Contouring control of a parallel mechanism based on equivalent errors

This study is concerned with the contouring control of a parallel mechanism, which is a constrained multi-axis motion system. The method of equivalent errors, previously proposed for unconstrained systems, is applied to design a contouring controller for such systems. It is found that the definition of equivalent errors is not affected by constraints. Hence, the design procedure of contouring controller is exactly the same as that for the unconstrained system. Due to the constraints, however, the state variables in the control law are not fully independent. Some of the states, which are not available from measurement, are actually function of the other available states. In general, it is impossible to directly solve the constraint equation that may contain transcendental functions. Therefore, a linear approximation is used to estimate the unavailable states. Numerical simulations are carried out for the contouring of several paths, including circular and elliptic paths. The results indeed confirm the validity of the proposed method.