## 2 Structure Overview and Modeling of a DDTV
### Longitudinal Dynamics of a DDTV  
As the walking structure of a tracked vehicle and a wheeled vehicle varies greatly, a suitable longitudinal dynamic model should be built appropriately for a DDTV. There are three main components including the vehicle body, the tracks, and the wheels, as shown in Figure 2, so that several freedoms of motion should be taken into consideration, and they are the rolling of the drive wheel, the longitudinal motion of the vehicle body, the rotational motion of the track, and the rolling of the road wheels, idler, and support rollers, respectively. Assuming that the track is uniform and soft and there is no slip or  
Figure 1: Schematic diagram of a dual-motor electric drive tracked vehicle (DDTV) structure. MCU, motor control unit; TCU, transmission control unit; ECU, engine control unit. slide between the track and drive wheel, or the track and road wheels, the idler, or support rollers, a semi-vehicle longitudinal dynamic model in the braking situation can be established as follows. Selecting the forward direction of the vehicle and the corresponding rotational direction of the drive wheel as the positive direction, the dynamics of the longitudinal motion of the vehicle body and rolling of the drive wheel when braking can be denoted as:  
\[\left\{ \begin{array}{c}F_{x}+F_{aero}+M\dot{v}_{x}=0\\ J\dot{\omega}-F_{t}r+T_{b}=0\end{array} \right.\, \tag{1}\]  
where \(F_{x}\) is the track-ground resultant force of one track, \(F_{aero}\) is half of the air drag, \(M\) is half of the DDTV's total mass, \(v_{x}\) is the longitudinal velocity of the vehicle, \(J\) is the rotational inertia of the drive wheel and transmission system attached to it, \(\omega\) is the rotational speed of the drive wheel, \(F_{t}\) is the force applied on the drive wheel by the track, \(r\) is the radius of the drive wheel, and \(T_{b}\) is the braking torque applied on the drive wheel by the transmission system. The track is a component that turns the rotation of the drive wheel into the motion of the vehicle and causes the rotation of the road wheels, idler, and support rollers. Since the mass of the track and the rotational inertia of the attached wheels are far more than an amount that can be ignored and the speeds of each part of the track are not the same due to its irregular shape, a method of calculating the equivalent rotational inertia (ERI) with respect to the rotational axis of the drive wheel based on energy conservation theory can be used to simplify the dynamics of tracks and wheels attached to them [34]. The ERI of the wheels and track can be expressed as follows according to [35]:  
\[J_{eri}^{ru}=n_{ru}J_{ru}\frac{r^{2}}{r_{ru}^{2}}\ \, \tag{2}\]  
\[J_{eri}^{sr}=n_{sr}J_{sr}\frac{r^{2}}{r_{sr}^{2}}\ \, \tag{3}\]  
\[J_{eri}^{l}=J_{l}\frac{r^{2}}{r_{l}^{2}}\, \tag{4}\]  
where \(J_{ru}\), \(J_{sr}\), and \(J_{l}\) are the rotational inertia of the road wheel, support roller, and idler, respectively, and \(n_{ru}\), \(r_{ru}\), \(n_{sr}\), \(r_{sr}\), and \(r_{l}\) are the quantity and the radius of them. The track can be separated into four parts, which are the front part, rear part, upper part, and bottom part, respectively, as shown in Figure 2, and the ERI of them can be expressed as follows according to [34; 35]:  
\[\left\{ \begin{array}{c}I_{ori}^{t-f}=2m_{t-r}r^{2}(1-\cos\varphi_{A})\\ I_{ori}^{t-r}=2m_{t-r}r^{2}(1-\cos\varphi_{D})\\ I_{ori}^{t-u}=4m_{t-u}r^{2}\end{array} \right.\, \tag{5}\]  
Figure 2: Schematic diagram of force and torques acting on a DDTV when braking. In Equation (5), \(m_{t,f}\), \(m_{t,r}\), and \(m_{t,u}\) are the masses of the first three parts of the track, and the ERI of the bottom is zero due to the speed of it when the slip of the track and ground is ignored.