**Abstract**

In this chapter, two controllers are investigated for stabilisation, path tracking and leader-follower team formation. The first controller is a PD2 implemented for attitude stability. The second controller is an Integral Backstepping IBS control algorithm presented for the path tracking and leader-follower team formation problems of quadrotors. This nonlinear control technique divide the control into two loops, the inner loop is for the attitude stabilisation and the outer loop is for the position control. The dynamic model of a quadrotor is represented based on Euler angles representation and includes some modelled aerodynamical effects as a nonlinear part. The IBS controller is designed for the translational part to track the desired trajectory and to track the leader quadrotor by the followers. Stability analysis is achieved via a suitable Lyapunov function. The external disturbance and model parameters uncertainty are considered in the simulation tests. The proposed controllers yielded good results in terms of Root Mean Square Error RMSE values, time-consumption, disturbance rejection and model parameter uncertainties change coverage.

**Keywords:** integral backstepping, adaptive controller, Euler angles, UAVs quadrotors, team formation

## **1. Introduction**

In recent years, research on the control of Unmanned Aerial Vehicles (UAVs) has been growing due to its simplicity in design and low cost. Quadrotor helicopters have several advantages over fixed-wing air crafts, such as taking off and landing vertically in a limited space and hovering easily over fixed or dynamic targets, which gives them efficiency in applications that fixed-wing air crafts cannot do, in addition to being safer [1–3]. Based on its structure the UAV offers the power of sensing and computing in many applications. Quadrotor UAVs can be used to perform several tasks in the applications of dangerous areas for a manned aircraft in a high level of accuracy. They can be utilised in different applications, such as inspection of power lines, oil platforms, search and rescue operations, and surveillance [4–6]. Increasing the applications of quadrotors encourages the growth in their technologies and raises the requirements on autonomous control protocols. Moreover, using swarm robotics has advantages over individual robots in that they perform their tasks faster with high accuracy and use a minimum number of sensors by distributing them to the robots [7]. Researchers are focusing on the design and implementation of many types of controllers to control the take-off, landing and

hovering of individual quadrotor UAVs with some applications which require the creation of a trajectory and tracking in three dimensions, benefiting from the wide developments in sensors.

Research in the field of control of individual and multi-robot quadrotor team formation is still facing some challenges. Challenges of individual quadrotor control come from the complexity of modelling its dynamic system because of its complex structure and the design issue. The dynamic model equations present four input forces with six output states, which mean that the system is in under-actuated range [5, 7]. Further challenges of multi-robot control come from evaluating the control architecture and communication network limitations.

The formation problem of quadrotors has had a vast area of interesting research in the past few years. Researchers have been motivated to contribute to this field of research by the development of materials, sensors and electronics used in designing quadrotors, which consequently has an effect on minimising their size, weight and cost. Working as a team of quadrotors has many benefits over using a single quadrotor in several applications.

Team formation control includes many problems to be addressed, including communication loss, delay between the robots or packet drop problems [8–11]. Simultaneous localization and mapping is another problem in team formation control, in which the vehicle builds up its maps and estimates its location precisely at the same time; this problem has also been addressed in [12–14]. The third problem is the collision and obstacle avoidance, which includes avoiding collisions with both other robots and static or moving unknown obstacles while flying to their destination and maintaining their positions. Solutions to this problem have been handled by [12, 15]. Now, team formation control adopts a combination of some functions; the first is to perform the mission between two points, the second is to preserve the comparative positions of the robots over the formation and maintain the shape consequently, the third is to avoid obstacles and the forth is to divide the formation. In this chapter, we focus on designing only a control law for the leader-follower team formation problem with collision avoidance between team members by maintaining the distance between the leader and the follower.

In the leader-follower approach, at least one vehicle performs as a leader and the other robots are followers. The leader vehicle tracks a predefined path, whereas the followers maintain a certain distance with the leader and among themselves to obtain the desired shape. Each robot has its own controller and the robots keep the desired relative distance between themselves. However, two types of control architecture may be used to control the vehicle: one loop control scheme and two loop control scheme. If a two loop control scheme is used to control each vehicle, the outer loop is used for position control and its *x* and *y* output is the desired roll and pitch angles. These desired angles with the desired yaw angle are used to calculate the vehicle torques; in other words, they stabilise the quadrotor angles. This type of control is built according to time scale separation, where the attitude dynamics are much faster than translation dynamics. In the one loop control scheme, on the other hand, separation of the vehicle dynamics to attitude and translation is not considered. In this case, the position tracking error is used directly to calculate the vehicle torques to achieve its path tracking. According to these definitions, leader-follower team formation requires attitude stabilisation and path tracking to be achieved.

Abundant literature exists on the subject of attitude stabilisation, path tracking and leader-follower team formation control. Several control techniques have been demonstrated to control a group of quadrotors varying between the linear PID, PD or LQR controllers to more complex nonlinear controllers as neural networks and BS controllers. These controllers achieved good results and some of them

*Integral Backstepping Controller for UAVs Team Formation DOI: http://dx.doi.org/10.5772/intechopen.93731*

guaranteed the performance, such as the LQR controller, and some of them guaranteed their stability. The performance of an individual quadrotor or a group of quadrotors in formation control is often affected by external disturbances such as payload changes (or mass changes), wind disturbance, inaccurate model parameters, etc. Therefore, the IBS controller was proposed to reject the effect of disturbances and handle the change in model parameter uncertainties. On the other hand, improving the control performance is another aspect.

Dynamic model representation of the quadrotors is a major demand for designing these controllers. In this chapter, Euler angles technique was used to represent the quadrotors.
