# Development and Evaluation of the Traction Characteristics of a Crawler EOD Robot
## 3 Geometric Configuration of the Crawler Propeller
### Conditions Regarding the Crossing of the Step Type Obstacle  
The step type obstacle is often encountered in urban environments (curbs, stairs in buildings, etc. ), which requires a detailed study of this process for an optimal geometric configuration of the crawler engine (Figure 4). The crossing of the step-type obstacle presupposes the obligatory completion of two successive stages: the approach to the obstacle; crossing the obstacle. The ascending force arises \(T_{asc}\) [N]. Its value is limited by: \(\varphi_{t}\) [\(-\)] and \(\varphi_{\text{obs}}\) [\(-\)]. \[T_{t}=\varphi_{t}\cdot G\ [N], \tag{1}\]  
where: \(T_{t}[N]\)--traction force, manifested at the wheel; \(G[N]\)--the weight of the robot. The ascending force is given by the following relation:  
\[T_{asc}=\varphi_{obs}\cdot Z=\varphi_{obs}\cdot T_{t}=\varphi_{obs}\cdot \varphi_{t}\cdot G\ [N], \tag{2}\]  
where: \(T_{asc}[N]\)--the ascending force, manifested in front of the tensioning roller, at the contact of the track with the obstacle. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Characteristics** & **U.M.** & **Amount** \\ \hline Fully equipped mobile robot table & kg & 250 \\ Maximum speed on horizontal terrain & m/s & 1 \\ Maximum slope when walking straight & deg & 30 \\ The height of the steps & mm & 150 \\ Average ground pressure & MPa & 0.05 \\ The height of the stepped obstacle crossed & mm & 225 \\ The width of the ditch crossed & mm & 800 \\ Depth of water on hard horizontal ground & mm & 100 \\ Race of turns & mm & continuously variable \\ Minimum turning radius & mm & 0-rotation \\ Travel control & - & wireless \\ The mass of the manipulated object & kg & 25 \\ Range of the manipulator arm & mm & 1000 \\ Rotate the manipulator arm to the side & deg & 30 \\ The gripping length of the gripping mechanism & mm & 150 \\ Arm displacement position & - & folded/extended \\ Omnidirectional video camera for travel & buc. & 2 \\ Video camera for inspection & buc. & 2 \\ Riding the platform while working & - & no \\ Working autonomy & h & 6 \\ Construction type & - & modular \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Type-dimensional and actuation requirements for the EOD robot under analysis. Figure 4: Geometric diagramming of the robot while approaching the step-type obstacle. The limiting condition for them of climbing the obstacle is:  
\[T_{asc}(L_{a}+l_{a})=G\cdot x_{G}\ [N], \tag{3}\]  
\[\varphi_{obs}\varphi_{l}\geq\frac{x_{G}}{L_{a}+l_{a}}\equiv\varphi_{obs}\varphi_{ l}\geq\frac{x_{G}}{L}, \tag{4}\]  
where: CG--weight center; \(y_{G}[m]\)--distance from the CG to the running surface, on the axle Oy; \(r_{m}[m]\)--drive wheel radius; \(r_{a}[m]\)--the radius of the tension roller; \(h_{a}[m]\)--distance from the axis of the tension roller to the tread, on the axis Oy; \(\alpha_{a}[\text{deg}]\)--the angle of inclination of the ascending branch of the track to the axis Ox; \(x_{G}[m]\)--distance from the CG to the axle of the drive wheel, on the axle Ox; \(L_{a}[m]\)--the distance from the axle of the drive wheel to the last roller, the one at the beginning of the ascending branch of the track, on the axis Ox; \(l_{a}[m]\)--distance from the center of the last roller to the center of the tension roller, on the axis Ox. The coefficient of friction between the tracked thruster and the obstacle (Figure 5), \(\mu\)\([-]\), is given by the following calculation relation [60; 61; 62]:  
\[\mu\geq\frac{L-L_{1}}{L_{1}+R/\sqrt{1-\left(\frac{h-R}{L}\right)^{2}}}\ [-], \tag{5}\]  
where: \(h[m]\)--the height of the obstacle step, on the axis Oy; \(\Delta=h-h_{a}\ [m]\)--the difference between the height of the step obstacle and the height of the axis of the tension roller, on the axis Oy; \(L_{1}[m]\)--the distance from the axis of the drive wheel to the CG, along the longitudinal axis of the robot; \(L-L_{1}[m]\)--the distance from the CG to the axis of the tension roller, along the longitudinal axis of the robot; \(\beta[\text{deg}]\)--the angle of inclination of the longitudinal axis of the robot with respect to the axis Ox.