不确定曲面上非完整移动机器人的鲁棒镇定  

ROBUST STABILIZATION OF NONHOLONOMIC MOBILE ROBOTS MOVING ON UNCERTAIN UNEVEN SURFACE

作　　者：祝晓才[1] 董国华[1] 蔡自兴[2] 胡德文[1] 

机构地区：[1]国防科技大学机电工程与自动化学院,长沙410073 [2]中南大学信息科学与工程学院,长沙410083

出　　处：《动力学与控制学报》2006年第4期299-307,共9页Journal of Dynamics and Control

基　　金：国家自然科学基金重点项目(60234030);国家杰出青年科学基金(60225015);高校青年教师奖资助.~~

摘　　要：针对在不确定曲面上运动的非完整轮式移动机器人设计了鲁棒实际镇定控制律,使得机器人系统具有对曲面而引入的重力干扰的鲁棒性。设计过程中使用参数有界但未知的二次曲面来近似不确定曲面。整个设计过程构建于李群,综合了横截函数方法、积分器backstepping和Lyapunov重设计技术.在讨论了轮式移动机器人的运动学子系统对李群SE(2)的标准群运算的左不变性之后,构造了一个有界横截函数,由它确定了相应的嵌入目标子流形.然后,对移动机器人的运动学误差系统设计了光滑的“虚拟”镇定律,使得误差变量指数镇定,从而也将机器人运动学子系统的状态镇定到先前定义的目标子流形.最后,使用积分器backstepping将该光滑“虚拟”控制律拓展到标称动力学系统,并通过重设计,得到鲁棒实际镇定控制律.仿真结果验证了算法的有效性.Robust control laws were proposed for the stabilization of nonholonomic wheeled mobile robots moving on an uneven surface, which was not exactly known. The proposed control laws rendered the closed -loop dynamic system practically stable and robust with respect to the effect of the gravity introduced by the uneven surface. Quadratic surfaces with unknown but bounded coefficients were utilized in the design process to locally approximate the uneven surfaces. The design procedure was based on the transverse function method, integrator backstepping,and Lyapunov redesign technique. After exploring the left - invariance property of the kinematic subsystem of the wheeled mobile robots with respect to the standard group operation of the Lie group SE （2）, we constructed a bounded transverse function by which a corresponding embeded target submanifold was defined, and derived the smooth ＂ virtual＂ control laws , which rendered the error subsystem exponentially stable, thus the states of the kinematic subsystem converged to a smooth embedded submanifold defined by the transverse function. Then, the integrator backstepping technique was applied to the nominal dynamic system due to the smoothness of the obtained ＂ virtual＂ control laws. Finally, a Lyapunov redesign component was constructed to handle the disturbance of the gravity. Driven by the proposed control laws, the wheeled mobile robots had the ability of adaptation to varying uneven surface condition. Simulations were provided to validate the effectiveness of the algorithm.

关 键 词：轮式移动机器人 李群 横截函数 Lyapunov重设计 鲁棒镇定 

分 类 号：O231[理学—运筹学与控制论]