## 5 Optimal Collision-Avoidance Trajectory Planning Based on dsRNA Splicing Evolutionary Algorithm
### Trajectory Planning Simulation for a Space Robot
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Initial Condition** & **Notation** & \multicolumn{3}{c}{**Value**} \\ \hline \(p_{b0}\) & (the initial position of base) & \(\left[\begin{array}{cccc}-0.2832&0.3107&0.3248\end{array}\right]^{T}\) (m) \\ \(\sigma_{b0}\) & the initial attitude of base & \(\left[\begin{array}{cccc}1&0&0&0&0\end{array}\right]^{T}\) \\ \(p_{c0}\) & the initial position of end-effector & \(\left[\begin{array}{cccc}-0.2832&0.3107&0.3248\end{array}\right]^{T}\) (m) \\ \(\sigma_{c0}\) & the initial attitude of end-effector & \(\left[\begin{array}{cccc}0&0.8191&0&0.5736\end{array}\right]^{T}\) \\ \(\theta_{0}^{1}\) & the initial joint angle of Arm-1 & \(\left[\begin{array}{cccc}0&47.72&-93.91&0&-23.82&0\end{array}\right]^{T}\)(\({}^{\circ}\)) \\ \(\theta_{0}^{2}\) & the initial joint angle of Arm-2 & \(\left[\begin{array}{cccc}0&-47.72&176.09&0&-23.82&0\end{array}\right]^{T}\)(\({}^{\circ}\)) \\ \(p_{t}\) & the position of the target & \(\left[\begin{array}{cccc}0.7147&0.4150&-0.1758\end{array}\right]^{T}\) (m) \\ \(\sigma_{t}\) & the position and attitude of the target & \(\left[\begin{array}{cccc}0.0215&0.9027&0.1184&0.4132\end{array}\right]^{T}\) \\ \(p_{o}\) & the position of the obstacle point & \(\left[\begin{array}{cccc}-0.0691&0.6037&0.4742\end{array}\right]^{T}\) (m) \\ \(m\) & the initial fixed-time TPF parameter & \multicolumn{3}{c}{0.1} \\ \(T_{c}\) & \(\Delta\) & the initial CDF parameter [19] & \multicolumn{3}{c}{16.85} \\ \(t_{f}\) & (working time) & \multicolumn{3}{c}{25 s} \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The initial condition of the trajectory planning. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Notation** & **Value** \\ \hline M & Evolution generations & 100 \\ N & Quantity of (-)RNA & 10 \\ k & The number of gene segments with genetic information & 5 \\ \(P_{m}\) & Mutation probability of RNA & 0.001 \\ \(P_{s}\) & Splicing success rate & 0.9 \\ \(w_{3}\) & The weight of maximum input & 0.6 \\ \(w_{4}\) & The weight of input smoothness & 0.4 \\ \(T_{c}\) & The time parameter of (2) & 5 \\ \(\infty\) & The set value of \(\infty\) & 10,000 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The parameters of dsRNA Splicing Evolutionary Algorithm. Although the trajectory planning strategy based on pose feedback can improve by 99.99% compared with no-pose-feedback based optimal method c, it is undeniably difficult to solve the large trajectory input problem, which is shown in curve b and d given by Figures 8 and 9. Fortunately, as shown in Figures 8 and 9, the proposed method can optimize the joint motion trajectory of the manipulator, while ensuring the accuracy. In Figure 9, the joint angular velocities \(\theta_{6}^{2}\) of methods b and d are more than 180\({}^{\circ}\), which \begin{table}
\begin{tabular}{l c c c} \hline \hline  & **Method a** & **Method b** & **Method c** \\ \hline The converge time of end-effector position error (s) & 2.26 & 2.79 & 2.67 \\ The converge time of end-effector attitude error (s) & 2.35 & 2.79 & 2.26 \\ The converge time of base position error (s) & 1.06 & 1.13 & \(\infty\) \\ The converge time of base attitude error (s) & 1.03 & 1.30 & \(\infty\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The pose error converge time of three comparing methods. Figure 6: The pose errors of end-effector in four methods (three axis synthesis). Figure 7: The pose errors of base in four methods (three axis synthesis).