# Slip Estimation Model for Planetary Rover Using Gaussian Process Regression
## 6 Mars Condition Validation Results and Discussion
the linear deviation distance between the actual arrival point of the current move and the planned path point, while the horizontal dotted lines in each subfigure represent the offset \(\Delta L\) between the actual arrival point and the planned target point. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Sol**} & \multirow{2}{*}{\begin{tabular}{c} **Planning** \\ **Curvature** \\ **(1/m)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Planning** \\ **Distance** \\ **(m)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Rover's Yaw(°)** \\ **Start** \\ **Point** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Target** \\ **Point** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **\(X\_\)Plan** \\ **(m)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **\(Y\_\)Plan** \\ **(m)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **\(X\_\)Actual** \\ **(m)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **\(Y\_\)Actual** \\ **(m)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **\(\Delta I\)** \\ **(m)** \\ \end{tabular} } \\ \hline
27 & 0.038 & 8.459 & \(-135.508\) & \(-116.999\) & \(-4.9805\) & \(-6.7917\) & \(-4.9408\) & \(-7.1753\) & 0.386 \\
28 & \(-0.071\) & 9.196 & \(-129.597\) & \(-167.031\) & \(-7.6869\) & \(-4.7449\) & \(-7.8924\) & \(-4.9153\) & 0.267 \\
34 & \(-0.039\) & 9.23 & \(-162.377\) & \(176.774\) & \(-9.107\) & \(-1.1502\) & \(-9.7244\) & \(-1.4313\) & 0.678 \\
36 & \(-0.0594\) & 9.644 & \(-106.654\) & \(-139.298\) & \(-5.1775\) & \(-7.9800\) & \(-5.5369\) & \(-8.3848\) & 0.541 \\
40 & 0.0096 & 9.516 & \(171.782\) & \(177.010\) & \(-9.4670\) & 0.9290 & \(-10.0064\) & 0.7707 & 0.562 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Planning end points and actual end points of arrival. \begin{table} \begin{tabular}{c} **\(\Delta\)L\_GPR2** \\ **(m)** \\ \end{tabular}  \\ \hline
27 & 0.434 & 0.420 & 0.426 & 0.851 & 0.120 & 0.044 & 0.472 & 0.551 \\
28 & 0.312 & 0.241 & 0.739 & 0.896 & 0.222 & 0.144 & 0.688 & 0.880 \\
34 & 0.633 & 0. Figure 12: Cont. and * represent the estimation points of the GA-BP models based on TYII-2 and JLU Mars-2 datasets, respectively. In all subfigures, * path deviated the furthest from the planned path, and the end point of * path was always farther than the end point of *. Notably, on sol.40, \(\Delta L\) = 0.562 m, the \(\Delta L\)_GA-BP (TYII-2) was 1.129 m, while \(\Delta L\)_GA-BP of JLU Mars-2 was just 0.242 m, which demonstrated that the GA-BP models established based on TYII-2 data performed poorly in comparison to the others. The GPR models based on two soil datasets also showed the same regularity. The slip-corrected * path based on the JLU Mars-2 dataset exhibited better performance than the * path based on the TYII-2 dataset. The end point of the * path was closer to the actual arrival point, and the actual arrival point was always within the * 95% confidence interval. \(\Delta L\)_GPR1 and \(\Delta L\)_GPR2 represent the end-point deviation from the actual arrival point of the 95% confidence interval boundary predicted by the GPR model. The maximum possible point the rover could reach was always over 0.5 m away from the real arrival point. Comparing the GA-BP model and the GPR model, based on the same soil dataset, the GPR model always achieved a better estimation effect. \(\Delta L\)_GA-BP of TYII-2 were always larger than or roughly equal to \(\Delta L\), while most \(\Delta L\)_GPR of JLU Mars-2 were smaller than \(\Delta L\). The best es-timation points all appeared on the GPR model based on JLU Mars-2; on sol.27, \(\Delta L\)_GPR even reached 0.044 m, meaning that the predicted point was very close to the real arrival point. In conclusion, the model established based on the data of the JLU Mars-2 dataset had the best adaptability to the Martian environment near Zhurong's landing site, which means the properties of the Martian soil in this region may be more similar to the simulated soil, JLU Mars-2.