拉格朗日与牛顿欧拉方法：差动机器人动力学建模详解

需积分: 16 166 浏览量更新于2024-08-30 收藏 1.14MB PDF 举报

本文主要探讨了动态建模在差动驱动移动机器人(Differential-drive Mobile Robots, DDR)领域的应用，由Rached Dhaouadi和Ahmad Abu Hatab两位作者在《先进机器人与自动化》(AdvRobotAutom)期刊的第二卷第二期发表。他们通过结合拉格朗日法(Lagrange)和牛顿欧拉法(Newton-Euler)对DDR的动力学模型进行了深入研究。首先，背景部分指出近年来，随着移动机器人技术和教育技术的快速发展，对轮式移动机器人(如WDRI, Wheeled Differential Drive Robots)的控制及其应用的研究兴趣显著增长。然而，尽管关于轮式机器人运动学建模的文献丰富且易于理解，对于其动力学模型的探讨却相对不足。这是因为轮式机器人的动力学特性非常复杂，非holonomic约束使得动力学分析具有挑战性，对于刚接触这一领域的工程学生来说，这是一大难点。作者强调了开发一个详尽而精确的动态模型的重要性，该模型能够为学生提供一个全面的框架，用于仿真分析和基于模型的设计。他们通过拉格朗日法构建了动力学模型，这是一种在机械系统动力学分析中常用的方法，它将系统的总动能和势能转化为一组称为拉格朗日函数的量，然后通过对拉格朗日方程求解来揭示系统的运动规律。牛顿欧拉法则是一种更为细致的局部分析方法，它将系统分解为各个质点或刚体，并考虑它们之间的相互作用力，以便于计算每个部分的运动。在文中，Dhaouadi和Hatab可能详细阐述了如何处理DDR的特殊性，例如双轮布局带来的非对称性、驱动力矩的分配以及如何处理由于车轮滚动和地面摩擦等因素引起的复杂运动。他们可能还讨论了如何将这些模型应用于实际控制策略的设计，比如路径规划、稳定性和动态平衡问题，以及如何通过数值方法进行模拟，以便优化机器人的性能和避免潜在的不稳定行为。这篇论文为理解和掌握差动驱动移动机器人动力学模型提供了宝贵的资源，为教育工作者和学生提供了一个清晰的动态模型基础，促进了机器人领域尤其是动态建模技术的发展和教学。

Volume 2 • Issue 2 • 1000107

Adv Robot Autom

ISSN: 2168-9695 ARA, an open access journal

Open Access

Research Article

Dhaouadi and Hatab, Adv Robot Autom 2013, 2:2

DOI: 10.4172/2168-9695.1000107

Keywords: Dierential-drive; Mobile robot; Dynamics; Modeling;

Lagrange; Newton-Euler

Introduction

In recent years, there has been a considerable interest in the area

of mobile robotics and educational technologies [1-7]. For control

engineers and researchers, there is a wealth of literature dealing

with wheeled mobile robots (WMR) control and their applications.

However, while the subject of kinematic modeling of WMR is

well documented and easily understood by students, the subject of

dynamic modeling of WMR has not been addressed adequately in the

literature. e dynamics of WMR are highly nonlinear and involve

non-holonomic constraints which makes dicult their modeling

and analysis especially for new engineering students starting their

research in this eld. erefore, a detailed and accurate dynamic model

describing the WMR motion need to be developed to oer students

a general framework for simulation analysis and model based control

system design.

In the case of a dierential drive mobile robot (DDMR), for

example, there is no textbook available that investigates thoroughly

the dynamic modeling approach taking into consideration the non-

holonomic constraints in a step by step procedure. e analysis is

available mainly in journals, conference papers, and technical reports

[8]. Moreover, the material presented diers from one paper to

another with dierent variables and reference frames used, and various

assumptions. In addition, some papers present dierent results for the

same DDMR used, which adds to the confusion of dynamic modeling.

For the case of DDMR, the methods used are either the Lagrangian

approach [9-15] or the Newton-Euler approach [16-19]. Other

formalisms such as the Kane’s method have been also suggested as

viable approaches of modeling DDMR [20]. erefore, it is not clear

for new engineering students and researchers which concept to use and

which method oers a better physical insight on the dynamic behavior

of the system and the eect of the non-holonomic constraints. Also, it

is not clear if both methods will lead to the same nal dynamic model.

In the Newton Euler method, one has to take into account two

kinds of forces applied to a system: the given forces and the constraint

forces. e given forces include the externally impressed forces by

the actuators while the constraint forces are the forces of interaction

between the robot platform and ground through the wheels. Moreover,

in a system with interconnected elements, the components may

interact with each other through gears, springs, and frictional elements.

erefore, we need to take into account all of these forces. It is clear that

the Newtonian approach includes a few practical diculties since in

most cases these forces are not easily quantiable.

e methodology developed by Lagrange overcomes these problems

by expressing the forces in terms of the energies in the system, i.e., the

kinetic energy and the potential energy, which are scalar quantities

easily expressible in terms of the system coordinates. e derivation of

the Lagrange equations requires also that the generalized coordinates

be independent.

e Lagrangian approach usually provides a powerful and versatile

method for the formulation of the equations of motion for holonomic

systems. However, for non-holonomic systems, the usual method is to

introduce the motion constraint equations into the dynamic equations

using the additional Lagrange multipliers. ese multipliers are not

constants and are usually functions of all the generalized coordinates

and oen of time as well. ey represent a set of unknowns whose

values should be obtained as a part of the solution. To solve this

computational complexity, additional methods have been suggested to

remove the presence of the multipliers from the dynamic equations of

the given system [21,22].

e focus of this paper is to derive simple and well-structured

dynamic equations of the DDMR taking into account the non-

holonomic constraints. First, the Lagrange formulation is presented.

Coordinates transformation is used to cancel the Lagrange multipliers

to obtain well-structured equations. Second, the Newton-Euler method

is used to derive the dynamic equations of the DDMR. Major diculties

experienced in using both methods are illustrated and procedures are

outlined to oer a systematic approach to the dynamic modeling of

*Corresponding author: Rached Dhaouadi, College of Engineering, American

University of Sharjah, P.O. Box 26666, Sharjah, UAE, E-mail: rdhaouadi@aus.edu

Received

June 19, 2013; Accepted September 16, 2013; Published September

19, 2013

Citation: Dhaouadi R, Hatab AA (2013) Dynamic Modelling of Differential-Drive

Mobile Robots using Lagrange and Newton-Euler Methodologies: A Unied

Framework. Adv Robot Autom 2: 107. doi: 10.4172/2168-9695.1000107

under the terms of the Creative Commons Attribution License, which permits

unrestricted use, distribution, and reproduction in any medium, provided the

original author and source are credited.

Abstract

This paper presents a unied dynamic modeling framework for differential-drive mobile robots (DDMR). Two

formulations for mobile robot dynamics are developed; one is based on Lagrangian mechanics, and the other on

Newton-Euler mechanics. Major difculties experienced when modeling non-holonomic systems in both methods are

illustrated and design procedures are outlined. It is shown that the two formulations are mathematically equivalent

providing a check on their consistency. The presented work leads to an improved understanding of differential-

drive mobile robot dynamics, which will assist engineering students and researchers in the modeling and design of

suitable controllers for DDMR navigation and trajectory tracking.

Dynamic Modelling of Differential-Drive Mobile Robots using Lagrange and

Newton-Euler Methodologies: A Unified Framework

Rached Dhaouadi* and Ahmad Abu Hatab

College of Engineering, American University of Sharjah, Sharjah, UAE

Advances in Robotics

& Automation

ISSN: 2168-9695

下载后可阅读完整内容，剩余6页未读，立即下载

寒墨阁

粉丝: 5171
资源: 33

拉格朗日与牛顿欧拉方法：差动机器人动力学建模详解

JACKET-PIPE-MODELLING.doc

信息安全_数据安全_AppSecEU2016-Christian-Mainka-Breaking-And-Fixing.pdf

Snake Robots - Modelling, Mechatronics and Control

在工程设计中，代理优化模型的构建与应用流程是怎样的？请结合《Engineering Design via Surrogate Modelling: A Practical Guide-1.pdf》中的内容给出详细说明。

obotics - modelling, planning and control

在工程设计中，如何利用代理模型优化方法提升设计效率和准确性？请结合《Engineering Design via Surrogate Modelling: A Practical Guide-1.pdf》中的内容进行详细阐述。

有关系统辨识与分数阶PID控制的英文文献

构建木材非线性和多尺度的本构模型的相关文献

基于merton跳扩散模型的实证研究最新文献

最新资源