### Assembly Error Modeling  
Error modeling's purpose is to elucidate the propagation and accumulation law of errors such as manufacturing deviation, installation position deviation, and installation clearance in the assembly process. An accurate error model can precisely predict a product's final assembly quality [14; 15; 16]. To ensure the final performance, constructing an error propagation model for the assembly process is necessary [17]. Regarding the assembly error modeling, many scholars have studied the influence of part manufacturing errors on the assembly accuracy [18; 19; 20]. [PERSON] et al. [21] classified and elaborated the geometric errors generated in the assembly process of parts, and constructed the error transfer digraph model for the whole assembly process of mechanical products. [PERSON] et al. [22] proposed an assembly precision prediction method considering the manufacturing error and deformation of parts for an aeroengine high-pressure rotor system. In this method, each mating surface of the assembly's error model is effectively constructed using the small displacement torsor theory. [PERSON] et al. [23] integrated form errors and local surface deformations in the assembly error with the help of the skin model and the boundary element method. These studies have good application value in general mechanics, but their applicability in spacecraft assembly is weak due to the different environments between assembly and service.  
As a complex multi-loop closed-chain hinge mechanism, the LSDM's assembly accuracy is more difficult to control due to the closed-loop coupling and hinge clearance. Therefore, it is particularly important to establish an error propagation and accuracy prediction model during their assembly process. [PERSON] et al. [24] proposed a method for describing the error accumulation during a planar truss structure's assembly process. This method's central idea is developing universal model and reusing it to calculate the uncertainty of each part of the system. This method performs independent calculations for each module but ignores the coupling effect between them. To address a coupling's impact between adjacent modules on error propagation, [PERSON] et al. [25] proposed two new concepts, independent loops and coupling loops, to describe all types of closed loops present in any planar closed-chain mechanism and used them to obtain an error propagation model  
Figure 1: The LSDM of a satellite and its assembly scene.  
for multi-loop closed-chain mechanisms. For multi-loop closed-chain mechanisms, the clearance of hinge significantly impacts the final assembly quality [26]. Therefore, many scholars have conducted in-depth research on characterizing hinge clearance errors and their impact on the geometric accuracy. [PERSON] et al. [27] used the concept of virtual links to establish a clearance model for single, multi, and locking joints. Based on this, they developed a multi-loop closed-chain angle error analysis model considering hinge errors and used this model to analyze the LSDM's assembly angle errors.  
Due to the significant differences in the environment between the ground assembly and the service in space and the fact that the current technology for simulating the space environment in a ground assembly is limited, the service performance of the LSDM may be improved by taking the factors of different environment into the assembly error model. However, by summarizing the existing literature, it is found that the error models built in the previous research did not take into account the factor of different environments, and they were still constrained by the ground assembly index. It creates some uncertainty about the performance of the LSDM.