{"title":"Lie-group modeling and simulation of a spherical robot, actuated by a yoke–pendulum system, rolling over a flat surface without slipping","authors":"Simone Fiori","doi":"10.1016/j.robot.2024.104660","DOIUrl":null,"url":null,"abstract":"<div><p>The present paper aims at introducing a mathematical model of a spherical robot expressed in the language of Lie-group theory. Since the main component of motion is rotational, the space <span><math><mrow><mi>SO</mi><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow><mn>3</mn></mrow></math></span> of three-dimensional rotations plays a prominent role in its formulation. Because of friction to the ground, rotation of the external shell results in translational motion. Rolling without slipping implies a constraint on the tangential velocity of the robot at the contact point to the ground which makes it a non-holonomic dynamical system. The mathematical model is obtained upon writing a Lagrangian function that describes the mechanical system and by the Hamilton minimal-action principle modified through d’Alembert virtual work principle to account for non-conservative control actions as well as frictional reactions. The result of the modeling appears as a series of non-holonomic Euler–Poincaré equations of dynamics plus a series of auxiliary equations of reconstruction and advection type. A short discussion on the numerical simulation of such mathematical model complements the main analytic-mechanic development.</p></div>","PeriodicalId":49592,"journal":{"name":"Robotics and Autonomous Systems","volume":null,"pages":null},"PeriodicalIF":4.3000,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0921889024000435/pdfft?md5=b71bc8a7516e2f385020960bdfa91a60&pid=1-s2.0-S0921889024000435-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Robotics and Autonomous Systems","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0921889024000435","RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
The present paper aims at introducing a mathematical model of a spherical robot expressed in the language of Lie-group theory. Since the main component of motion is rotational, the space of three-dimensional rotations plays a prominent role in its formulation. Because of friction to the ground, rotation of the external shell results in translational motion. Rolling without slipping implies a constraint on the tangential velocity of the robot at the contact point to the ground which makes it a non-holonomic dynamical system. The mathematical model is obtained upon writing a Lagrangian function that describes the mechanical system and by the Hamilton minimal-action principle modified through d’Alembert virtual work principle to account for non-conservative control actions as well as frictional reactions. The result of the modeling appears as a series of non-holonomic Euler–Poincaré equations of dynamics plus a series of auxiliary equations of reconstruction and advection type. A short discussion on the numerical simulation of such mathematical model complements the main analytic-mechanic development.
期刊介绍:
Robotics and Autonomous Systems will carry articles describing fundamental developments in the field of robotics, with special emphasis on autonomous systems. An important goal of this journal is to extend the state of the art in both symbolic and sensory based robot control and learning in the context of autonomous systems.
Robotics and Autonomous Systems will carry articles on the theoretical, computational and experimental aspects of autonomous systems, or modules of such systems.