# Data-Driven Identification of Crane Dynamics Using Regularized Genetic Programming
## 1 Introduction  
Cranes are material-handling machines widely used in the industrial and logistic sectors. Load transportation is often performed by cranes using ropes, cables, or chains that incorporate the unactuated degrees of freedom to the system, making the transportation tasks more challenging in terms of safety and efficiency as the transient and residual swing of a payload suspended on a rope adversely affects the load positioning performances and may present a safety hazard for the personnel working on-site, the surrounding objects, and the transported cargo, as well as the crane's structure and equipment affected by the dynamic forces caused by the swinging of the payload. The aforementioned problem is extensively studied in the literature and addressed via different modeling approaches and various anti-sway open-loop and closed-loop control strategies [1; 2; 3; 4]. An accurate dynamic model of a crane system, ensuring the precise prediction of actuated and unactuated states, especially in model-predictive control strategies, is crucial for improving crane operational and energy efficiency, as well as to mitigate the safety hazard. Additionally, the compromise between model performance and complexity is significant for real-time applications, andmodel structure reduction enhances its interpretability, which is helpful in designing model-based control systems. The accurate prediction of payload positioning is also useful in monitoring applications. In automated crane systems, the monitoring of the position of the load enables one to reduce the risk of collisions with obstructions and restrict motions considering a safety margin and residual sway prediction. A comprehensive review of various crane dynamic modeling methods and model-based control strategies reported in the literature is presented in [5; 6; 7]. A majority of the presented approaches are derived from the Euler-Lagrange equation. However, an accurate mathematical model of an underactuated crane dynamic system (e.g., overhead crane, gantry crane, boom crane, tower crane) can be difficult to derive due to the multibody interaction of crane mechanisms and construction elements, cables, hook assembly, load, and other electromechanical components. The dynamic behavior of a crane can be complex, taking into account the variation in payload mass and hoisting rope, nonlinearities and complexities arising from mechanical friction, parameter uncertainty, and possible external disturbances when a crane operates outdoors. Since an accurate model of crane dynamics can be difficult to obtain using analytical methods, machine learning and soft computing techniques are implemented in the identification approaches recently reported in the literature. In terms of controller design, a data-driven approach to develop a model-free controller directly from input-output data is also an interesting alternative (as opposed to a model-based control) that has been successfully applied recently for solving complex dynamic problems [8; 9], including the model-independent control of underactuated mechanical systems [10; 11]. In [12], Bayesian optimization is used to optimize the crane model and controller with training data collected from experiments carried out on a laboratory-scale overhead crane. A flat output identification algorithm is proposed in [13] to identify a rotary crane based on data measured on a laboratory stand. The idea to approximate the dynamics of a nonlinear underactuated crane system through local linear models is implemented in several papers using Takagi-Sugeno fuzzy (TSF) modeling [14; 15; 16; 17]. An incremental online identification algorithm is proposed to evolve the structure of a TSF model for a laboratory-scale overhead crane [18] and a tower crane [19]. Also, artificial neural network (ANN) models as universal approximators are used to generate black-box nonlinear structures of crane dynamic models and controllers.