Dynamic Modeling and Adaptive Robust Synchronous Control of Parallel Robotic Manipulator for Industrial Application

Control of parallel manipulators is very hard due to their complex dynamic formulations. If part of the complexity is resulting from uncertainties, an effective manner for coping with these problems is adaptive robust control. In this paper, we proposed three types of adaptive robust synchronous controllers to solve the trajectory tracking problem for a redundantly actuated parallel manipulator. The inverse kinematic of the parallel manipulator was firstly developed, and the dynamic formulation was further derived by mean of the principle of virtual work. Furthermore, linear parameterization regression matrix was determined by virtue of command function "equationsToMatrix" in MATLAB. Secondly, the three adaptive robust synchronous controllers (i.e., sliding mode control, high gain control, and high frequency control) are developed, by incorporating the camera sensor technique into adaptive robust synchronous control architecture. The stability of the proposed controllers was proved by utilizing Lyapunov theory. A sequence of simulation tests were implemented to prove the performance of the controllers presented in this paper. The three proposed controllers can theoretically guarantee the errors including trajectory tracking errors, synchronization errors, and cross-coupling errors asymptotically converge to zero for a given trajectory, and the estimated unknown parameters can also approximately converge to their actual values in the presence of unmodeled dynamics and external uncertainties. Moreover, all the simulation comparative results were presented to illustrate that the adaptive robust synchronous high-frequency controller possess a much superior comprehensive performance than two other controllers.