An Analytical Trajectory Planning Method for Underactuated Overhead Cranes with Constraints

In this paper, an analytical acceleration trajectory planning approach with constraints is proposed for underactuated overhead cranes. The allowable maximum velocity and acceleration of the physical system are taken into account, the payload swing is guaranteed to be under the preset amplitude during movement, and the transportation time can be estimated in advance. Specifically, by solving the inhomogeneous differential equation of the kinematic model, we analyze the coupling behavior of the cart motion and the payload swing, and provide the analytical expression between the payload swing and the cart acceleration. Subsequently, an analytical acceleration trajectory is proposed by introducing some smooth functions into the existing three-segment acceleration trajectory. The performance of the proposed trajectory is proven by rigorous mathematical analysis. Numerical simulation results are included to demonstrate the effectiveness of the proposed motion planning method.