A Low-Cost Solution for Leader-Follower Formation Control of Multi-UAV System Based on Pixhawk

In recent years, cooperative multi-UAV systems have shown great performance in a variety of potential applications. Aiming at the problem of fixed-wing UAVs cooperative formation flight, this paper presents a low-cost system based on Pixhawk autopilot for keeping the shape of the formation. The kinematic relationship of a leader-follower UAV formation is established and a fuzzy PID control law is designed for the follower to maintain the expected position relative to the leader. Wireless data transmission between the leader and followers is achieved by using several radio telemetry modules. The proposed formation control system is validated by a series of successful flight experiments using 3 small-scaled UAV models, which has proven its feasibility and reliability.


Introduction
The past few years have witnessed a rapid development in the field of unmanned aerial vehicle (UAVs), which are playing an increasingly important role in both military and civil sectors such as, search and rescue (SAR), traffic monitoring, power cable inspection and package delivery [1][2][3]. However, in a dynamic environment, as the difficulty and complexity of the tasks increase, a single UAV platform with limited payload and energy supply is not enough to execute different operations at the same time. So autonomous multi-UAV system is used to deal with the situation in which multiple UAVs form a team cooperating to perform a specified mission [4]. Combined with the latest technologies in fields like novel sensors, deep learning and machine vision, the multi-UAV system will become more and more intelligent, leading to a variety of potential applications [5]. This field has received great attention in recent years.
[6] presented a low-cost UAV formation flight control architecture and used three experimental flying wing models with expanded polypropylene (EPP) foam frame to detect the nuclear radiation. The contour mapping of the nuclear radiation is finally simulated. [7] presented a communication and autonomous control system for multi-UAVs in disaster response tasks, which demonstrated a combination of tracking data and scanning mission creating a high-quality safe map for the refugees after the disaster occurrence. In [8], a modular architecture of an autonomous UAV system for search and rescue (SAR) tasks using multiple quadcopters coordinated by a distributed control system, which is implemented in the Robot Operating System (ROS).
But there still exists great challenges in real applications that need to be carefully considered and solved, especially in dynamic complex environments, including task assignment, path planning, formation control and collision avoidance [9]. In [10], the path planning strategies for UAV swarm, formation maintenance and reconstruction are described, which looks forward to some potential  [11] proposed a cooperative formation control strategy with collision-avoidance capability for a multi-UAV system by using decentralized model predictive control (MPC) and consensus-based algorithm, which was finally validated by simulations. In [12], based on a combinatorial optimization model, a modified two-part wolf pack search (MTWPS) algorithm was proposed and a systematic framework was presented to solve the multi-UAV cooperative task assignment problem.
Formation control is one of the most important tasks for multi-UAV system. The formation strategies that research communities have studied in the past few decades are primarily divided into four categories: the leader-follower [13], behaviour-based [14], consensus-based [15] and virtual structure algorithms [16]. Compared with other three types, the leader-follower method is relatively a simple and feasible way to achieve formation maintenance, which is suitable for low-cost multi-UAV systems. In a leader-follower mode, one UAV is defined as the leader, while the others are controlled to follow the leader keeping a particular distance and bearing with respect to the leader. Quadrotor is a popular platform used in multi-UAV systems, due to its ability to hover with minimal translational velocity achieving a quasi-stationary state [17][18]. However, it is more difficult for fixed-wing UAVs to fly and maneuver while still maintaining the formation [19]. Kim et al [20], presented a modified nonlinear guidance logic for leader-follower formation control, which was tested via various numerical simulation. We believe that this method will achieve good performance, if it is implemented on an experimental multi-UAV system.
The motivation of this work is to develop a low-cost multi-UAV system based on Pixhawk autopilot [21], which enables multiple fixed-wing UAVs to fly in formation. The formation relative kinematic model is established based on geometric relationship between the leader and the followers. A fuzzy controller is designed to keep the close formation of multi-UAVs while flying along a certain route. The wireless data communication has been successfully established by using the radio telemetry modules supported by the Pixhawk-4 controller. The formation control system is experimentally validated by a successful flight test using 3 low-cost foam frame UAV models.

Model of Autopilot
For the i-th UAV in a formation, it is assumed that the following two decoupled autopilots are in place: heading-hold autopilot, and velocity-hold autopilot. Considering that the UAV's altitude remains unchanged in flight, the model of the autopilot can be simplified as follows [22]. 1 ( )  Figure 1 shows the kinematic relations between the leader and the follower in formation flight where a planar situation is considered. The heading and position of the leader in the inertial reference frame, provided by its navigation system, are transmitted to the follower through wireless communication. So a body fixed frame centered at i F , the instantaneous position of the i-th follower, is defined. The axis i x is aligned with the instantaneous velocity vector and the axis i y is along i F starboard wing.

Leader-Follower Formation Kinematics
is considered as an additional exogenous input to the system.

Control Design
The x-channel and y-channel scalar error are given by mixing the lateral position error, the longitudinal position error, the heading error and the velocity error as follows. ( e k y y k ( 7 ) A fuzzy proportional-integral-derivative (PID) controller is proposed shown below:

Experimental Setup
Most of the experimental UAV platforms are expensive with high-intensity body structure made of composite materials such as carbon fibre, glass fibre, and Kevlar fibre, which will definitely increase the cost. In this paper, a low-cost fixed wing UAV platform is used for formation flight tests, which are primarily made of expanded polyolefin (EPO) foam reinforced by wood laminates. The wingspan of the model UAV is only 1300 mm and the total take-off weight is less than 1.5 kg including all the onboard devices, which makes it highly portable. As shown in figure 2, Each UAV model is equipped with a Pixhawk-4 autopilot, and the two ports, Telemetry 1 and 2, are connected with radio telemetry modules to achieve wireless data transmission. Telemetry 1 is used to communicate with the ground station and Telemetry 2 is used to communicate with companion computers on the followers.

Flight Test Results
An autonomous formation flight test is shown in figure 3, figure 4, figure 5 and figure6. The leader UAV is the first one to take off and autonomously fly along a predefined route. After a few seconds, the followers take off and fly to the set altitude. Once the formation command is transmitted to the leader UAV, the two followers are controlled to follow the leader in a straight line. During the flight test, the three UAVs fly at different altitudes for collision avoidance. The formation changes several times from a line to a triangle to test the system, which is finally validated by good results.    After analysis of the flight logs recorded by each autopilot, the trajectory of the formation is shown in figure 7. The line in red is the trajectory of the leader UAV including the take-off and landing phase. The dotted line in blue and green are the trajectory of the follower 1and 2, respectively, and the positions where the two followers form and leave the formation are also given. The results show that the formation is well controlled by the system, whether the UAVs are in a line or triangle formation with acceptable lateral and longitudinal position errors. The formation maneuver will significantly increase the position error, such as making a turn with a small turn radius. This cannot be completely eliminated because of the transmission delay. We would like to improve the performance of the control system in the near future by upgrading the hardware configuration.

Conclusions
This paper presents a low-cost autonomous formation flight control system based on Pixhawk framework using three small-scaled UAV models. A leader-follower kinematic model is established and a fuzzy control law is proposed to eliminate the position errors during formation flight. The wireless data transmission between the leader, the followers and the ground station is achieved by using the radio telemetry modules supported by Pixhawk-4 autopilot. Finally, successful flight experiments have been performed to validate the proposed autonomous formation flight control system.