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This paper considers a transportation system consisting of a quadrotor with a cable-suspended payload. The main focus of this paper is to investigate the effect of polynomial trajectories on the vibration of the cable-suspended payload and to show which polynomial trajectory results in less vibration. A mathematical analysis and a parametric study were carried out to investigate the effect of the degree of the polynomial trajectory on its kinematic behavior. A conjecture relates the degree of the polynomial trajectory and its kinematic behavior to the corresponding payload vibration was introduced. The base excitation model of vibratory systems was proposed as the model of the transportation system of interest. The vibration analysis of both the transportation system and the polynomial trajectories was conducted analytically to show which polynomial trajectory has the least payload vibration. A second stage of payload vibration reduction was provided by introducing a method to reduce the transmitted vibration from the quadrotor to the payload for any quadrotor trajectory. A roadmap to design the transportation task that can reduce the payload vibration was proposed. Both the simulation and the experimental results were presented, discussed and analyzed to verify the findings of this paper.

Vibration reduction of a quadrotor with a cable-suspended payload using polynomial trajectories