Research On Unmanned Aerial Vehicle Formation Control Based On Dual Quaternion

Coordinated formation flight is the basis of the multiple UAVs( Unmanned Aerial Vehicle) carrying out diversified missions cooperatively. In order to represent the position and attitude simultaneously in three-dimensional space for UAVs, the unit dual quaternions, known as the most concise mathematical representation with the highest efficiency in computing for this purpose, are employed as a mathematical tool in this thesis. However, the current dual quaternion control laws mainly take the general rigid as the object, directing at holonomic constraint and all-wheel driving systems( in general,whose controllable inputs are no less than the degrees of its freedom, such as the omnidirectional mobile robots and the quadrotors), rather than nonholonomic constraint and underactuated systems.In the thesis, the fixed-wing UAVs and their formation control are taken as the research objects, by expanding the applications of the unit dual quaternion control laws on nonholonomic constraint and underactuated systems. The purpose is to explore modeling,optimal trajectory planning, trajectory tracking for a UAV and multiple UAVs formation control. The main contributions are listed as follows:(1) The fixed-wing UAV modeling method is put forward on the basis of the theory of dual quaternion, compared with classic six degrees of freedom model.UAV's orientation and position control in three dimensional space is the foundation of the UAV autonomous formation flight. One of the keys to realizing UAV control is the representating method of a general rigid motion including rotation and movement,namely modeling. The dual quaternion is one of the mathematical tools to describe the general rigid motion in three dimensions. Establishing the mathematical model of fixedwing UAV motion based on dual quaternion can avoid the singularity and complexity of euler angles in SE(3) space, and provide the basic model for integrated control of positon and orientation.(2) The optimal trajectory method planning and tracking control is realised based on the dual quaternion model and the Guass Pseudo-spectral method.According to the characteristics of the UAV underactuated and nonholonomic constraint and the advantages of the dual quaternion, feedback linearization controller is designed on the basis of non-decoupling dynamics model and the pseudo-inverse method to achieve the gradual convergence of the position and posture movement. Then, using the basic principle of the GPM, continuous fixed-wing optimal control problem is transformed into the discrete nonlinear programming problem. We can obtain the time and energy optimal trajectory through the software package GPOPS. In the end, we can design the integrated feedback linearization tracking law by extending the feedback linearization control law to the tracking law. So, the position and attitude of the UAV can be controlled to track the optimal trajectory.(3) Position and orientation control of UAV in formationThe multiple UAVs formation flight control law is seemingly designed based on the orientation and position control law. Compared with the existing formation control technology which is based on linear model, this paper first establishes a double UAVs model in the dual quaternion form by using decoupling or SE(3) means. Combined with the graph theory related content, we can extend the control of double UAVs to the multiple UAVs formation system. Then the formation control law is designed based on specific topology. Simulation results show that follower can track the leader effectively and keep the specified configuration related to it. As a result, the specific formation is formed.