# An Orthogonal Wheel Odometer for Positioning in a Relative Coordinate System on a Floating Ground
## 3 Experiments
### The Experiment of Random Curve Motion  
Before we talk about the experiment, let us first introduce the Steam VR tracking system based on HTC VIVE used in the experiment [30]. This system has long been used in VR motion-sensing games. It is equipped with STEAM tracking technology that allows accurate positioning within a space area of 6 m \(\times\) 6 m, with an accuracy of less than 1 mm. It includes two HTC VIVE2.0 location base stations and a tracker. By installing the tracking device used in the joystick in the motion sensing game on the chassis of the mobile robot, we can obtain the most accurate actual curve in the random curve movement so as to carry out comparative experiments with the orthogonal wheels positioning system and gyro positioning system designed by us. First, we introduce the experimental site of random curve motion experiment. Figure 28 shows the site layout of the laboratory. The HTC VIVE2.0 base stations are placed on both sides. The base station is placed on the same axis with a height of one meter. The tracker as shown in Figure 29 is mounted on the mobile chassis, which is fixed in the center of the mobile chassis, that is, the center of the orthogonal wheels system. The mobile robot is randomly moved, S-shaped, by the remote control. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Theoretical Movement Value**} & \multicolumn{3}{c}{**Actual Movement Value**} & \multicolumn{3}{c}{**Error**} \\  & **x(m)** & **y(m)** & **\(\theta\)(*)** & **x(m)** & **y(m)** & **\(\theta\)(*)** & **\(\Delta\)d(m)** & **\(\Delta\theta\)(*)** \\ \hline \(P_{0}\) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \(P_{1}\) & 1.80 & 0 & 90 & 1.802 & \(-\)0.008 & 90.02 & 0.008 & 0.02 \\ \(P_{2}\) & 1.80 & 1.80 & 180 & 1.808 & 1.795 & 181.45 & 0.009 & 0.45 \\ \(P_{3}\) & 0 & 1.80 & 270 & 0.011 & 1.805 & 270.87 & 0.012 & 0.87 \\ \(P_{0}^{\prime}\) & 0 & 0 & 360 & 0.013 & \(-\)0.010 & 361.42 & 0.016 & 1.42 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The actual movement value and error of the positioning system for each point along the square. Figure 27: The angle of chassis coiling around pitch and roll axis. In this experiment, we conducted a comparative experiment on our own positioning system, the gyroscope positioning system and the HTC VIVE positioning system. In the experiment, the gyroscope positioning system can obtain the rotation angle in the movement process by itself, and at the same time, the data of two mutually perpendicular wheels of the four wheels in the orthogonal wheel system serve as the data of X and Y. According to the solution method mentioned in Section 2.1, coordinate information of gyroscope positioning can be obtained. In the process of random S-shaped motion, the upper computer can obtain the data of orthogonal wheel positioning and gyroscope positioning at the same time for comparison test. In combination with the data obtained by HTC VIVE, three experimental curves can be obtained at the same time in one movement for comparison. Figure 30 shows the gyroscope position curve, orthogonal wheels position curve, HTC VIVE position curve and the error curve of orthogonal wheels relative to HTC VIVE, respectively. As can be seen from the comparison curve, the positioning curve of the orthogonal wheels positioning system is basically consistent with that of HTC VIVE in the random S-shaped motion, and the maximum error is 1.18 (\(\pm\)0.075) cm in the process of moving. As for the positioning curve of the positioning system using a gyroscope, the deviation degree of the curve is increasing with the progress of the motion, due to the accumulated error of gyroscope rotation during the traveling process. This is due to the orthogonal  
Figure 28: The site layout of the laboratory. HTC VIVE2.0 base stations are placed on both sides of the site, and the base stations are placed on the same axis with a height of one meter. Figure 29: The tracker is fixed in the center of the moving chassis, which is the center of the orthogonal wheels system.