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针对两轮自平衡机器人在斜坡上的建模和控制问题，首先采用Lagrange方法建立了斜坡面上的动力学模型，然后对模型的平衡状态进行了分析，得出了平衡时车身倾角和偏航角之间的关系。并将模型在指定的平衡状态下进行线性化，分析了线性模型的能控性，得出系统完全能控的结论。另外，针对斜坡面上车身姿态不能直接测量的问题，找到了一种斜坡面上姿态及斜坡倾角检测的方法。最后在此基础上，设计了LQR控制器，仿真结果表明两轮机器人能在斜坡面上指定偏航角处实现自由平衡，并具有一定的抗干扰能力。“,”Modeling and controlling of self-balancing robot on the slope are difficult and challenging problems.Few researches have been done in this field.Two-wheeled self-balancing mobile robot dynamic model and balancing control on the slopes was proposed in this paper. The method includes the main steps as follows: Firstly, the dynamic model is established using Lagrange method. Secondly, the model of the equilibrium is analyzed and then the relationship between balance body angle and yaw angle is obtained.Thirdly, the model is specified in the equilibrium state linearization and the controllability of the linear model is analysed. Therefor the conclusion that the system is controllable has been drawn.In addition, because the body attitude of slope surface can not be directly measured,a method of detection attitude and angle on slope surface was introduced in this paper.Finally, a LQR controller is designed for the two-wheeled self-balancing mobile robot.Simulation results show that the two-wheeled robot in specified yaw angle on slope surface is able to achieve free equilibrium.Meanwhile,the robot has certain anti interference ability.