## 2 Analysis of Autonomous Control Algorithm for Mining Electric locomotives
### Adhesion and Creep  
After the analysis, we will focus on the constraints considered in the algorithm design process. When designing the algorithm, conditions are taken into consideration,such as speed limits, road obstacles, and safe following of mining electric locomotives. However, the road surface of the coal mine roadway is very slippery and muddy. The contact condition between the wheels and rails is also one of the factors that needs to be carefully considered.  
Two conditions must be met simultaneously to enable rail vehicles to run along the track [17]. One is that the rotating torque is applied to the moving wheel, and the other is that the contact between the moving wheel and the steel rail has a frictional effect. As shown in Figure 6, the moving wheel is in contact with the track due to the vertical force \(P\) applied by the vehicle body, and generates a motion trend under the torque \(M\) transmitted by the transmission device [18]. Assuming that there is static friction between the wheel and rail, the force \(F\) generated by the moving wheel on the track is equal in magnitude to the force \(F\) generated by the track on the moving wheel, but in opposite directions. For the mining electric locomotive, rim traction force \(F\) is the driving traction force. But the wheels of rail vehicles mostly have conical tread, which can cause elastic-plastic deformation when the wheels come into contact with the rail. The mining electric locomotive is subjected to shock and vibration during operation. When the wheel set rolls on the rail, it is accompanied by longitudinal and transverse sliding. There is no pure static friction state between the wheel and rail, but rather'slight movement in stillness' and'slight sliding in rolling'. This phenomenon is creep, also known as adhesion between wheel and rail. The maximum longitudinal horizontal force in the adhesive state is the adhesive force, and the ratio of adhesive force \(F_{H}\) to vertical load \(P\) is the adhesive coefficient \(\mu\). According to Hertz elasticity contact theory [19], the contact area between the wheel and rail is approximately elliptical. The area where the wheel and rail are relatively stationary and do not slide under the action of positive pressure is called the adhesion zone. The area where slight sliding occurs is called the creep zone. As the driving torque \(M\) increases, the creep zone becomes larger and the adhesion zone decreases to 0, and the wheels are in a sliding state. Therefore, when the vehicle is in traction or braking conditions, if the traction or braking force is greater than the adhesion between the wheels and rails, the wheels will idling or slip. This phenomenon can cause damage to the wheel rail tread and even affect the safety of rail vehicles.  
According to the International Union of Railways (UIC) definition of creep rate, the creep rate is represented as follows:  
Figure 6: Schematic diagram of adhesion between wheels and rails.  
\[\left\{\begin{array}{l}CR_{longitudinal}=\frac{(VW_{longitudinal}-VT_{longitudinal})_{At} \text{ {the contact patch}}}{Nominal\text{ {forwardvelocity}}}\\ CR_{lateral}=\frac{(Wheel\text{ {lateral velocity}}-Track\text{ {lateral velocity}})_{At}\text{ {the contact patch}}}{Nominal\text{ {forwardvelocity}}}\\ CR_{spin}=\frac{(Wheel\text{ {angular velocity}}-Track\text{ {Wheel angularvelocity velocity}})_{At}\text{ {the contact patch}}}{Nominal\text{ {forwardvelocity}}}\end{array}\right. \tag{10}\]  
Based on the operating results when the friction between the wheel and rail is 0.3 (Figure 2), it can be observed that there is a sudden change in the interaction of wheel and rail during vehicle acceleration, and the creep rate value is abnormal.