Motion planning approach for payload swing reduction in tower cranes with double-pendulum effect

Highlights

• The jib and trolley positioning and payload sway suppression problems of double-pendulum tower cranes are investigated.

• The trajectory planning method is presented.

• The performance of the proposed trajectory is proved by the Lyapunov technique, LaSalle’s invariance theorem and Barbalat’s lemma.

• The control performance is demonstrated by comparative simulations.

Abstract

Tower crane system is usually considered as single-pendulum system to design controllers. However, in reality, tower crane often exhibits more complex double-pendulum characteristics, which makes it more difficult for positioning and swing angles elimination. To this end, a composite trajectory planning method is designed. The first part of the proposed trajectory guarantees the motion positioning of the jib and trolley, and the second part achieves the purpose of swing suppression by using a damping component. The proposed method can be implemented online that does not need to advance or offline planning. After a series of proof and simulations, it is shown that the proposed method can achieve the desired effect, and at the same time it is robust to uncertain system parameters and external disturbances.

Introduction

Underactuated systems have a wide range of applications, both in industrial site and real life. As one of the most common underactuated systems, the control methods of cranes have been designed by many scholars for years. There are many types of cranes, such as tower cranes commonly found on construction sites, bridge cranes in factories, convenient rotary cranes, and so on. However, no matter its structure, its control is mainly divided into two parts, one is to achieve accurate boom/cart positioning, and the other is to eliminate the payload swing angle in time [1].

However, due to the complex underactuated characteristics of the system, in order to meet the above requirements, many methods have been presented such as input-shaping method [2], [3], [4], [5], trajectory planning method [6], [7], [8], [9], energy-shaping-based control [10], partial feedback linearization method [11], [12], [13], adaptive algorithm [14], [15], [16], [17], [18], [19], model predictive control [20], [21], sliding mode variable structure control [22], [23] and some intelligent algorithms [24], [25], [26]. Nonetheless, the current researches are almost to regard the crane model as a single-pendulum model. However, when the mass of the hook is not negligible, or when there is a non-negligible rope length between the hook and the real payload, the swinging portion often exhibits a double-pendulum characteristic. The analysis of its mathematical model and the design of the controller will be more difficult.

For the controller design of the double-swing crane, some scholars have also conducted research. Sun et al. constructed a new flat output signal, and transformed trajectory planning task into a convex optimization problem. Meanwhile, the trajectory fully considered the safety and physical constraints, ensuring that the state variables are kept within the limited range [27]. Chen et al. proposed a time-optimal trajectory planning method for the double-swing crane system after discretizing the system, and finally proved the accurate positioning of the trolley and the elimination of swing angle by the proposed method through simulation and experiment [28]. After analyzing the model characteristics of the double-pendulum overhead crane, Ouyang et al. proposed a simple LMI-based robust controller. Simulations and experiments demonstrated the effectiveness of the presented method [29]. Masoud et al. designed a hybrid command-shaper to suppress the swing oscillation. The results showed that the controller can effectively reduce the oscillation of all levels [30]. Tuan and Lee designed two robust controllers for overhead cranes. The simulation results showed that the designed controller has a good positioning and angle suppression effect in a short period of time [31]. Some scholars also combined the intelligent algorithm with the traditional one, and they have achieved good control performance for the double-pendulum cranes. Adeli et al. used Takagi–Sugeno fuzzy model with a parallel distribution compensation and a linear quadratic regulation controller to obtain good effect of positioning and swing suppression for overhead crane [32].

In this paper, the mathematical model of the tower crane with double-pendulum effect is established firstly. After analyzing the internal coupling relationship of the system, an online composite trajectories method including a positioning part and an anti-swing part is presented, and its performance is proved by using Lyapunov method, LaSalle’s invariance theorem and Barbalat’s lemma. Finally, a large number of comparative simulations verify the advantages of the designed controller.

In summary, the major contributions of this study are as follows:

• The proposed planned trajectory can be implemented online that does not need to advance or offline planning. Simultaneously, the method can ensure that the payload sways are always within the allowable range during the operation of the jib and trolley by adjusting the gain of the swing damping term.

• Through a series of comparative simulations, it is proved that the proposed method not only has good control performance, but also has good robustness to parameter uncertainties and external disturbances.