must consider joint flexibility while designing the controller; otherwise, the system may become unstable. In this article, we devise a robust model predictive controller scheme for flexible joint robots modeled as sampled-data Lipschitz nonlinear systems with unknown bounded disturbances. It is assumed that the state of the system is accessible for feedback. Therefore, a state-feedback control law is designed using a robust stability criterion and can be computed by solving an online optimization problem. The control law optimizes the performance index by reducing its worst-case value. The proposed control design scheme is applied to the one-link flexible joint robot. Simulation results validate the effectiveness of the controller in handling nonlinearities while minimizing the effect of unknown bounded disturbances.