非惯性系下弹性欠驱动机器人动力学建模及应用

中国机械工程 ›› 2014, Vol. 25 ›› Issue (15): 2080-2085.

非惯性系下弹性欠驱动机器人动力学建模及应用

耿明超1,2;赵铁石1,2;赵飞1,2;刘晓1,2;苑飞虎1,2

1.燕山大学河北省并联机器人与机电系统实验室,秦皇岛,066004
2.燕山大学先进锻压成形技术与科学教育部重点实验室,秦皇岛,066004

出版日期:2014-08-10 发布日期:2014-08-13
基金资助:
国家自然科学基金资助项目(51375240,50975244)

Dynamics Model of Elastic Underacutated Robot in a Non-inertial Frame and Its Applicaitons

Geng Mingchao1,2;Zhao Tieshi1,2;Zhao Fei1,2;Liu Xiao1,2;Yuan Feihu1,2

1.Hebei Provincial Key Laboratory of Parallel Robot and Mechatronic System, Yanshan University, Qinhuangdao, Hebei, 066004
2.Key Laboratory of Advanced Forging & Stamping Technology and Science of Ministry of Education of China, Yanshan University, Qinhuangdao,Hebei,066004

Online:2014-08-10 Published:2014-08-13
Supported by:
National Natural Science Foundation of China（No. 51375240,50975244）

摘要/Abstract

摘要：

以旋量为基本运算单元，建立了非惯性系下弹性欠驱动机器人的动力学模型。首先以两个旋量的李括弧运算为基础，得到了惯性系下机器人的加速度映射关系。利用多刚体系统的速度、加速度旋量在不同坐标系之间的变换，推导出非惯性系下机器人在惯性系中的加速度映射关系。然后利用刚体的牛顿-欧拉公式，建立了非惯性系下机器人的动力学模型。推导的过程中始终以运动旋量、力旋量为基本的运算单元，简化了动力学建模过程。最后，以空中加油系统这种典型的非惯性系下的弹性欠驱动的应用为例，建立了其在非惯性系下的动力学模型，并用动力学仿真软件进行了验证，验证了理论分析的正确性和可行性。

关键词: 弹性欠驱动, 旋量, 动力学, 非惯性系

Abstract:

A dynamics model of elastic underacutated robot in a non-inertial frame was established based on screws. Firstly, the acceleration mapping of robot which was in inertia frame was obtained referring to the Lie bracket of two screws. The acceleration mapping in a non-inertia frame was deducted through the transformation of the rigid-body velocity and acceleration in different frames. Then the dynamics model of robot in a non-inertia frame was obtained using the rigid-body Newton-Euler equation. The dynamics model is simple because of the use of the twist and wrench in the process of derivation. Finally, the aerial refueling system, which was a typical application of an elastic underactuated robot in a non-inertia frame, was taken as an example. The dynamics model of the system was presented, and was verified by dynamics simulation software, which demonstrates the correctness and feasibility of the theoretical analysis.

Key words: elastic underactuated;screw;dynamics;non-inertia , frame

中图分类号:

TP242
TP391

耿明超, 赵铁石, 赵飞, 刘晓, 苑飞虎, . 非惯性系下弹性欠驱动机器人动力学建模及应用[J]. 中国机械工程, 2014, 25(15): 2080-2085.

Geng Mingchao, Zhao Tieshi, Zhao Fei, Liu Xiao, Yuan Feihu, . Dynamics Model of Elastic Underacutated Robot in a Non-inertial Frame and Its Applicaitons[J]. China Mechanical Engineering, 2014, 25(15): 2080-2085.

参考文献

[1]Spong M W.Underactuated Mechanical System[C]//International Workshop on Control Problems in Robotics and Automation. San Diego,California,1997:1-15.
[2]陈炜,余跃庆,张绪平.欠驱动机器人研究综述[J].机械设计与研究,2005,25(4):22-26.
Chen Wei,Yu Yueqing,Zhang Xuping.A Survey on the Underactuated Robots[J].Machine Design and Research, 2005, 25(4): 22-26.
[3]赖旭芝.一类非完整欠驱动机械系统的智能控制[D].长沙:中南大学,2001.
[4]理查德·摩西,李泽湘，夏恩卡·萨思特里.机器人操作的数学导论[M].北京:机械工业出版社，1995.
[5]De Luca,Iannitti S.A Simple STLC Test for Mechanical System Underactuated by One Control[C]//Proc. of IEEE International Conference on R&A.Washington.D C,2002:1735-1740.
[6]Mullhaupt Ph,Srinivasan B, Bonvin D.Analysis of Exclusively Kinetie Two-link Underactuated Mechanical System[J]. Automatica,2002,38:1565-1573.
[7]方道星,余跃庆,周刚,等.2R平面欠驱动机器人轨迹控制研究[J].中国机械工程,2008,19(9):1016-1021.
Fang Daoxing,Yu Yueqing,Zhou Gang,et al.Study on the Trajectory Control of a 2R Horizontal Underactuated Robot[J]. China Mechanical Engineering,2008,19(9):1016-1021.
[8]Lai Xuzhi,Pan Changzhong,Min Wu,et al.Unified Control of N-link Underactuated Manipulator with Single Passive Joint: A Reduced Order Approach[J].Mechanism and Machine Theory,2012,56:170-185.
[9]邓秀娟,陆震.基于微分几何的欠驱动机器人动力学建模和控制[J].机械工程学报,2007,43(10):132-136.
Deng Xiaojuan,Lu Zhen.Underactuated Robot Dynamic Modeling and Control Based on Differential Geometry. Journal of Mechanical Engineering,2007,43(10):132-136.
[10]Bergerman M,Lee C,Xu Yangsheng.Dynamic Coupling of Underactuated Manipulators[C]//Prc. of the 4th IEEE Comference on Control Application.Albany,USA,1995:500-505.
[11]Tie Shizhao,Jian S D.Dynamic and Coupling Actuation of Elastic Underactuated Manipulators[J].Joural of Robtic System,2003,20(3):135-146.
[12]陈炜,余跃庆,张绪平,等.欠驱动柔性机器人的动力学建模与耦合特性[J].机械工程学报,2006,42(6):16-23.
Chen Wei,Yu Yueqing,Zhang Xuping,et al.Dynamic Modeling and Coupling of Underactuated Flexible Robtot[J].Journal of Mechanical Engineering,2006,42(6):16-23.
[13]Selig J M.Geometrical Foundations of Robotics[M].New York:World Scientific Publishing Co. Pte. Ltd.,2000.
[14]黄真,赵永生,赵铁石.高等空间机构学[M].北京:高等教育出版社,2006.
[15]Zhao Tieshi,Geng Mingchao,Liu Xiao,et al.Kinematics and Dynamics Hessian Matrixes of Manipulators Based on Lie Bracket.[2013-03-06].http://www.paper.edu.cn/releasepaper/content/201303-167.
[16]Zhao Tieshi,Liu Xiao,Geng Mingchao,et al.Acceleration Analysis of Rigid Body and Its Application for Ship-based Stabilized Platform System.[2013-02-25].http://www.paper.edu.cn/releasepaper/content/201302-420.