## 6 Field Experiments  
### Experimental Setup  
Moving from simulations to field experiments, we present the experiments carried out in CERN's experimental test facilities. A youBot [47] mobile robot platform (shown in Figure 14a) is used as the relay node, and two stand-alone Raspberry Pi mini-computers (shown in Figure 14b) are used as the server and client nodes. As the youBot has omni-directional wheels, navigation is efficient given the space restrictions in constrained spaces (hostile environments). Figure 15 shows the experimental setup in an indoor facility containing large metallic objects. Due to the nature of the experiments and the confined space in the environment, the need to have an obstacle avoidance feature for the relay node is inevitable. We detect obstacles within a 4-m range of the robot platform using a 2D laser range (LiDAR) sensor and make use of a basic obstacle avoidance system using the vector field histogram technique [48]. Figure 14: Raspberry Pi and youBot being used as client/server and relay nodes, respectively. (**a**) Multiple spatially-distributed RSS sensors on the relay node; (**b**) Raspberry Pi computer (connected to a battery) used as client or server nodes. Figure 15: Experimental setup of the server-relay-client nodes at a CERN facility. As the robot platform used is velocity-controlled, the position controller part of the algorithm is modified to a velocity controller using state-space transitions. The control equations for the relay node located in the inertial frame of reference with pose \((x,y,\theta)\) are given as follows:  
\[\left[ \begin{array}{c}x_{t}\\ y_{t}\\ \theta_{t}\end{array} \right]=\left[ \begin{array}{c}x_{t-1}\\ y_{t-1}\\ \theta_{t-1}\end{array} \right]+\left[ \begin{array}{ccc}\pm\vartheta_{X}&0&0\\ 0&\pm\vartheta_{Y}&0\\ 0&0&\pm\omega\end{array} \right]\left[ \begin{array}{c}\tau_{\theta}\\ \tau_{\theta}\\ \tau_{\omega}\end{array} \right] \tag{24}\]  
where \(\vartheta_{x},\vartheta_{y}\) and \(\omega\) are the longitudinal, transverse and rotational velocities, respectively. \(\tau_{\theta}\) and \(\tau_{\omega}\) are time constants that determine the displacements \(\delta x,\delta y\) and \(\delta\theta\) in \(x,y,\,\mathrm{and}\,\theta\) directions. \[\tau_{\vartheta}=\frac{\sqrt{(\delta x)^{2}+(\delta y)^{2}}}{\vartheta}\; \mathrm{and}\;\tau_{\omega}=\frac{\delta\theta}{\omega}\]  
Because the laser scanner is fitted on the front side of the relay node, the relay robot is made to move only in the forward direction, and therefore, it will first turn towards the necessary control direction and then move to the corresponding position in each iteration. This means that the control output of algorithm has been transferred from the Cartesian space \((x,y)\) to the polar domain \((r,\theta)\), as follows. \[r=\sqrt{x^{2}+y^{2}};\;\;\;\;\;\theta=\tan^{-1}(y/x);\;\;\;\;\;\text{if($x<0$) then $\theta=\theta+\pi$} \tag{25}\]  
The wireless devices used are the following: Edimax EW-7811 un WiFi USB card as the \"access points (transmitter)\" on the client and server nodes and Zyxel NWD2105 WiFi USB card as the \"receiver stations\" (RSS sensors) on the relay node. The spatial distribution of the RSS sensors on the relay node can be seen in Figure 14a. Each receiver is set to Channel 3 in the IEEE 802.11n standard 2.4-GHz spectrum, and all of the receivers have the same characteristics (internal omni-directional antenna, receiver sensitivity (\(R_{\chi}\)) = \(-182\,\)dBm). They are placed on the relay node with the same orientations to minimize antenna orientation effects in the RSS. The RSSI metric, which directly provides the RSS values in dBm (as the Zyxel NWD2105 uses the RALink 3070 driver), is assessed using the iwconfig command in Linux. Each RSSI sample is measured at a 100-Hz sampling rate, and then, the corresponding temporal and spatial RSS filters are employed, as described in Section 4.4. The wireless receivers on the relay node are separated with \(\Delta x=16\,\mathrm{cm}\) and \(\Delta y=20\,\mathrm{cm}\).