四旋翼无人机轨迹跟踪与避障控制研究

Abstract

Due to excellent flexibility and maneuverability, the study of quadrotor has become more and more popular among researchers. With the joint efforts of many engineers and scholars, the quadrotor UA V has been widely used in many fields such as military reconnaissance, police patrol, agricultural inspection, entertainment aerial photography, and logistics transportation. As the application is getting wider and wider, the control demand for quadrotor’s rapidity, safety and accuracy is stricter and stricter. However,the model of quadrotor is underactuated, strong coupled and nonlinear, which makes the design of controller complicating. For quadrotor, the most critical issues are the contrl of trajectory tracking and obstacle avoidance. To solve these problems, the following aspects will be researched in this paper:

Based on the analysis of the quadrotor’s working principle, the mathematical model of quadrotor was established. In order to establish the connection between the attitude loop and the position loop, the mathematicla model is processed by introduce virtual controllers, and the problem of underactuation in the quadrotor is solved, which lays the foundation for the following chapters.

In the trajectory tracking of quadrotor, considering the different demands for the quadortor’s attitude and position, a finite-time terminal sliding mode controller is designed for the inner loop and a PID controller is designed for the outer loop. Besides, Considering that the linear velocity of quadrotor is unmeasurable in practical, a finite-time observer is designed to estimate the velocity. Furthermore, in order to make the transition process smoother, a differential tracker was designed. To further improve the quadrotor’s system performance, on one hand, the traditional exponential reaching law is replaced by the multi-power reaching law in inner loop, which fastens convergence speed to the sliding mode plane. On the other hand, in outer loop, a nonlinear PID controller is developed, which improves the rapidity of position tracking. Besides, an extended state observer(ESO) is designed to estimate external disturbances and model uncertainties, which improves the robustness of the quadrotor.

When quadrotor drones fly, the position tracking error needs to be kept within a certain range. To solve this problem, two control strategies are designed to constrain the position tracking error. Firstly, based on the Barrier Lyapunov function and the backstepping method, the outer loop controller is designed. When states approach the boundary, the Barrier Lyapunov function will tend to be infinite, which will constrain the position error within the boundary. In addition, an outer loop controller is designed based on a prescribed performance method, which uses a known function to describe the boundary, so that the tracking error satisfies prescribed performance.

In the autonomous landing of the quadrotor, considering that the obstacle information is already known, a Gaussian potential function controller is designed, and which uses Gaussian function to describe characters of the obstacles. By introducing Gaussian function, the obstacles will reject quadrotor when it approaches obstacles. Besides, inspired by the Barrier Lyapunov function, a obstacle avoidance controller based on the Barrier Lyapunov potential function is designed, which uses the boundary of the Lyapunov function to described the real boundary of obstacle.

Finally, numerical simulation experiments are designed for all proposed controllers to prove their validity.

Keywords:Quadrotor, Finite time, Trajectory Tracking, Error Constraint, Obstacle Avoidance Control

摘要 ............................................................................................................................... I Abstract ............................................................................................................................. I I 第1章绪论 .. (6)

1.1 课题研究的背景和意义 (6)

1.2 国内外研究现状及分析 (9)

1.2.1 四旋翼无人机姿态控制 (9)

1.2.2 四旋翼无人机位置控制 (11)

1.3 主要研究内容与结构安排 (13)

第2章四旋翼无人机动力学建模 (15)

2.1 引言 (15)

2.2 四旋翼无人机结构及工作原理 (15)

2.3 四旋翼无人机动力学建模 (16)

2.3.1 坐标系定义 (16)

2.3.2 四旋翼无人机动力学模型 (16)

2.3.3 动力学模型分析与处理 (19)

2.4 本章小结 (21)

第3章四旋翼无人机轨迹跟踪控制律设计 (22)

3.1 引言 (22)

3.2 轨迹跟踪控制 (22)

3.2.1 微分跟踪器设计 (22)

3.2.2 有限时间状态观测器设计 (24)

3.2.3 有限时间终端滑模控制器设计 (26)

3.2.4 数值仿真与分析 (29)

3.3 改进控制器设计 (32)

3.3.1 外环非线性PID控制器设计 (33)

3.3.2 改进终端滑模控制器设计 (35)

3.3.3 扩张状态观测器设计 (37)

3.3.4 数值仿真与分析 (38)

3.4 本章小结 (40)

第4章四旋翼无人机误差约束控制律设计 (42)

4.1 引言 (42)

4.2 基于障碍Lyapunov函数的反步控制器设计 (42)

4.2.1 反步法与障碍Lyapunov函数介绍 (42)

4.2.2 障碍Lyapunov函数反步控制算法设计 (44)

4.2.3 数值仿真与分析 (47)

4.3 基于预设性能的误差约束控制律设计 (49)

4.3.1 预设性能方法简介与分析 (49)

4.3.2 外环预设性能控制器设计 (51)

4.3.3 数值仿真与分析 (53)

4.4 本章小结 (55)

第5章四旋翼无人机避障着陆控制律设计 (56)

5.1 引言 (56)

5.2 基于高斯势函数自主避障着陆控制 (56)

5.2.1 着陆方法介绍 (57)

5.2.2 控制算法设计 (57)

5.2.3 数值仿真与分析 (59)

5.3 基于障碍Lyapunov函数势函数自主避障着陆控制 (62)

5.3.1 改进障碍Lyapunov函数势函数介绍 (62)

5.3.2 改进控制器设计 (64)

5.3.3 数值仿真与分析 (66)

5.4 本章小结 (69)

结论 (70)

参考文献 (72)

攻读硕士学位期间发表的论文及其它成果 (77)

哈尔滨工业大学学位论文原创性声明和使用权限 (78)

致谢 (79)