# Visuo-Haptic Mixed Reality Simulation Using Unbound Handheld Tools
## 4 Validation Experiments and Results
### Haptic Rendering Experiments  
This group of experiments had two stages. In the first stage, we recorded data from a real-life object, in this case, a tennis ball, to build a simple haptic model. In the second stage, we haptic-rendered a virtual tennis ball based on our model.  
We built a test rig to measure force versus deflection from a real-life tennis ball. This data was the basis of our haptic model. The ball was confined just above the haptic-tip, as shown in Figure 7, and deflected by the hexapod using a spherical probe with a 10 mm radius. The tool tracker was not used in this experiment. The instantaneous position of the probe's tip was obtained from the hexapod at 1 kHz and recorded alongside the corresponding force vector.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Velocity (mm/s)** & \multicolumn{2}{c}{**0**} & \multicolumn{2}{c}{**20**} & \multicolumn{2}{c}{**40**} \\ \hline
**Error (mm)** & **RMSE** & **MAE** & **RMSE** & **MAE** & **RMSE** & **MAE** \\ \hline \(x\) & 0.0802 & 0.0779 & 0.2734 & 0.2542 & 0.5117 & 0.4883 \\ \(y\) & 0.0669 & 0.0659 & 0.2746 & 0.2503 & 0.4891 & 0.4675 \\ \(z\) & 0.1197 & 0.1192 & 0.2494 & 0.2296 & 0.4151 & 0.3761 \\ \(\sqrt{x^{2}+y^{2}+z^{2}}\) & 0.1588 & 0.1579 & 0.4609 & 0.4242 & 0.8206 & 0.7736 \\ \hline \hline \end{tabular} RMSE: root mean square error; MAE: mean absolute error.  
\end{table}
Table 1: Relative error in tooltip position tracking: tool tracker versus hexapod.  
Figure 6: Experiment setup for tool tracking validation.  
Data was collected for three different indentations of the ball and each experiment was repeated five times. The first indentation (A in Figure 7) was vertically upwards along the radius of the ball. The second one (B in Figure 7) was also vertically upwards but 10 mm offset to the center of the ball. The third one (C in Figure 7) was along the radius of the ball but 10\({}^{\circ}\) offset to the vertical axis. As expected, the data shows a hysteresis loop for a press and release cycle. Hence, we fitted two 4 th order polynomials for each cycle, i.e., one for press one for release, and used them as reference curves (Figure 8) in haptic rendering experiments.  
In haptic rendering experiments, an experienced user manually replicated the indentations A, B, and C on a virtual tennis ball from above by using a handheld tool. Figure 9 shows the real and mixed reality views of the indentations. Tool tracking was adapted to guide the user to the correct tool position and orientation. The ETHD limits the user at the maximum deflection (i.e., 6 mm). The instantaneous deflection and the applied force is recorded at every cycle of the haptic loop, which runs at 1 kHz frequency. Results for all indentations show good agreement with the reference curves in Figure 8. The RMSE and MAE values are listed in Table 2. Figure 10 shows the results of five experiments where the user performs the indentation A. Zoomed sections show that the repeatability is within 0.2 N.  
Figure 8: Measured and simulated force versus deflection plots for indentations (**A**–**C**).  
Figure 7: Test rig for measuring force versus deflection.