## 3 Vehicle Model and Experimental Setup
### Experimental Setup  
The experimental validation of the proposed method is done using an all-terrain vehicle (ATV) built for the BAJA SAE-India student competition, as shown in Figure 3. The vehicle is equipped with a double-wishbone front suspension and a semi-trailing-arm rear suspension (for details, see [31]). The front suspensions have Float 3 and the rear suspensions have Float 3 EVOL R shocks [32]. The suspensions and tires are characterized on an MTS 850.25 damper test rig and MTS 370.10 elastomer test rig at the National Automotive Test Tracks (NATRAX) facility of the Government of India at Indore [33]. The suspension and tire mounted on the test rig is also shown in Figure 3a.  
The vehicle chassis parameters (sprung mass, C.G. location and roll and pitch inertias) are obtained from the detailed CAD model of the vehicle, as shown in Figure 3b. The vehicle parameters \(P\) obtained from rig testing (suspension and tire) and the CAD model are reported in Table 2.  
From measured suspension properties using the test rig (\(k_{f,r}\) and \(c_{f,r}\)), the equivalent suspension properties at the wheels (\(K_{f,r}\) and \(C_{f,r}\)) are obtained after multiplying by the square of the motion ratios. These motion ratios are functions of the suspension geometry and can be determined either from the ADAMS half car suspension models or can be measured experimentally [34]. In this paper, the motion ratios of the BAJA ATV are measured experimentally by raising and lowering the wheel of interest and measuring the spring compression and extension; for details of these experiments, see [35].  
The vehicle ride performance is characterised by recording the acceleration responses of the suspension-to-body attachment points \(B_{i}\) and the wheel accelerations measured at axle locations \(A_{i}\). For this purpose, the vehicle is instrumented with MEMS-based ADXL326 accelerometers (a total of eight). These accelerometers are mounted on wheel axle locations and suspension-to-body pivot points using magnetic mounting strips (see Figure 4a). The data acquisition system consists of a FAT32 microSD card module and an Arduino ATMega328P microcontroller board. These systems are compatible with a breadboard, making it easy to connect them together and power the circuit using a standard 9V battery. The data acquisition system is mounted on the vehicle dashboard (see Figure 4b).  
\begin{table}
\begin{tabular}{l l l l l l l l l l} \hline
**Parameters** & \(k_{f}\) & \(K_{f}\) & \(k_{r}\) & \(K_{r}\) & \(c_{f}\) & \(C_{f}\) & \(c_{r}\) & \(C_{r}\) & \(l\) \\
**Values** & 25 & 10.5 & 15 & 6.5 & 1.5 & 0.63 & 1.36 & 0.59 & 1.6 \\
**Parameters** & \(K_{t}\) & \(C_{t}\) & \(M_{\text{uf}}\) & \(M_{\text{ur}}\) & \(l_{xx}\) & \(l_{yy}\) & \(M_{s}\) & \(l_{f}\) & \(b\) \\
**Values** & 40 & 0.2 & 15 & 12.5 & 257 & 246 & 240 & 0.85 & 1.2 \\ \hline \end{tabular}
\end{table}
Table 2: Baseline vehicle parameters \(P\) known beforehand.  
Figure 3: (**a**) Testing the suspension and tire on MTS rigs at NATRAX, Indore. (**b**) CAD model of the ATV used to estimate chassis parameters.  
In addition to this, a gyro sensor and a vertical accelerometer is also mounted at the C.G. location of the vehicle in order to record the pitch and roll rates and the vertical acceleration of the sprung mass, which are used for vehicle characterisation in addition to the axle and body point acceleration responses.