基于能量成型的四旋翼空中机器人有界输入条件下的飞行控制方法研究

In recent years, a kind of Quad-Rotor aerial robot has quickly emerged as a popular unmanned aerial vehicle (UAV) platform. It is capable of vertical taking off and landing in limited space, and hovering over a target accurately. Due to its simple mechanical structure and high maneuverability, the robot has potential for many civil and military applications including surveillance, intervention in hostile environments, air pollution monitoring, and so on. But influenced by the under-actuation and bounded input features, the trajectory tracking of a Quad-Rotor robot becomes a complex control question which has not been solved effectively yet. According to this question, this project will introduce the Controlled Lagrangians(CL) function technique based on the energy-shaping theory into the design process of flight control system. The major work of this project will be studied through an integrated method composed of the theoretical analysis, numerical simulation and flight test of a prototype, and divided into two sections. In the first section, the dynamics model of a Quad-Rotor robot will be built based on its energy function, the relationship between the solvability of control matching condition and the stabilization of controlled energy will be analyzed, and the matching robot attitude stability control system will be devised. The research work in the second section includes devising closed-loop controlled energy in order to change the trajectory tracking question into equilibrium stabilization problem, solving the matching algorithm of robot control system with under-actuation degree two and bounded input, and achieving the application of Controlled Lagrangians technique on the robot trajectory tracking control system. The results can be used to support the development of a Quad-Rotor prototype in order to improve its flight quality under the influence of bounded input, and provide reference experiences to the rotor robots with other configurations. In addition, for the Quad-Rotor robot is a new research object to the CL method, some problems which have not been solved effectively by CL method will be encountered in the research process. Thereby, the related research work in this project, which can be considered as a kind of development of CL method, has remarkable theoretical meaning.

由于受到欠驱动与有界输入特性等的共同作用，四旋翼机器人的轨迹跟踪成为了一个复杂的控制问题，相关研究尚未能取得有效成果。针对这一问题，本课题拟基于能量成型的观点，引入受控拉格朗日函数（CL）法，采用理论分析、数值仿真以及原型机实验相结合的方式进行研究。首先利用能量函数构建机器人的动力学模型，分析有界输入条件下匹配条件可解性与受控能量可镇定性之间的关系，建立机器人的姿态稳定控制系统；最后通过构造受控能量函数将轨迹跟踪问题转化为镇定问题，确定二阶欠驱动度与有界输入共同作用下的控制匹配条件，实现CL法在机器人轨迹跟踪控制系统中的应用。本课题从能量的角度扩展了四旋翼机器人控制方法的研究思路，相关研究成果将有效提高四旋翼机器人在欠驱动和有界输入共同影响下的飞行品质，并为其它多旋翼机器人的控制方法研究提供借鉴经验。此外，本课题相关研究内容也是对CL法本身的一种发展，具有显著的理论研究意义和应用价值。

近些年来，一种四旋翼空中机器人凭借其结构紧凑、操纵简单、灵活机动的优点越来越受到人们的重视，在商业领域以及科研领域都取得了长足的发展。由于受到欠驱动与有界输入特性等的共同作用，四旋翼机器人的轨迹跟踪成为了一个复杂的控制问题，相关研究尚未能取得有效成果。针对这一问题，在自然基金的支持之下，本课题基于能量成型的观点，引入受控拉格朗日函数（CL）法，采用理论分析、数值仿真以及原型机实验相结合的方式进行研究。引入了地面坐标系以及机体坐标系作为建立模型的参考基准，并建立各个参考坐标系之间的转换矩阵求取机器人运动学模型；引入构型空间、李群以及Lie导数的概念，构建了表示机器人能量的拉格朗日函数；并在其基础之上利用 Euler-Poincare方程得到机器人的动力学模型。构造了机器人的闭环受控能量函数来表示系统的姿态稳定性，分析受控方程与原始方程间的匹配条件，并求解得到了匹配方程构建机器人的姿态控制系统；基于受控能量构建机器人的Lyapunov 函数，利用受控方程与原始方程并的匹配性证明了闭环系统的稳定性。为降低二阶欠驱动系统匹配研究的复杂性，将机器人的轨迹跟踪控制系统分为了并联的两个单欠驱动系统；针对各个系统设计受控能量、研究匹配条件、设计稳定控制器并分析系统的稳定性。本课题从能量的角度扩展了四旋翼机器人控制方法的研究思路，相关研究成果将有效提高四旋翼机器人在欠驱动和有界输入共同影响下的飞行品质，并为其它多旋翼机器人的控制方法研究提供借鉴经验。