# Sampling-Based Motion Planning for Free-Floating Space Robot without Inverse Kinematics
## 3 Motion Planning Algorithm for FFSRs
The dynamic parameters and size parameters of the space robot are shown in Table 4. The D-H parameters are shown in Table 5. In order to simplify the calculation, the base satellite and links of the manipulator are rectangular. The obstacles are also rectangular. Three rectangular obstacles are given in the environment. The centroid positions and sizes of obstacles are (1, 1, 2.8) m, 2/l/1 m, (4, 0, \(-\)1) m, 1/2/2 m, (6, 1.5, 2.5) m, and 1/2/2 m, respectively. The geometry of the space robot and obstacles is far more complex than rectangular in practice. However, shape complexity will only increase the complexity of the collision detection algorithm. The purpose of this article is to study motion planning issues, not collision detection problems. Collision detection is only a module of the planning algorithm. Therefore, the simplified geometric model does not affect the verification of the algorithm. Collision detection includes two parts. The first part is the collision between the robot and the obstacle. The second part is the collision between the robot's own parts. Collision detection is realized based on the separation axis theorem. Moreover, there is no big difference between motion planning with stationary obstacles and motion planning with movable obstacles that have predictable trajectories. If we know the trajectories \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Rigid Body No.** & **Mass/kg** & **Length/Width/Height (m)** & **I\({}_{\text{xx}}\) (kg.m\({}^{2}\))** & **I\({}_{\text{yy}}\) (kg.m\({}^{2}\))** & **I\({}_{\text{zz}}\) (kg.m\({}^{2}\))** \\ \hline
0 & 900 & 1/1/1 & 6000 & 12,000 & 8000 \\ \hline
1 & 20 & 0.35/0.16/0.16 & 20 & 20 & 30 \\ \hline
2 & 20 & 0.35/0.16/0.16 & 20 & 20 & 30 \\ \hline
3 & 40 & 4/0.16/0.16 & 1 & 40 & 40 \\ \hline
4 & 40 & 4/0.16/0.16 & 1 & 40 & 40 \\ \hline
5 & 20 & 0.35/0.16/0.16 & 20 & 20 & 30 \\ \hline
6 & 20 & 0.35/0.16/0.16 & 20 & 20 & 30 \\ \hline
7 & 40 & 1.2/0.16/0.16 & 10 & 8 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Dynamic and geometric parameters of the FFSR. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**i** & \(\boldsymbol{a}_{i-1}\)**(\(\boldsymbol{m}\))** & \(\boldsymbol{a}_{i-1}\)**(\(\boldsymbol{c}\))** & \(\boldsymbol{d}_{i}\)**(\(\boldsymbol{m}\))** & \(\boldsymbol{\theta}_{i}\)**(\(\boldsymbol{c}\))** \\ \hline
1 & 0 & 0 & 2.5 & 600 \\ \hline
2 & 0 & 90 & 0.35 & 20 \\ \hline
3 & 0 & 90 & 0.35 & 20 \\ \hline
5 & 4 & 0 & 0.35 & 40 \\ \hline
6 & 0 & 90 & 0.35 & 20 \\ \hline
7 & 0 & 90 & 1.2 & 20 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: D-H parameters of the FFSR. of obstacles, we will know the position of each obstacle at any time. As we know the position of each obstacle at any time, it is easy, for collision-checking, to test if the point in the trajectory is in collision or not. Additionally, this paper focuses on dealing with the differential constraints and restricting base attitude disturbance, so in order to simplify the simulation process, we do not consider the movable obstacles. The simulation in this paper is divided into two parts: the first part verifies the advantages of the local planner for goal EE pose guiding growth; the second part verifies the effectiveness of the proposed RRTs for an FFSR. ### The Advantages of a Local Planner for Goal EE Pose Guiding Growth

This paper proposed a local planner that can adjust the attitude of the base when necessary. We compare it with the local planner based on the general Jacobian matrix and the local planner based on the extended Jacobian matrix by simulation. The former does not adjust the base attitude in the whole local planning process, and the latter always adjusts the base attitude in the whole local planning process.