Trajectory planning is an effective feed-forward control technology for vibration suppression of flexible manipulators. However, the inherent drawback makes this strategy inefficient when dealing with modeling errors and disturbances. An optimal trajectory planning approach is proposed and applied to a flexible piezoelectric manipulator system in this paper, which is a combination of feed-forward trajectory planning method and feedback control of piezoelectric actuators. Specifically, the joint

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... controller is responsible for the trajectory tracking and gross vibration suppression of the link during motion, while the active controller of actuators is expected to deal with the link vibrations after joint motion. In the procedure of trajectory planning, the joint angle of the link is expressed as a quintic polynomial function. And the sum of the link vibration energy is chosen as the objective function. Then, genetic algorithm is used to determine the optimal trajectory. The effectiveness of the proposed method is validated by simulation and experiments. Both the settling time and peak value of the link vibrations along the optimal trajectory reduce significantly, with the active control of the piezoelectric actuators.