Vibration suppression during trajectory tracking of a PRR manipulator.

Flexible manipulators are light in weight, provide a high payload-to-weight ratio, consume less power, and can be operated at high speed compared to rigid manipulators, however, these manipulators are subjected to structural vibrations that can be suppressed using a suitable controller. This work presents such a control scheme to suppress vibrations for PRR (prismatic-revolute-revolute) rigid-flexible manipulator while tracking curved and linear path trajectories in three-dimensional space. The dynamic modeling of the rigid-flexible manipulator is performed using the assumed mode method (AMM) where equations of motion are derived using Decoupled Natural Orthogonal Complement (DeNOC) matrices. The control scheme is implemented by developing a hybrid controller which consists of proportional-derivative (PD) feedback and open-loop command shaping techniques to suppress the vibrations while tracking the trajectory. The desired hub/joint angles are calculated using the inverse kinematics approach. The results show the comparison of shaped vs unshaped tip deflections of all the links and hence demonstrate the effectiveness of the developed hybrid controller in reducing the vibration level while maintaining good positional accuracy.