# Formation Control of Dual Auto Guided Vehicles Based on Compensation Method in 5G Networks
## 3 Formation Control System Design
### Discussion on Control Method Considering 5G Delay  
The time delay caused by the 5G transmission and control cycle has been analyzed in Section 3.1. These delays cannot be ignored in real-time systems, and control method needs to be considered to reduce the impact of delays on the system. There are two main directions to reduce the impact of delay on the control system. One is to modify the network configurations to reduce the delay as much as possible. The other is to design a control method that considers the delay. This paper uses compensation control method to design the control system considering 5G delay.  
The idea of the compensation control method is to estimate the current state of the system by using the delay value and the state model, and then compensate the control  
Figure 6: Total delay in multi-cycle system.  
signal to reduce the influence of delay on the control system. Most industrial motion equipment has a relatively complete motion state model, which makes it possible to estimate its posture. Meanwhile, for different control objects, the compensation method can be quickly transplanted. Delay estimation is a common algorithm for all equipment. For each equipment, it only needs to replace the state model according to its own.  
The scenario studied in this paper is of two AGVs in collaborative transport. It is necessary to ensure that the AGVs in the transport processing could maintain a stable formation. The leader-follower method is widely used due to its high reliability. The idea of the leader-follower method is to designate one AGV as the leader and the other AGVs as followers. The followers keep the distance and angle from the leader. In this paper, the leader AGV sends its posture to the follower and the follower regulates its motion state according to its own posture and the posture of the leader after receiving. To ensure that single AGV can operate stability in poor network conditions, the path tracking control still operates in local. The formation control will offer additional velocity command to regulate the corresponding posture to leader AGV. The actual planning velocity will be a composition of path tracking velocity and formation velocity. Therefore, the content of compensation is that the follower uses the time delay value obtained in Section 3.1 and the motion model of the AGV to obtain the current posture of the leader AGV then obtain the formation control signal.  
Figure 7 shows the control system structure of follower AGV. \(RTT\) is the round-trip time measured by follower AGV and \(\tau\) is the estimated E2E delay of the data from leader AGV. \(P_{L}\), \(q_{L}\) are the posture and velocity of leader AGV in data packet, and \(\textbf{P}^{\prime}_{L}\) is the estimated posture of leader AGV in current time. \(\textbf{P}_{Fr}\), \(q_{Fr}\) are the planning posture and velocity of follower AGV. \(q_{r}\) is the path tracking velocity of follower AGV, and \(\Delta q\) is the additional formation velocity of follower AGV. \(q_{c}\) is the actual command velocity composed by \(q_{r}\) and \(\Delta q\). \(\omega\) is the actual command angle velocity of drive wheels.\(\textbf{P}_{F}\), \(q_{F}\) are the posture and velocity of follower AGV.