# Slip Estimation Model for Planetary Rover Using Gaussian Process Regression
## 6 Mars Condition Validation Results and Discussion  
Zhurong operated in a highly efficient detection mode within its design life; the most commonly used movement scheme is shown Figure 11. When Zhurong arrived at Station \(N\), its surrounding environment was imaged with navigation cameras located on the mast. Ground flight controllers performed visual positioning, target point selection (intermediate transition Station \(X\) and target Station \(N+1\)), and path planning (the path from Station \(N\) to Station \(X\)) according to images obtained at Station \(N\). From station \(N\) to station \(X\), the rover drove in blind movement mode; that is, [PERSON] drove completely according to the path planned by the ground controllers without autonomous obstacle avoidance. Meanwhile, visual positioning was performed at Station \(X\) to obtain the relative position of Station \(X\) to Station \(N\). From station \(X\) to station \(N+1\), [PERSON] drove in blind autonomous obstacle avoidance movement mode; that is, the rover autonomously planned a path to drive toward the target, Station \(N+1\). It should be noted that the rover controller is not equipped with the slip estimation model at present, thus the actual rover arrival point is reached without slip compensation. From the above-described process, the ground cannot obtain real-time rover coordinates when the rover is driving, thus it is impossible to directly verify the accuracy of the slip estimation value during the driving process. However, we knew the planning path and the actual end point/arrival after blind movement. In this paper, the predicted slip_\(x\) and slip_\(y\) were converted into the longitudinal slip offset \(\Delta x\) and the lateral offset \(\Delta y\), respectively, and the planned path was corrected according to the longitudinal and lateral offset values. Thus, we were able to obtain the slip estimation corrected path. The end point of the slip-corrected path was compared with the actual points the rover reached (accurate coordinates obtained by visual positioning) to evaluate the estimation effects of the slip estimation models against the telemetry data. The required telemetry information is shown in Table 5, and more details of the specific implementation steps are available in [22]. It should be noted that the frequency of telemetry data for the rover's attitude and wheel driving motor is about 0.2-0.3 Hz, which is lower than the sampling frequency of the ground tests. It means that it needs to use a estimated slip value to represent the mean slip within 3 to 5 s, which may causes errors in slip offset calculations where the terrain was extremely rugged. Since the terrain of the landing area of Zhurong is relatively flat, the data of Zhurong does not change drastically when driving; we can consider this frequency to be acceptable. In this paper, validation was conducted based on data obtained from mid-June 2021 (sol.27-sol.40). Table 6 shows the planning path information and actual end points of arrival. As shown, there was always an offset \(\Delta L\) between the actual arrival point and the planned target point. The \(\Delta L\) varied from 0.267 m to 0.678 m, and the largest offset occurred at sol.34. Due to the limited sample, there was no uniform linear relationship between the \(\Delta L\) of these five movements, the planned distance, and the planned curvature. According to the planned path information shown in Table 6 and the models' estimation results, Figure 12 displays the slip-corrected path and planning path (left figure of each subfigure). In order to quantify and compare the estimation accuracy of the GA-BP and GPR models, the offsets, \(\Delta L\)_GA-BP and \(\Delta L\)_GPR, between the actual arrival point and the planned target point, are summarized in Table 7. Figure 12 visualizes the offset results of each movement (right figure of each subfigure); the points in all subfigures represent  
Figure 11: The Schematic diagram of Zhurong station.