Behavior Analysis and Control by Amplitude Modulation of Nonholonomic Mechanical Systems via the Averaging Method
Behavior Analysis and Control by Amplitude Modulation of Nonholonomic Mechanical Systems via the Averaging Method
复制标题
非完整机械系统的平均法调幅行为分析与控制
DOI：
10.7210/jrsj.16.407
复制
发表时间：
1998
期刊：
影响因子：
--
通讯作者：
Takahiro Suzuki
中科院分区：
文献类型：
--
作者：
Yoshihiko Nakamura;Takahiro Suzuki
具有自由关节的机械臂属于一类动力学约束不可积的二阶非完整系统。这类系统的控制是机器人学和控制工程的主要研究课题之一。在文献中，作者分析了具有自由关节的两关节机械臂响应于周期输入的非线性行为。该机械臂在较大的输入幅值下表现出混沌行为。提出了一种通过输入幅值调制实现双关节定位的控制方法。该策略虽然有效，但存在算法复杂、难以推广等问题。本文采用一阶和二阶平均法对具有周期输入的自由关节机械臂的行为进行了近似。通过在“输入振幅归一化相平面”上定义一个“伪哈密顿量”，分析和识别了平均行为的不变流形。提出了一种通过调节输入幅值达到期望不变流形的控制方法，并给出了在目标点的终止控制。计算机仿真验证了所提出的控制方法的有效性。
Manipulators with free joints fall in a class of second-order nonholonomic systems whose dynamical constraints are nonintegrable. Control of such systems is one of major research topics in robotics and control engineering. In the literature, the authors analyzed nonlinear behaviors of a two joint manipulator with a free joint in response to a periodic input. The manipulator showed chaotic behaviors for larger input-amplitudes. A control method to position both joints via modulation of the input-amplitude was also proposed. Although the strategy was effective, it sufferes from heuristics and difficulty for generalization. In this paper, behaviors of the free-joint manipulator with a periodic input are approximated via the 1st-order and 2nd-order averaging methods. The invariant manifolds of the averaged behavior are analyzed and identified by defining a “pseudo-Hamiltonian” on an “input-amplitude normalized phase plane”. A control method to reach a desired invariant manifold via modulation of the input-amplitude is also proposed and a termination control at the destination is formulated. The effectiveness of the proposed control methods is verified by computer simulations.
DOI：
10.2307/3620310
发表时间：
1989-10
期刊：
--
影响因子：
--
作者：
S. Wiggins
通讯作者：
S. Wiggins