Design of Input Shaping Control for Planar Parallel Manipulators

Parallel manipulators are well known for their superior stiffness, higher accuracy, lower inertia and faster response compared to the serial counterparts and hence is widely used for high-speed machining and heavy load applications. However, controller limitations as well as design constraints can result in un-optimized designs causing unsettling residual vibrations at the end effector and limit their applications. Though many have discussed improving the structural design, augmenting with redundant sensors/ dampers and advanced feedback control methods for serial and mobile manipulators for vibration attenuations, very few investigated such techniques for parallel manipulators (PM). In this manuscript, we evaluate a specific type of feed-forward technique for planar PM. Lagrangian based dynamic models of platform manipulators and a simple trajectory level proportional-derivative control will be used with the gains tuned to force oscillations at the end effector to ensure stability. We will then demonstrate the applicability of basic input shapers for PM based on computation of natural frequencies and damping ratio for each mode, and resulting improvements in terms of appropriate performance measures.