Time-Polynomial-Based Optimal Trajectory Planning for Double-Pendulum Tower Crane With Full-State Constraints and Obstacle Avoidance

Abstract

Double-pendulum dynamics increase the difficulty of the control for the tower cranes. Especially, it would be a greater challenge with obstacle avoidance while satisfying full-states constraints. A time-polynomial-based optimal trajectory planning strategy is proposed for double-pendulum tower crane with full-state constraints and obstacle avoidance. First, with the dynamic model of double-pendulum tower crane system, the trajectory planning problem is formulated by taking positioning, anti-swing, state constraints, and obstacle avoidance into account. Then, a group of auxiliary signals are introduced to express the state variables. The trajectory planning problem for jib slewing is transformed into that for the auxiliary signals. The time-based polynomial functions are introduced for trajectory planning of the auxiliary signals. By planning proper trajectories for the auxiliary signals and trolley translation displacement, we obtain time suboptimal trajectory for the jib slewing and the trolley transferring. The jib and the trolley can reach their destination accurately with suppressing swing of the payload and the hook while avoiding obstacles. The time suboptimal solution not only makes transportation time as short as possible, but also ensures that full-states constraints and obstacles avoidance are satisfied. Finally, hardware experiments demonstrate that the proposed trajectory planning strategy has better control performance than existing state-of-the-art methods.