# Slip Estimation Model for Planetary Rover Using Gaussian Process Regression
## 3 Data Collection
### Input Features  
Input features were expected to reflect the wheel-ground interaction state and were available from sensors on Zhurong. Four features were selected to form the input feature vector:  
(1) The rover's pitch, \(\theta\).  
The rover body frame is shown in Figure 5; as shown, the \(X_{\text{B}}\)-axis and \(Y_{\text{B}}\)-axis were parallel to the ground, with the \(X_{\text{B}}\)-axis pointing toward the driving direction and the \(Y_{\text{B}}\)-axis along the wheel axis. The \(Z_{\text{B}}\)-axis was taken to be perpendicular to the \(X_{\text{B}}\)-axis and \(Y_{\text{B}}\)-axis and pointed to the ground. \(\theta\) represents the angle between the \(X_{\text{B}}\)-axis of the rover body frame and the horizontal plane, which could be used to characterize the terrain slope. There was a highly nonlinear relationship between slip and slope [27], so it was selected as one of the feature inputs.  
(2) The rover's roll \(\varphi\).  
\(\varphi\) represents the angle between the \(Y_{\text{B}}\)-axis of the rover body frame and the horizontal plane. It was selected for different rolling states corresponding to different wheel force distributions, which affect slip behavior.  
(3) The average current of six wheel-driving motors \(\overline{I}\).  
According to the wheel-soil theory, the slip value directly affects the wheel drive torque \(T\)[28], so \(T\) can reflect the slip situation. Torque is known to be roughly proportional to motor current [29]; therefore, there was also a mapping relationship between the wheel drive motor current and the wheel slip. Since this paper focused on the rover slip, the slip conditions of the six wheels needed to be comprehensively considered. Therefore, the average current of six wheel-driving motors \(\overline{I}\) was chosen as an input feature.  
(4) The average angular velocity \(w\) of six wheel-driving motors \(\overline{w}\).  
Considering the nonideal behavior of the motor in the actual operation process, the speed of the wheel was not exactly the same as the command speed. Fluctuating within a  
Figure 5: The body frame of Zhurong.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \(\mathbf{c}\) (\(\mathbf{kPa}\)) & \(\mathbf{\varphi}\) (\(\mathbf{\lx@math@degree}\)) & \(\mathbf{K}\) (\(\mathbf{m}\)) & \(\mathbf{k_{c}}\) (\(\mathbf{kPa}\cdot\mathbf{m}^{-(\mathbf{n+1})}\)) & \(\mathbf{k_{p}}\) (\(\mathbf{kPa}\cdot\mathbf{m}^{-(\mathbf{n+2})}\)) & \(\mathbf{n}\) \\ \hline TYII-2 & 0.035 & 30.49 & 0.016 & 3.71 & 1.10 & 1.12 \\ JLU & 0.609 & 37.20 & 0.019 & 15.69 & 983.36 & 1.02 \\ Mars-2 & & & & & & \\ \hline \hline \end{tabular} \(c\): cohesion; \(\varphi\): internal friction angle; \(k\): shear deformation modulus; \(k_{c}\): the cohesive modulus of the soil; \(k_{\varphi}\): the frictional modulus; \(n\): slip-sinkage.  
\end{table}
Table 1: The mechanical parameters of TYII-2 and JLU Mars-2.  
certain range, wheel speed actually had some correspondence to wheel slip [30]. Therefore, the average rotational speed of the six wheel-drive motors was chosen as one of the input features.