## 5 Discussion  
This section will discuss the proposed method from two perspectives: dynamic modeling and control. * Dynamic modeling: (1) The free-floating dual-arm space robot studied in this paper is a complex multi-body system with nine DOF. The modeling efficiency of the traditional explicit multibody system dynamic modeling method needs to be improved. For example, when the pseudo inertia matrix method [19; 20] is used, the pseudo inertia matrix, the homogeneous transformation matrix, and other intermediate variables need to be calculated; when the generalized momentum method [21] is used, although the computational efficiency of the inertia matrix is higher than that of the pseudo inertia matrix method, it is also necessary to derive and calculate the intermediate variables such as the Jacobian matrix, and the generalized momentum method cannot explicitly establish the bias force vector. The space robot modeling method in this paper avoids the definition and operation of intermediate variables, and its modeling efficiency is higher than the traditional explicit modeling method. The highest computational complexity is obtained when all joint types of the robot are considered as rotational joints. Table 2 shows the comparison of the computational complexity of the inertia matrix \(M\) and the bias force vector \(\mathbf{h}\) in the calculation of an \(n\)-DOF robot with full rotational joints when the three different explicit dynamics modeling methods are adopted. Table 2 shows that the computational complexity of the explicit canonical method in this paper is significantly lower than those of the other two methods. Figure 8: Error comparison of base attitude stability control. (**a**) Comparison of the x-axis error of the base. (**b**) Comparison of the y-axis error of the base. (**c**) Comparison of the z-axis error of the base. (2) Due to the floating characteristics of the base of the free-floating space robot, it is difficult to combine the traditional explicit dynamic modeling method with DEM, because it requires tedious and complex analysis processes, such as the definition and operation of complex intermediate variables. When combined with DEM, our explicit canonical dynamic modeling method can avoid the tedious and complex analysis of intermediate variables. (3) Due to the inconvenient modeling method, most of the literature in the study of space robot dynamics and control only simulates the plane situation of the two-DOF manipulator, which makes it difficult to reflect the real working state of the complex multi-DOF space robot. When using the proposed explicit dynamic modeling method, it is easy to establish a dynamic model for complex multi-DOF space robot for control research. (1) Compared with other traditional control methods, research on the NMPC method applied to space robots is not extensive enough. Recently, [PERSON] [11; 44] explored the possibility of using the NMPC method to control manipulators mounted on free-floating space robots. However, [PERSON] [11; 44] only considered the trajectory tracking control of the end manipulator of the free-floating space robot, and did not consider the stable control of the attitude of the base of the free-floating space robot. In addition, [PERSON] [11; 44] only carried out dynamic modeling and simulation verification of the NMPC method for a two-DOF planar manipulator. This paper not only considers the trajectory tracking control of the end manipulator of the free-floating space robot, but also considers the stable control of the base attitude of the free-floating space robot. In addition, the dynamic modeling and control simulation of the free-floating dual-arm space robot with nine DOF are carried out in this paper. (2) The free-floating space robot has high requirements on the accuracy of trajectory tracking and the stability of the base attitude. The traditional NMPC method has difficulty meeting these requirements. This paper innovatively introduces the idea of sliding mode variable structure to improve the traditional NMPC method.