采用四元数 ,古典的 Rodrigues参数和修改的 Rodrigues参数来描述刚体旋转运动。基于微分几何中的零动态设计原理 ,首先构造一个输出映射 ,使系统具有相对阶 { 1,… ,1}且零动态渐近稳定。然后求出一类反馈控制器 ,使得系统部分线性化为一指数稳定的线性方程。仿真结果表明 ,所求控制器能使闭环系统稳定。 Quaternion, classical Rodrigues and modified Rodrigues parameters are used to describe rigid body rotational motion. Based on the principle of zero dynamic design in differential geometry, an output map is first constructed so that the system has relative dynamics {1, ..., 1} and zero asymptotic stability. Then a kind of feedback controller is obtained, which makes the system linearized into an exponential stable linear equation. The simulation results show that the controller can make the closed-loop system stable.