利用反馈稳定振动底座上球形机器人的稳定旋转

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED Regular and Chaotic Dynamics Pub Date : 2023-12-07 DOI:10.1134/S1560354723060060

Alexander A. Kilin, Tatiana B. Ivanova, Elena N. Pivovarova

{"title":"利用反馈稳定振动底座上球形机器人的稳定旋转","authors":"Alexander A. Kilin, Tatiana B. Ivanova, Elena N. Pivovarova","doi":"10.1134/S1560354723060060","DOIUrl":null,"url":null,"abstract":"<div><p>This paper treats the problem of a spherical robot with an axisymmetric pendulum drive\nrolling without slipping on a vibrating plane. The main purpose of the paper is\nto investigate the stabilization of the upper vertical rotations of the pendulum\nusing feedback (additional control action). For the chosen type of feedback,\nregions of asymptotic stability of the upper vertical rotations of the pendulum are constructed\nand possible bifurcations are analyzed. Special attention is also given to the question of\nthe stability of periodic solutions arising as the vertical rotations lose stability.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"28 6","pages":"888 - 905"},"PeriodicalIF":0.8000,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1134/S1560354723060060.pdf","citationCount":"0","resultStr":"{\"title\":\"Stabilization of Steady Rotations of a Spherical Robot on a Vibrating Base Using Feedback\",\"authors\":\"Alexander A. Kilin, Tatiana B. Ivanova, Elena N. Pivovarova\",\"doi\":\"10.1134/S1560354723060060\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper treats the problem of a spherical robot with an axisymmetric pendulum drive\\nrolling without slipping on a vibrating plane. The main purpose of the paper is\\nto investigate the stabilization of the upper vertical rotations of the pendulum\\nusing feedback (additional control action). For the chosen type of feedback,\\nregions of asymptotic stability of the upper vertical rotations of the pendulum are constructed\\nand possible bifurcations are analyzed. Special attention is also given to the question of\\nthe stability of periodic solutions arising as the vertical rotations lose stability.</p></div>\",\"PeriodicalId\":752,\"journal\":{\"name\":\"Regular and Chaotic Dynamics\",\"volume\":\"28 6\",\"pages\":\"888 - 905\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2023-12-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1134/S1560354723060060.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Regular and Chaotic Dynamics\",\"FirstCategoryId\":\"4\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S1560354723060060\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Regular and Chaotic Dynamics","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1134/S1560354723060060","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

本文讨论了一个带有轴对称摆锤驱动器的球形机器人在振动平面上无滑动运行的问题。本文的主要目的是利用反馈（附加控制作用）研究摆锤上部垂直旋转的稳定性。对于所选的反馈类型，本文构建了摆锤上部垂直旋转的渐近稳定区域，并分析了可能出现的分岔。还特别关注了随着垂直旋转失去稳定性而产生的周期解的稳定性问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

摘要图片

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Stabilization of Steady Rotations of a Spherical Robot on a Vibrating Base Using Feedback

This paper treats the problem of a spherical robot with an axisymmetric pendulum drive rolling without slipping on a vibrating plane. The main purpose of the paper is to investigate the stabilization of the upper vertical rotations of the pendulum using feedback (additional control action). For the chosen type of feedback, regions of asymptotic stability of the upper vertical rotations of the pendulum are constructed and possible bifurcations are analyzed. Special attention is also given to the question of the stability of periodic solutions arising as the vertical rotations lose stability.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Regular and Chaotic Dynamics 物理-力学

CiteScore

2.50

自引率

7.10%

发文量

审稿时长

>12 weeks

期刊介绍： Regular and Chaotic Dynamics (RCD) is an international journal publishing original research papers in dynamical systems theory and its applications. Rooted in the Moscow school of mathematics and mechanics, the journal successfully combines classical problems, modern mathematical techniques and breakthroughs in the field. Regular and Chaotic Dynamics welcomes papers that establish original results, characterized by rigorous mathematical settings and proofs, and that also address practical problems. In addition to research papers, the journal publishes review articles, historical and polemical essays, and translations of works by influential scientists of past centuries, previously unavailable in English. Along with regular issues, RCD also publishes special issues devoted to particular topics and events in the world of dynamical systems.