# Optimization-Based Input-Shaping Swing Control of Overhead Cranes
## 1 Introduction  
As important transport equipment, overhead cranes are widely used in ports, docks, large factories, reservoir areas, and other places where large goods are transported. With the improvement in intelligence, overhead cranes are developing in a faster, more efficient, and wider direction. An overhead crane is mainly composed of lifting, pitching, trolley operation, cart operation, and other mechanisms, as well as special hangers [1]. Through the coordinated control of the cart and the trolley, the payload can be moved from one place to another. However, due to the requirement of high efficiency, this leads to an increase in the payload swing and difficulty in trolley positioning. In particular, the large swing of the payload may cause safety accidents [2]. Therefore, it is of great practical significance to design a crane control system with rapid positioning and small swing. Many control strategies, such as input shaping, sliding mode control, and machine learning, are applied to overhead cranes [3; 4; 5]. As a typical open-loop control method, input shaping is widely used to reduce the residual vibration of flexible systems because of its simple structure and low cost [6]. In reference [7], an extra insensitivity (EI) input shaper was designed by calculating the time-varying vibration period of a crane. The anti-swing performance was verified with experiments, but the time delay and stability of the shaper were not taken into account. Based on model feedback and partial feedback linearization, a frequency adjustment strategy for input shaping was used in reference [8]. In reference [9], an EI shaper and a closed-loop control method based on swing angle estimation were designed for a tower crane, and the results showed that the EI shaper was more effectivein swing suppression. However, non-zero initial conditions and disturbances make these control systems less effective in swing suppression. In order to solve the problem of traditional input shapers being sensitive to initial disturbances, a zero-vibration (ZV) shaper with non-zero initial conditions was proposed in reference [10]. The effectiveness of the shaper was verified with comparative experiments under different initial disturbances. To deal with the same problem, a re-parameterizing shaper method was proposed to counteract initial disturbances in reference [11]. An optimization technique was used to provide a step input acceleration function for a system acted via a shaper, which not only satisfies the system constraints and expected conditions but also reduces the sensitivity of the control system to variations in the internal parameters [12]. In reference [13], a genetic algorithm was used to determine the parameters of an input shaper, which can reduce the negative impact of the motor parameter error and obtain better output results. In addition, a method based on deep reinforcement learning was proposed in reference [14], and its swing suppression effect was verified in different situations. However, these two techniques need to be further improved in terms of optimization efficiency. In references [15,16], the particle swarm optimization (PSO) algorithm was used to optimize the parameters of the traditional unit amplitude zero-vibration shaper and the ZV shaper so that the optimized shapers could effectively restrain the payload swing under the system modeling errors. However, the PSO is not suitable for the real-time optimization of shapers because of its mechanism. In order to further improve the real-time robustness of crane systems, some adaptive algorithms have been introduced into the parameter optimization of shapers. In [3,17], neural networks were used to realize adaptive shaping after the PSO operations. In [18], the pulse amplitude and time of a ZV shaper were iteratively updated in real time according to the constructed performance index and the measured output and control data. Moreover, an adaptive input-shaping method based on an extreme learning machine (ELM) was proposed in [19].