Adaptive RISE Feedback Control for Robotized Machining With PKMs: Design and Real-Time Experiments

The development of high-precision tasks, such as machining, needs a positioning device for the cutting tool with the smallest possible error. Multiple design factors need to be considered to ensure a mechatronic device successfully performs such tasks. One of these factors may be attributed to the control scheme, which is responsible for controlling the position of the machine. In view of the importance of designing a good control scheme for a robotic system, in this article, we propose a new extension of the robust integral sign of the error (RISE) for the positioning device a parallel kinematic machine (PKM). This extension consists in including a nominal feedforward term based on the inverse dynamic model of the robot and replacing the RISE fixed feedback gains with adaptive ones. The RISE part of the proposed controller ensures semiglobal asymptotic stability. Moreover, it can accommodate sufficiently smooth bounded disturbances. The feedforward part cancels the nonlinearities of the system, improving the tracking performance of the controller. The adaptive feedback gains produce corrective actions when an increase in the tracking errors is due to the contact forces that occur during the machining process. A Lyapunov-based stability analysis is conducted to prove the semiglobal asymptotic stability of the proposed control solution. To show its effectiveness, real-time experiments are performed for two case studies; the first one is on a free motion trajectory and the second on machining experiments under three different forward speeds on SPIDER4, a redundantly actuated PKM.