无滑滚动圆盘的平衡运动及轨迹控制

Balance Motion and Path Tracking Control of Disk Rolling Without Slipping

研究水平面内无滑滚动圆盘的平衡运动及轨迹跟踪控制,建立了圆盘的无滑纯滚动的非完整约束模型。从姿态最容易实现稳定控制的角度出发,提出了一种姿态平衡条件,并以此条件为基础运用李亚普诺夫函数稳定设计理论导出了姿态平衡的速度控制律,同时利用反演控制技术设计了水平面内轨迹的跟踪控制律。最后通过仿真验证了姿态平衡控制律的有效性以及轨迹跟踪控制的稳定性和快速精确性。

Balance motion and path tracking control of disk rolling without slipping on the horizontal plane were researched.Noholonomic restriction model of disk rolling without slipping was built.Considering the most easiness of disk posture control,a posture balance condition was put forward.Based on the posture balance condition,using Lyapunov's stability design theory,angle velocity control strategy was acquired.By using Backstepping design method,path tracking control strategy on the horizontal plane was designed.The simulation results revealed that posture balance control strategy is valid,and path tracking control strategy is stable,rapid and precise.