# Research on the Obstacle-Avoidance Steering Control Strategy of Tracked Inspection Robots
## 3 Kinetics of Tracked Robot during Steady-State Turning  
### Traction Force Analysis  
To calculate the traction force of the robot track, the following assumptions were made.  
1. The robot moves at a low and uniform speed on the horizontal ground.
2. When the robot is driving, the deformation resistance of the tracks on both sides is equal.
3. Ignoring the influence of track width, the tracks on both sides of the ground have an equal and symmetric appearance, and the pressure at the track contact area is equal and evenly distributed along the track-length direction of the robot.
4. The influence of the swing-arm track on the steering performance of the robot is ignored.  
Therefore, the load per unit length of the robot track is:  
\[q=\frac{G}{2L} \tag{1}\]  
where \(G\) is the weight of the robot and \(L\) is the length of the robot track in contact with ground.  
The driving forces of the track interfere with each other while controlling tracked vehicles using driving force feedback. Therefore, the driving force distribution that decouples the driving forces must be considered [21; 22]. During the steering process of the robot, there are many types of force on the track, and the different steering modes bear different forces. In [PERSON]'s model, the shear forces at any point on the track-soil interface were assumed to have a direction opposite to that of the sliding velocity of that point with respect to the ground [23]. The force of the robot during steering is shown in Figure 2. During steering, the two tracks of the robot simultaneously provide traction. Point M of the track on the right side of the robot slipped during the steering process. The tangential force \(F_{M}\) caused by sliding is opposite to the sliding velocity \(v_{jM}\), and the component force \(F_{My}\) in its \(y\)-direction constitutes the traction force of the robot. Consider a micro-element Dy at point M, and the tangential reaction force on this micro-element is proportional to the positive pressure per unit length. The traction force on the right track of the robot is:  
\[F_{qRy}=\int_{-L/2-y_{y}}^{L/2-y_{y}}q\mu\sin(\pi+\alpha_{R})dy \tag{2}\]  
where \(\mu\) is the friction resistance coefficient \(\mu=\frac{\mu_{\max}}{0.925+0.15\rho};\rho=R/B\), \(R\) is the steering radius, \(B\) is the distance between the center of the robot's driving wheel tracks, and \(\rho\) is the relative steering radius.  
\(\sin\alpha_{R}=\frac{v_{Ry}}{\sqrt{v_{Ry}^{2}+v_{Rx}^{2}}}=\frac{-s_{R}}{ \sqrt{s_{R}^{2}+\left(y+s_{y}\right)^{2}}}\), and the above equation is integrated to obtain:  
\[F_{qRy}=\frac{\mu G\alpha_{R}}{2}ln\Big{|}\
icefrac{{1}}{{a_{R}}}+\sqrt{ \
icefrac{{1}}{{a_{R}^{2}}}+1}\Big{|} \tag{3}\]  
where \(a_{R}=\frac{s_{R}}{\left(L/2\right)}\), \(a_{R}\) is the relative lateral offset of the right track.  
Similarly, the traction force expression of the left track can be expressed as:  
\[F_{qLy}=-\frac{\mu Ga_{L}}{2}ln\Big{|}\
icefrac{{1}}{{a_{L}}}+\sqrt{ \
icefrac{{1}}{{a_{L}^{2}}}+1}\Big{|} \tag{4}\]where \(a_{L}=\frac{s_{l}}{(L/2)}\) and \(a_{L}\) are the relative lateral offsets of the right track, and its negative sign indicates that it is in the opposite direction.