摘    要
随着科学技术的迅速发展，移动机器人得到越来越多的关注。两轮自平衡机器人作为一种典型的轮式移动机器人，具有适应环境能力强，移动和转向灵活方便、运动效率高、能量损耗小等特点，能够完成多轮机器人无法完成的复杂运动与操作，特别适用于工作环境变化大、任务复杂的场合，因此自平衡两轮机器人在工业、民用、军事以与太空探索等领域具有广泛的应用前景。但是，由于两轮自平衡机器人属于非完整约束、欠驱动系统，具有多变量、非线性和欠驱动的特点，因此其动力学方程复杂，控制系统设计难度大，限制了该类机器人的发展。
本文在总结现有各种两轮自平衡机器人样机构型的基础之上，提出一种新型的两轮自平衡机器人构型方案——低重心式两轮车，该两轮车能够进行全方位行走，运动速度快，零转弯半径，具有灵活的运动能力。不同于倒立摆式的设计结构，由于采用下垂摆式的结构，因此该两轮车系统具有本质稳定性。针对一般两轮车车体产生的震荡现象，我们提出采用磁流变效应的原理，对车体震荡现象进行主动抑制。通过对低重心式两轮车的运动规律，转向机理进行分析，建立了低重心式两轮车的动能、势能和磁流变阻力矩的数学模型，进而利用拉格朗日方程建立了低重心式两轮车的动力学模型，为低重心式两轮车控制策略的设计提供了理论依据。
最后利用MATLAB对得到的动力学模型进行了仿真分析，以获得期望的低重心式两轮车的位移、速度、摆角的实验曲线。通过分析仿真数据验证了建立的动力学模型正确性与有效性。
关键词：两轮车汽车漂移教学；非完整约束；动力学建模；拉格朗日乘子法

Dynamic Modeling and Analyzing of a Two–wheeled Vehicle with Low-gravity
Abstract
With the development of the science and technology, more attention focus on the mobile robot. As a kind of wheeled mobile robot, two-wheeled self-balanced robots have the capability to adapt the complex situations. It can move and shiftflexibility. Therefore, two-wheeled self-balanced robot can perform several rounds of the complicated motion which the multi-wheeled robot can not achieve, especially in the changeful environment such as space exploration, topographic reconnaissance and transportation of dangerous goods. So it is suitable for detecting in narrow and dangerous space and has a wide foreground both i
n civilian and space explore. But two-wheeled self-balanced robothas multi-variable, non-linear and parameter uncertainty characteristics. Therefore, the dynamic equation is quite complex and it is difficult to design a control system .Both of the negative factorslimited the development of such robots.
Based on summarizations of the present two-wheeled self-balanced robot in view of structure, a new two-wheeled self-balanced robothas been proposed. That is Two-wheeled Vehicle with Low gravity. Two-wheeled Vehicle with Low gravity is characterized by rapid motion, it can both run in omni direction and turn with zero radius. The design of the structure is different from the inverted pendulum. Due to adopt the structure of hanged pendulum, the two wheeled vehicle with low gravity has the nature of stability. In order to address the vibration phenomenon which is generally existed in the two wheeled vehicle, we propose a methed to use the principle of magnetorheological effect on the body to suppress the shock phenomena. This paper analyzes the law of motion and steering mechanism of the two-wheeled vehicle with low gravity. Through analysis of robot in detail,we getrobot’s model of kinetic energy and potential energy. Two-wheeled self-balanc
ed robot’s dynamic model is established by using Lagrangeequation,and it will provide a theoretical basis for the controller design.