Robust sliding mode control of redundantly actuated parallel mechanisms with respect to geometric imperfections

The paper deals with the modeling and control of redundantly actuated parallel mechanisms. The redundant actuation means the redundant number of actuators, that is, more actuators than degrees of freedom of the mechanism. These machines bring the possibility of removing the backlash by the so-called antibacklash control. However, control of such a structure suffers from several new control problems like the danger of mutual fighting of the redundant actuators. This is especially problematic if the geometric imperfections appear. The presented solution is based on the usage of robust sliding mode control for uncertain dynamics. The paper explains classic approach of sliding mode control and its new modification based on the uniform usage of all actuators replaced by the fictitious auxiliary drives. The verification of the proposed algorithms is presented by two planar mechanisms with four actuators and three degrees of freedom. The first one is the fiber-driven mechanism, and the second one is the rigid 4RRR mechanism “Crosshead.”