Vibration control for a nonlinear three-dimensional flexible manipulator trajectory tracking

This paper proposes an innovative approach to the trajectory tracking in three-dimensional space and vibration control problems in the presence of a nonlinear three-dimensional flexible manipulator based on the partial differential equation model. Unlike two-dimensional plane, we select spherical coordinates to describe the position of the end point in three-dimensional space. This novel approach makes it possible to realise the trajectory tracking by controlling the two angles in spherical coordinates, meanwhile, a vibration control scheme is proposed to restrain vibrations. In addition, the existence and uniqueness of solutions are demonstrated. Finally, the performance of the desired trajectory tracking, the proposed vibration control scheme and their convergence properties are demonstrated by numerical simulations.