# Capturing a Space Target Using a Flexible Space Robot
## 5 Numerical Simulations
Figures 11 and 15 are the angular displacement change of the six joints of the robot manipulator, Figures 12 and 16 are the rotation angle change of the two hands of the end effector, Figures 13 and 17 are the tip responses of the flexible links \(B_{2}\) and \(B_{3}\) in the floating frames \(O_{2}\)-\(X_{2}Y_{2}Z_{2}\) and \(O_{3}\)-\(X_{3}Y_{3}Z_{3}\). Figures 18 and 19 are the attitude change of the target \(B_{8}\). The conclusions drawn from Figures 10-19 are:Figure 11: Time histories of angular displacements of the manipulator (\(v\) = 0.05 m/s): (**a**) Axis 1, (**b**) Axis 2, (**c**) Axis 3, (**d**) Axis 4, (**e**) Axis 5, and (**f**) Axis 6. Figure 12: Time histories of the rotation angles of the two hands (\(v\) = 0.05 m/s): (**a**) \(B_{6}\), (**b**) \(B_{7}\). Figure 14: Time histories of angular displacements of the robot base \(B_{1}\) (\(v\) = 0.1 m/s): (**a**) the \(X\) axis, (**b**) the \(Y\) axis, and (**c**) the \(Z\) axis. Figure 13: Tip displacements of the flexible links \(B_{2}\) and \(B_{3}\) (\(v\) = 0.05 m/s): (**a**) \(B_{2}\) in the \(Y_{2}\) direction, (**b**) \(B_{2}\) in the \(Z_{2}\) direction, (**c**) \(B_{3}\) in the \(Y_{3}\) direction, and (**d**) \(B_{3}\) in the \(Z_{3}\) direction. Figure 16: Time histories of the rotation angles of the two hands (\(v=0.1\) m/s): (**a**) \(B_{6}\), and (**b**) \(B_{7}\). Figure 3.0 Time histories of angular displacements of the manipulator (\(v=0.1\) m/s): (**a**) Axis 1, (**b**) Axis 2, (**c**) Axis 3, (**d**) Axis 4, (**e**) Axis 5, and (**f**) Axis 6. Figure 3.1 Tip displacements of the flexible links \(B_{2}\) and \(B_{3}\) (\(v\) = 0.1 m/s): (**a**) \(B_{2}\) in the \(Y_{2}\) direction, (**b**) \(B_{2}\) in the \(Z_{2}\) direction, (**c**) \(B_{3}\) in the \(Y_{3}\) direction, and (**d**) \(B_{3}\) in the \(Z_{3}\) direction. 1. From Figures 10 and 14, we can observe that central impact only causes the attitude change of the robot base \(B_{1}\) in the \(X\) direction, but the eccentric impact could cause the attitude change in all directions. 2. From Figures 11 and 15, we can observe that the controller designed in this paper can stabilize the motion of joint angles of the manipulator. It is observed from Figure 11a,e,f and Figure 15a,e,f that eccentric impact could cause the joint angle change of the manipulator in the Axis 1, Axis 5, and Axis 6 directions, while central impact could not. 3. It is observed from Figures 12 and 16 that the end effect can successfully capture the target for the four cases. 4. From Figures 13 and 17, we can observe that central impact and eccentric impact can both lead to the deformation of the flexible links \(B_{2}\) and \(B_{3}\) in the \(Y_{2}\) and \(Y_{3}\) directions, but only the eccentric impact can lead to the deformation of \(B_{2}\) and \(B_{3}\) in the \(Z_{2}\) and \(Z_{3}\) directions. 5. As depicted in Figures 18 and 19, we can observe that eccentric impact causes obvious attitude change of \(B_{8}\), meaning \(B_{8}\) is tumbling, but central impact cannot. Meanwhile, it is observed that the attitude evolution trend is changed several times in eccentric impact cases, which shows that there are multiple instances of contact during capturing. Moreover, it demonstrates that the tumbling motion of the target object makes the capturing operation complicated. 6. Figures 10-19 show the impact on the robot system caused by capturing when the target cylinder moves towards the manipulator are more significant than those when the target moves away from the manipulator. impact with negative relative velocity may cause more complex dynamic behavior of the robot than others. So, to reduce the risk, that scenario should be avoided. Furthermore, when the proposed active compliance controller is considered, the capture impact on the robot can be effectively offset. Conceptualization, X.-F.L. and X.-Y.Z. ; methodology, X.-F.L. ; software, X.-F.L. and X.-Y.Z. ; validation, X.-F.L. and X.-Y.Z. ; formal analysis, X.-F.L. and X.-Y.Z. ; investigation, X.-F.L. and X.-Y.Z. ; resources, X.-F.L. and X.-Y.Z.