# Reservation-Based 3D Intersection Traffic Control System for Autonomous Unmanned Aerial Vehicles
## 4 UAV's Behavior in the Approaching Area
### Avoiding Collision with a UAV Ahead  
For \(UAV_{B}\) to avoid collision with \(UAV_{A}\), \(UAV_{B}\) should control its speed such that its distance from \(UAV_{A}\) is always greater than or equal to the minimum allowed distance between UAVs, \(d_{min}\). To control its speed, \(UAV_{B}\) determines \(r_{B,j+1}\) at \(t_{j}\) such that its distance from \(UAV_{A}\) is always at least \(d_{min}\), where \(r_{min}\leq r_{B,j+1}\ \leq r_{max}\). In order to determine \(r_{B,j+1}\) such that the distance between \(UAV_{B}\) and \(UAV_{A}\) is always at least \(d_{min}\) until \(UAV_{A}\) enters the intersection, \(UAV_{B}\) should know the rates that \(UAV_{A}\) will use from \(t_{j+1}\) until it enters the intersection. However, \(UAV_{B}\) cannot obtain this information since \(UAV_{A}\) determines the acceleration rate it will use only one \(\Delta t\) in \begin{table}
\begin{tabular}{c l} \hline \hline
**Symbol** & **Definition** \\ \hline \(\Delta t\) & Time is discretized every \(\Delta t\) \\ \hline \(r_{min}\) & Fastest possible negative deceleration rate of all UAVs \\ \hline \(r_{max}\) & Fastest possible positive acceleration rate of all UAVs \\ \hline \(d_{min}\) & Minimum allowed distance between two UAVs \\ \hline \(dr_{max}\) & Absolute value of \(r_{min}\) \\ \hline \(s_{B,j}\) & Speed of \(UAV_{B}\) at \(t_{j}\) \\ \hline \(r_{B,j}\) & Acceleration/ deceleration rate of \(UAV_{B}\) from \(t_{j}\) to \(t_{j+1}\) \\ \hline \(d_{B,j}\) & Distance \(UAV_{B}\) travels from \(t_{j}\) to \(t_{j+1}\) \\ \hline \(d_{A,B,j}\) & Distance between \(UAV_{A}\) and \(UAV_{B}\) at \(t_{j}\). \\ \hline \(d_{A,B}^{stop}\) & Distance between \(UAV_{A}\) and \(UAV_{B}\) when both have stopped in the lane \\ \hline \(r_{B,j+1}^{d_{min}}\) & Value of \(r_{B,j+1}\) such that \(d_{A,B}^{stop}\) is equal to \(d_{min}\) \\ \hline \(r_{B,j+1}^{s_{max}}\) & Value of \(r_{B,j+1}\) such that \(s_{B,j+2}\) is equal to \(s_{max}\) \\ \hline \(d_{A,j+1}^{stop}\) & Distance \(UAV_{A}\) travels from \(t_{j+1}\) until it stops \\ \hline \(r_{B,j}^{school}\) & Time \(UAV_{B}\) is scheduled to enter the intersection from \(t_{j}\) \\ \hline \(t_{B,j}^{inter}\) & Time \(UAV_{B}\) spends from \(t_{j}\) until it enters the intersection \\ \hline \(r_{B,j+1}^{q2}\) & Constant acceleration/deceleration rate \(UAV_{B}\) uses from \(t_{j+1}\) until it reaches the exit of the queueing zone \\ \hline \(t_{B,j}^{q2}\) & Time \(UAV_{B}\) spends in the queueing zone from \(t_{j}\) \\ \hline \(t_{B}^{quit}\) & Time \(UAV_{B}\) spends waiting at the entrance of the acceleration zone \\ \hline \(t_{B}^{q2}\) & Time \(UAV_{B}\) spends in the acceleration zone \\ \hline \(r_{B,j+1}^{stop}\) & Deceleration rate \(UAV_{B}\) uses from \(t_{j+1}\) such that its speed at the entrance of the acceleration zone equal to zero \\ \hline \(t_{B,j}^{sinter}\) & Value of \(t_{B,j}^{inter}\) when \(t_{B}^{initial}\) is set to zero and \(r_{B,j+1}^{q2}\) is set to \(r_{B,j+1}^{stop}\) \\ \hline \(s_{B}^{qzen}\) & Speed of \(UAV_{B}\) when it reaches the entrance of the acceleration zone \\ \hline \(t_{B}^{qcc}\) & Time \(UAV_{B}\) spends to accelerate from \(s_{B}^{qzen}\) to \(s_{max}\) in the acceleration zone \\ \hline \(d_{B}^{qcc}\) & Distance \(UAV_{B}\) travels while accelerating from \(s_{B}^{qzen}\) to \(s_{max}\). \\ \hline \(t_{B}^{maintain}\) & Time \(UAV_{B}\) spends to reach the exit of the acceleration zone while maintaining its speed after reaching \(s_{max}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: List of symbols used in this section. advance, just like \(UAV_{B}\). This means, \(UAV_{A}\) determines \(r_{A,j+1}\) at \(t_{j}\). Hence, at \(t_{j}\), \(UAV_{B}\) only knows \(r_{A,j-1}\). To address this problem, we assume that \(UAV_{A}\) decelerates at the fastest possible rate, \(dr_{max}\), from \(t_{j+1}\) until its stops. We assume this case since the distance between them at any time in the future will be greater than \(d_{min}\) when \(UAV_{A}\) either accelerates or decelerates at a rate smaller than \(dr_{max}\).