# Sampling-Based Motion Planning for Free-Floating Space Robot without Inverse Kinematics
## 3 Motion Planning Algorithm for FFSRs
\right]^{\lx@math@degree}\). #### 4.2.1 Simulation Results of Scenario 1

After 36 iterations, the FFSR reaches the target EE position. A generated configuration meets the requirements, as shown in Figure 4a. Figure 4b shows the movement history of the space robot from the initial configuration to the goal EE position and that the space robot does not collide with obstacles. Moreover, the rigid bodies of the space robot do not collide with each other. The joint trajectory and the base attitude disturbance trajectory are shown in Figure 5. It can be seen from Figure 5 that during the movement, the base attitude disturbance is effectively adjusted before reaching its limit. Figure 3: Time histories of EE position error, EE attitude error, base attitude trajectory, and joint trajectory of local planner for goal EE pose guiding growth. (**a**) Time histories of EE position error; (**b**) time histories of EE attitude error; (**c**) time histories of base attitude trajectory; (**d**) time histories of joint angle. #### 4.2.2 Simulation Results of Scenario 2

After 76 iterations, FFSR reaches the target EE pose. The generated configuration meets the requirements, as shown in Figure 6a. Figure 6b shows the movement history of the space robot from the initial configuration to the goal EE pose and that the space robot does not collide with obstacles. Moreover, the rigid bodies of the space robot do not collide with each other. The joint trajectory and the base attitude disturbance trajectory are shown in Figure 7. It can be seen from Figure 7 that during the movement, the base attitude disturbance is effectively adjusted before reaching its limit. Figure 4: Initial configuration, final configuration, and movement history of the space robot in Scenario 1. (**a**) The final configuration solved by the planning algorithm in Scenario 1; (**b**) The movement history of the space robot from the initial configuration to the goal EE position in Scenario 1. Figure 5: Joint trajectory and base attitude disturbance trajectory for Scenario 1. (**a**) Joint trajectory; (**b**) base attitude disturbance trajectory. ## 5 Conclusions

Based on the RRT framework, this paper designs a motion planner for FFSRs from an initial configuration to a goal EE pose. Compared with the existing works, it does not require us to solve the inverse kinematics. The differential constraints of FFSR can be handled by the designed local planners. Moreover, the planned trajectory meets the requirement that the attitude disturbance of its base does not exceed its limit. The main contribution is that two local planners are proposed to handle the special needs of motion planning of FFSRs:

1. A control-based local planner for random configuration guiding growth of the tree. This planner uses the configuration error as a reference to select actions. It can achieve rapid local planning while taking into account the disturbance of the base. 2. A control-based local planner for goal EE pose guiding growth of the tree. This local planner can adjust the attitude of the base when necessary. This planner mainly uses the EE pose error as a reference to select actions. Moreover, a reference goal base attitude and an error threshold for the base are introduced as a trigger for base attitude adjustment. The local planner

Figure 6: Initial configuration, final configuration, and movement history of the space robot in Scenario 2. (**a**) The initial configuration and the final configuration solved by the planning algorithm in Scenario 2; (**b**) the movement history of the space robot from the initial configuration to the goal EE pose in Scenario 2. Figure 7: Joint trajectory and base attitude disturbance trajectory for Scenario 2. (**a**) Joint trajectory; (**b**) base attitude disturbance trajectory. based on this mechanism can make the base attitude disturbance meet the limit while avoiding singularity as much as possible.