振动驱动移动机器人直线运动的滑移分岔

陈祺; 占雄; 徐鉴

doi:10.6052/0459-1879-16-157

振动驱动移动机器人直线运动的滑移分岔

同济大学航空航天与力学学院, 上海 200092

基金项目: 国家自然科学基金资助项目(11272236).

详细信息

通讯作者:
徐鉴,教授,主要研究方向:非线性动力学.E-mail:xujian@tongji.edu.cn

中图分类号: O313
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出版历程
- 收稿日期: 2016-06-05
- 修回日期: 2016-06-12
- 刊出日期: 2016-07-17

SLIDING BIFURCATIONS OF RECTILINEAR MOTION OF A THREE-PHASE VIBRATION-DRIVEN SYSTEM SUBJECT TO COULOMB DRY FRICTION

School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China

摘要

摘要: 近年来，随着移动型机器人设计技术水平的不断提高，其运动形式日趋多样. 借助于仿生学的思想，模仿蚯蚓等动物的蠕动成为不少机器人设计者所追求的目标. 为了实现这一目标，学者们提出并研究了振动驱动系统. 本文研究了各向同性干摩擦下，单模块三相振动驱动系统的粘滑运动. 考虑到库伦干摩擦力的不连续性，振动驱动系统属于Filippov 系统. 基于此，运用Filippov 滑移分岔理论，分析了振动驱动系统不同的粘滑运动情况. 根据驱动参数的不同，系统运动的滑移区域被分成4 种基本情形. 对这些情形分类讨论，得到系统的6 种运动情况. 然后对这6 种运动情况进行归纳，最终得出系统一共存在4 种不同的粘滑运动，而且也解析地给出了发生这4 种粘滑运动的分岔条件. 分岔条件包含系统的3 个驱动参数，通过变化这些参数，得到了系统运动的分岔图. 借助分岔图，详细分析了随着驱动参数的变化，系统如何实现不同粘滑运动类型之间的切换，并从分岔角度给出了相应的物理解释. 最后，通过数值方法直接求解原运动方程，数值解法得到的4 种运动图像与理论分析一致，验证了系统运动分岔研究的正确性.
- 振动驱动系统 /
- 三相驱动 /
- 各向同性干摩擦 /
- 分岔
Abstract: In recent years, mobile robots' locomotion becomes diversified assisted by the continuous development of technologies in designing them. Inspired from bionics, earthworms' peristalsis becomes an object that quite a few robot designers want their robots to imitate. To this end, vibration-driven system has been put forward and researched by scholars. In this paper, the stick-slip motion of a one-module vibration-driven system moving on isotropic rough surface is studied. In consideration of the discontinuity caused by dry friction, the system considered here is of Filippov type. Based on sliding bifurcation theory in Filippov system, different types of stick-slip motions are studied. According to the values of driving parameters, 4 situations with different sliding regions can be seen. By analyzing these situations one by one, 6 kinds of motions can be achieved. By combining these motions, 4 different stick-slip motion types are finally concluded and conditions for judging occurrence of them are also derived analytically from the view point of sliding bifurcation. In the bifurcation conditions, there are 3 bifurcation parameters which can be changed in drawing bifurcation graphs. Assisted by these bifurcation graphs, detailed analysis is given about how stick-slip motion types change from one to another when parameters change and physical explanations from the perspective of bifurcation theory are also given. At last, the original differential motion equation is solved in a numerical way and one can see that 4 different stick-slip motion types derived numerically correspond with the former analytical results, which verifies the correctness of the bifurcation analysis in this paper well.
- vibration-driven system /
- three-phase control /
- isotropic resistance /
- bifurcations

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