# Research on the Obstacle-Avoidance Steering Control Strategy of Tracked Inspection Robots
## 4 Analysis of Steering Characteristics of Tracked Robot  
### Relationship between Angular Velocity and Steering Radius  
When the body structure of the tracked robot is determined, the transmission relationship between the robot driving wheel motor and track wheel is also determined. When the linear velocity of the driving wheel is determined, the relationship between the relative steering radius, steering angular velocity of the robot, and driving parameters can be obtained as follows:  
\[\left\{\begin{array}{l}\rho=\frac{1}{2}\frac{v_{R}+v_{L}}{v_{R}-v_{L}}=\frac{1 }{2}\frac{w_{R}+w_{L}}{w_{R}-w_{L}}\\ w=\frac{v_{R}+v_{L}}{2R}=\frac{w_{R}+w_{L}}{2R}\text{R}_{w}i_{L}i_{L}\end{array}\right. \tag{12}\]  
When the tracked robot turns left, its right track always produces forward thrust, so it will slip. However, the left track may produce forward thrust or braking force; therefore, it is not clear whether the left track will skid or slip. Therefore, the relative steering radius and steering angular velocity of the tracked robot can be expressed as:  
\[\left\{\begin{array}{l}\rho_{s}=\frac{1}{2}\frac{w_{R}i_{R}+w_{L}i_{L}}{w_{ R}i_{R}-w_{L}i_{L}}\\ w_{\text{s}}=\frac{w_{R}i_{R}+w_{L}i_{L}}{2R}\text{c}\end{array}\right. \tag{13}\]  
where \(i_{L}\) and \(i_{R}\) are the skid and slip states, respectively, of the left and right tracks of the robot. When the left track slips \(i_{L}=1-i_{s}\), and \(i_{L}=1+i_{t}\) when the left track skids. The transmission coefficient from the robot driving motor to the track wheel is \(\text{c}\), \(\text{c}=\text{R}_{w}i_{c}i_{d}\).  
From the above equation, it can be seen that the relative steering radius \(\rho\) of the robot is not related to the robot transmission ratio but only to the angular velocity of the robot's driving motor. Because \(s_{R}\) and \(s_{L}\) are the lateral relative offsets of the robot's two tracks, the velocity of the robot's two tracks can also be expressed as:  
\[\left\{\begin{array}{l}v_{R}=w_{R}c-\frac{v_{R}+v_{L}}{2R}s_{R}\\ v_{L}=w_{L}c+\frac{v_{R}+v_{L}}{2R}s_{L}\end{array}\right. \tag{14}\]  
It can be obtained by the transformation of the formula:  
\[\left\{\begin{array}{l}v_{R}=\frac{2 kw_{R}-w_{R}s_{L}-w_{L}s_{R}}{2R+s_{R}-s _{L}}c\\ v_{L}=\frac{2 kw_{R}+w_{R}s_{R}+w_{L}s_{R}}{2R+s_{R}-s_{L}}c\end{array}\right. \tag{15}\]  
Figure 4: Relationship between \(a_{R}\), \(a_{L}\) and \(\rho\) under typical road conditions.  
Additionally, the relationship between the relative steering radius of the robot \(\rho\) and the angular velocity \(w\) of the motor can be expressed as:  
\[\left\{\begin{array}{l}\rho=\frac{1}{2}\frac{w_{R}(1-\frac{s_{L}}{L})+w_{L}(1- \frac{s_{R}}{L})}{(w_{R}-w_{L})}\\ w=\frac{(w_{R}+w_{R})}{2K+s_{R}-s_{L}}c\end{array}\right. \tag{16}\]  
When \(s_{H}\to 0\), \(s_{L}\to 0\), that is, the relative offset of the robot's two tracks toward each other is zero, which is the theoretical steering motion, this formula is consistent with Equation (12).  
After converting the formula, the relationship between the angular velocity of the left and right tracks of the robot can be obtained as follows:  
\[w_{L}=\frac{s_{L}-B+2\rho B}{(s_{R}-B-2\rho B)}w_{R} \tag{17}\]  
When the road parameters, robot structural parameters and relative steering radius are determined, \(s_{R}\) and \(s_{L}\) can be obtained from Figure 4. Additionally, the angular velocities with the motors on the left and right sides of the robot corresponded one-to-one.