A swing constrained time-optimal trajectory planning strategy for double pendulum crane systems

In practice, overhead crane systems are widely used and the traditional control methods for a crane system usually treat it as a single pendulum system. However, when the hook mass cannot be ignored or the payload is too large, the crane system may behave more like a double pendulum system, which leads to the fact that traditional control methods are not suitable in this situation. In this paper, we focus on the control problem of a double pendulum crane system and propose a time-optimal trajectory planning method with the consideration of various constraints which can achieve the objectives of both accurate trolley positioning and double pendulum swing suppression. Specifically, the discrete system model is obtained using the discretization technique firstly. Then by deeply analyzing and considering a series of constraints, we formulate a quasiconvex optimization problem. After that, the bisection method is chosen to solve the obtained optimization problem with the corresponding time-optimal trajectory constructed conveniently. A tracking controller is also designed for the double pendulum crane system, which achieves proper trolley tracking performance. At last, both simulation and experimental results are included to illustrate the superior performance of the proposed trajectory planning method.