中文摘要：

基于能量耗散形式下的拉格朗日方程，建立了基于状态观测器的球形机器人的动力学方程，得出这是一个非线性的仿射系统。根据机器人的实际运动情况和理论仿真曲线对方程进行了线性化处理和仿射变换，在新建立的平衡点处应用线性理论进行控制系统的设计。考虑到某些状态变量的不可测量性，构建了状态观测器对系统的全维状态进行实时观测，在此基础上设计了系统的状态反馈控制器。仿真结果表明了所设计控制器的有效性。

英文摘要：

The dynamic equation of a spherical robot was established,and a nonlinear affine system is derived based on energy dissipation Lagrangian equation. Linearization and affine transformation methods are used in the new equilibrium point to design control system by a powerful linear theory, according to the actual movements and theoretical simulated datum of robot. A state observer is built for estimating full state variables of system in real-time because some of state variables are immeasura bility. The state feedback controller is designed and the simulation results prove the validity of the controller.