## 1 Introduction
[22] introduced an efficient beam formulation using the ANCF to simulate and analyze the dynamic responses of PTL during deicing processes. [PERSON] et al. [23] used ANCF to model the PTL and implemented sliding joint constraints along with beam-beam contact detection methods to account for the different dynamic behaviors of the PTLs and protective steel structures. [PERSON] et al. [24] proposed an adaptive length-varying cable element method based on the ANCF, using a length-varying control model that considers contact tension and suspension height to simulate the initial equilibrium configuration of highspeed railway catenary systems. Overall, the discrete model offers efficiency and ease of implementation but sacrifices accuracy due to its simplified representation of flexible PTLs [18; 19]. FEM emphasizes stress and shape analysis for small to moderate deformations but is unsuitable for large deformations [20; 21]. Conversely, ANCF provides a global approach to managing node displacements and rotations, ensuring stable and efficient handling of large deformation and rotation challenges in flexible bodies [22; 23; 24]. Another critical aspect of describing HIR landing dynamics is constructing a contact model between the PTL and the robot. [PERSON] et al. [25] utilized an artificial neural network -based contact estimator to predict the contact forces between the robot and the PTL. They calculated the penetration depth by subtracting the sum of the radii from the relative position between the travelling wheel and the PTL center, without considering the two contact surfaces. [PERSON] et al. [26] proposed a rigid-flexible coupling dynamic modeling of an inspection robot, and simplified the dimension of contact forces to two. [PERSON] et al. [27] utilized a quasistatic mechanics model to optimize the performance of a two-wheel driven robot, which assumes the direction of the contact force is fixed without considering the movement of the contact surface. [PERSON] et al. [28] constructed a towed cable-sheave system model using the ANCF, incorporating shear geometry and vessel motion to analyze contact forces and cable detachment behavior. Most existing works ignored the number, dimensions, and dynamic variations of contact forces [25; 26; 27], but a few considered contact geometry, 3D contact forces, and the movement of contact bodies [28]. This study proposes a coupled model using the ANCF method to analyze the coupling effects of the FPTLIR and PTL, considering the contact forces between the PTL and the travelling wheels of the FPTLIR. The main objective is to evaluate the system's dynamics for preventing failures and establishing a safer landing process for the FPTLIR. The main contributions of this paper are as follows:  
1. A coupled FPTLIR/PTL dynamic model was derived to describe the FPTLIR landing process. The PTL was modeled using the ANCF method with a Euler-Bernoulli beam, neglecting shear and torsion to improve computational efficiency. A contact model based on the Hunt-Crossley theory was used to consider the deflection angle of the contact beam element and the traveling wheel groove, to ensure accuracy. 2. A modular simulation model was conducted with different landing positions and robot masses to enhance the adaptability and generalization of the model using MATLAB (R2020b) software. The simulation performed parallel updates for the mass matrices of the robot and PTL to improve efficiency, and separated the dynamics calculations of the PTL and the FPTLIR to reduce complexity. The modular design of the simulation enhanced the adaptability to other HIRs. 3. A comprehensive test platform was established to evaluate the landing performance of the FPTLIR. Six opposing force-sensing resistors (FSRs) were employed on the platform to handle the variability in contact point locations during force measurement. The platform enabled the measurement of attitude, displacements, and contact forces, demonstrating the capability to achieve high measurement accuracy and ensuring reliable evaluation of the proposed method.