Robust stabilization of uncertain nonholonomic kinematic systems
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摘要: 确定非完整运动学系统的镇定问题已有许多研究,然而当实际系统几何参数未知,特别是控制系统考虑不校准视觉测量时,运动学系统是不确定的.研究针对一类典型的不确定非完整运动学系统,即非完整移动机器人的鲁棒镇定问题.通过对质心和几何中心不重合情况下两轮独立驱动移动机器人镇定问题的研究,得到了以两独立驱动轮速度为控制输入的机器人运动学模型.对于车轮半径和两驱动轮之间距离参数已知情况下提出了光滑的时变镇定律,并针对这两个参数未知时,给出了鲁棒控制律设计方法.对这两类控制律下的闭环系统分别给出了严格的渐近稳定性证明.这类设计方法对于研究一般的不确定非完整运动学系统的镇定问题具有一定的启发意义.仿真试验验证了提出方法的有效性.Abstract: Lots of research on the stabilizing problem of certain nonholonomic kinematic systems has been developed. However, when the geometric parameters of systems are unknown, especially, considering uncalibrated vision measure in control systems, kinematic systems are uncertain. The stabilizing problem was investigated for a kind of uncertain nonholonomic control systems, i.e., nonholonomic mobile robots. A robot kinematic model with two driven wheel velocities as control inputs was obtained through the observation and analysis of mobile robots driven by two wheels with the different center of mass and geometric center. A smooth time varying stabilizing controller was proposed for these systems with the known wheel radius and the distance between the two driving wheels. For the circumstance with the unknown two parameters above, a robust stabilizing law was presented also. The asymptotic stability was rigorously proved for the closed loop systems by using the proposed control laws. A heuristic idea may be obtained for developing stabilizing problem of general uncertain nonholonomic control systems by considering this kind of design. The simulation illustrates the effectiveness of the proposed controllers.
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Key words:
- nonholonomic system /
- wheeled mobile robot /
- robust stabilization
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