谐振式微小型机器人动力学模型及参数研究
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摘要
微小型机器人具有小体积、高柔性、低成本等优点,在表面检测、微机电系统组装、微外科手术、生物工程、光学工程等领域有着广阔的应用前景。微小型机器人的特点及精密作业任务的需求通常要求其移动机构必须具备结构简单、运动分辨力高、运动速度快等特点,而现有的微小型机器人移动机构大都难以同时兼顾以上三个方面的要求。
针对微小型机器人移动机构存在的以上问题,哈尔滨工业大学提出一种由双压电膜驱动的移动机构。该机构可以采用粘滑驱动原理较高的运动分辨力;也可以采用谐振驱动原理实现较高运动速度。但由于谐振足配置方式不当导致机构尺寸过大,难以实现小型化。本文提出的机器人采用新的谐振足配置方式可以有效地减小机构尺寸。
本文的移动机构利用谐振足的弹性振动和与行走表面的碰撞实现运动。首先,本文基于模态分析结果,对高阶振动模态进行截断,针对低阶模态的振型与频率构造了谐振足的多刚体有限自由度简化动力学模型,基于Hertz接触理论与Coulomb摩擦理论建立了谐振足与行走表面的接触模型,由此建立了谐振足系统的完整模型。搭建实验系统测量谐振足的振动和机器人的速度曲线,验证建模方法和模型的正确性。研究谐振足在正弦信号激励和地面非线性约束下的运动状态,建立系统的庞加莱映射,发现系统随频率变化由周期运动过渡到混沌的过程。通过系统的能量分布分析了解影响系统运动的主导因素。
其次依据能量分析的结果,设计了几种不同结构的机器人样机,仿真研究了模态、刚度以及耦合角对机器人运动的影响,发现机器人在两种模态下的不同运动情况。仿真研究了系统在不同幅值的外界输入下的速度曲线,并细致研究了谐振足在高频信号激励下随着输入增大而发生的分岔和混沌现象,探讨了系统混沌运动的深层机理。面向应用场合的要求和能量分析的结果,仿真研究了系统的在不同负载下的运动情况。
最后研制几种不同刚度和耦合角的机器人样机,测量了空载下的速度曲线,并与仿真结果对照。测试了其中两种机器人在不同幅值的外界激励下的运动速度曲线。测试机器人在负载下的运动速度曲线。
Miniature mobile robot which is the typical micro electrical mechanical Systems have potential applications in many domains, such as, surface inspection, handling and assembly of MEMS (Micro-electro-mechanical systems), minimally invasive surgery, bio-engineering, and optical engineering, et al. The locomotion mechanisms in simple structures with high moving resolutions and high driving velocity are required by the micro and miniature robots as they will handle with the sophisticated tasks. Unfortunately, the existing locomotion mechanisms cannot satisfy these requirements at the same time.
To solve the problem mentioned above, a novel micro and miniature robot locomotion mechanism driven by bimorphs is proposed. The new locomotion mechanism can get high driving velocity with resonance principle and high moving resolutions with stick-slip principle. However the mechanism is still too large because of the configuration of the legs. New locomotion mechanism is proposed to solve these problems.
Mechanism is driven by the vibration of the flexible legs and the impacts between legs and the walking surface. To simple the analysis, a multi-rigid-body model with finite degrees of freedom of the flexible leg is constructed based on the results of modal analysis to reduce the dimensions of system. Then, the impact model between the flexible leg and the walking surface is constructed based on Hertz contact theory and Coulomb friction theory. A experiment system is establish to measure the vibration of the legs and the speed of the robot. The motions of the flexible leg are studied using the numerical simulation. Establish the Poincarésection, and the results show that the motions change from periodic to chaotic with the changing of the frequency. From the angle of changes in system energy, the investigation is on the drive principle when the motion is chaos. Get the dominate factors in the motion through the energy attribution in the system.
Base on the result of the energy analysis, robots with different structures are designed. The impacts of the modal, stiffness and the coupling angle are analyzed by the numerical simulation. And find different movement state in two modal. Simulate the robot speed under different amplitude input and research the Bifurcation and Chaos in detail. And simulate the robot motion with different load.
The robots with different structure and coupling angle are manufactured, the speed is tested. Test speed of the two robots under different amplitude input, and the speed of the robot under load.
针对微小型机器人移动机构存在的以上问题,哈尔滨工业大学提出一种由双压电膜驱动的移动机构。该机构可以采用粘滑驱动原理较高的运动分辨力;也可以采用谐振驱动原理实现较高运动速度。但由于谐振足配置方式不当导致机构尺寸过大,难以实现小型化。本文提出的机器人采用新的谐振足配置方式可以有效地减小机构尺寸。
本文的移动机构利用谐振足的弹性振动和与行走表面的碰撞实现运动。首先,本文基于模态分析结果,对高阶振动模态进行截断,针对低阶模态的振型与频率构造了谐振足的多刚体有限自由度简化动力学模型,基于Hertz接触理论与Coulomb摩擦理论建立了谐振足与行走表面的接触模型,由此建立了谐振足系统的完整模型。搭建实验系统测量谐振足的振动和机器人的速度曲线,验证建模方法和模型的正确性。研究谐振足在正弦信号激励和地面非线性约束下的运动状态,建立系统的庞加莱映射,发现系统随频率变化由周期运动过渡到混沌的过程。通过系统的能量分布分析了解影响系统运动的主导因素。
其次依据能量分析的结果,设计了几种不同结构的机器人样机,仿真研究了模态、刚度以及耦合角对机器人运动的影响,发现机器人在两种模态下的不同运动情况。仿真研究了系统在不同幅值的外界输入下的速度曲线,并细致研究了谐振足在高频信号激励下随着输入增大而发生的分岔和混沌现象,探讨了系统混沌运动的深层机理。面向应用场合的要求和能量分析的结果,仿真研究了系统的在不同负载下的运动情况。
最后研制几种不同刚度和耦合角的机器人样机,测量了空载下的速度曲线,并与仿真结果对照。测试了其中两种机器人在不同幅值的外界激励下的运动速度曲线。测试机器人在负载下的运动速度曲线。
Miniature mobile robot which is the typical micro electrical mechanical Systems have potential applications in many domains, such as, surface inspection, handling and assembly of MEMS (Micro-electro-mechanical systems), minimally invasive surgery, bio-engineering, and optical engineering, et al. The locomotion mechanisms in simple structures with high moving resolutions and high driving velocity are required by the micro and miniature robots as they will handle with the sophisticated tasks. Unfortunately, the existing locomotion mechanisms cannot satisfy these requirements at the same time.
To solve the problem mentioned above, a novel micro and miniature robot locomotion mechanism driven by bimorphs is proposed. The new locomotion mechanism can get high driving velocity with resonance principle and high moving resolutions with stick-slip principle. However the mechanism is still too large because of the configuration of the legs. New locomotion mechanism is proposed to solve these problems.
Mechanism is driven by the vibration of the flexible legs and the impacts between legs and the walking surface. To simple the analysis, a multi-rigid-body model with finite degrees of freedom of the flexible leg is constructed based on the results of modal analysis to reduce the dimensions of system. Then, the impact model between the flexible leg and the walking surface is constructed based on Hertz contact theory and Coulomb friction theory. A experiment system is establish to measure the vibration of the legs and the speed of the robot. The motions of the flexible leg are studied using the numerical simulation. Establish the Poincarésection, and the results show that the motions change from periodic to chaotic with the changing of the frequency. From the angle of changes in system energy, the investigation is on the drive principle when the motion is chaos. Get the dominate factors in the motion through the energy attribution in the system.
Base on the result of the energy analysis, robots with different structures are designed. The impacts of the modal, stiffness and the coupling angle are analyzed by the numerical simulation. And find different movement state in two modal. Simulate the robot speed under different amplitude input and research the Bifurcation and Chaos in detail. And simulate the robot motion with different load.
The robots with different structure and coupling angle are manufactured, the speed is tested. Test speed of the two robots under different amplitude input, and the speed of the robot under load.
引文
1 A. Kortschack, S. Fatikow.Smart Materials for actuation in microrobots. Smart Structures, Devices, and Systems, Erol C. Harvey, Derek Abbott, Vijay Varadan,Editors, Proceedings of SPIE Vol. 4935 (2002) ? 2002 SPIE·0277-786X/02
2张永顺,李海亮.超磁致伸缩薄膜驱动仿生游动微型机器人.机器人. 2006年3月:170~176
3李明东,奚汉达,储金荻,马培荪,程君实.一种形状记忆合金驱动的微小型六足机器人.上海交通大学学报. 2000, 34(10): 1425~1429
4梅涛,陈永.铁磁橡胶执行器与微型游泳机器人的尺度效应.光学精密工程.第9卷第6期. 2001年12月:523~526
5宋晓峰,谈士力.微型机器人的发展和研究现状.机床与液压.2004.8:1~2
6周群,何斌,岳继光.仿生微型机器人的研究与发展.机床与液压.2007.4: 225~228
7 G. Caprari, P. Balmer, R. Piguet, R. Siegwart.The Autonomous Micro Robot "Alice": a platform for scientific and commercial applications.1998 INTERNATIONAL SYMPOSIUM ON MICROMECHATRONICS AND HUMAN SCIENCE 0-7803-5131-4/98 01998 IEEE.
8李江昊,李振波,陈佳品.毫米级全方位移动微型装配机器人设计、运动学分析与控制.机器人, 2008, 30(1): 63~69
9李江昊,李振波,陈佳品.一种用于微型工厂的毫米级全方位移动微机器人设计与分析.机器人. 2007, 29(5): 423~427
10李江昊,陈佳品,李振波.毫米级全方位微机器人结构设计与控制对运动精度的影响.光学精密工程. 2008, 16(6): 1056~1062
11 H.Aoyama, O.Fuchiwaki, D.Misaki, T.Usuda. Desktop micro machining system by multiple micro robots. IEEE Conference on Robotics, Automation and Mechatronics, Bangkok, Thailand, IEEE, 2006: 4018735
12 O.Fuchiwaki, C.Kanomori, H.Aoyama, D.Misaki. Development of the orthogonal micro robot for accurate microscopic operations. IEEE International Conference on Mechatronics and Automation, Harbin, China, IEEE, 2007, 416~421
13 O.Fuchiwaki, A.Ito, D.Misaki, H.Aoyama. Multi-axial micromanipulation organized by versatile micro robots and micro tweezers. IEEE International Conference on Robotics and Automation, Pasadena, CA, United States, IEEE, 2008, 893~898
14 D.Misaki, S.Kayano, Y.Wakikaido, O.Fuchiwaki, H.Aoyama. Precise automatic guiding and positioning of micro robots with a fine tool for microscopic operations. IEEE/RSJ International Conference on Intelligent Robots and Systems, Sendai, Japan, IEEE, 2004, 1: 218~223
15 Young Pyo Lee, Byungkyu Kim, Moon Gu Lee and Jong-Oh Park.Locomotive Mechanism Design and Fabrication of Biomimetic Micro Robot Using Shape Memory Alloy.Proceedings of the 2004 IEEE International Conference on Robotics &Automation New Orleans, LA Aprll2004
16 H.W?rn, J.Seyfried, S.Fahlbusch, A.Bürkle, F.Schmoeckel. Flexible Microrobots for Micro Assembly Tasks. International Symposium on Micromechatronics and Human Science, United states, 2000, Institute of Electrical and Electronics Engineers Inc.: 135-143
17 H.Worn, F.Schmoeckel, A.Buerkle, J.Samitier, M.Puig-Vidal, S.Johansson, U.Simu, J.U.Meyer, M.Biehl. From decimeter- to centimeter-sized mobile microrobots - The development of the MINIMAN system. The International Society for Optical Engineering, Newton, MA, United states, SPIE, 2001, 4568: 175~186
18 S.Fatikow, J.Seyfried, S.Fahlbusch, A.Bürkle, F.Schmoeckel. Development of a Microrobot-based Microassembly Station, International Conference on Advanced Robotics, Tokyo, 1999: 205~210
19 S.Fatikow, J.Seyfried, S.Fahlbusch, A.Bürkle, F.Schmoeckel, H.W?rn. Intelligent Microrobotic System for Microassembly Tasks. International Conference on Mechatronics and Robotics, 2000
20 Walter Driesen, Thierry Varidel.Flexible micro manipulation platform based on tethered cm3-sized mobile micro robots.2005 IEEE international conference on robotics and biomimetics
21 Y.Nomura, H.Aoyama. Development of inertia driven micro robot with nano tilting stage for SEM operation. Microsystem Technologies. 2007, 13(8-10):1347~1352
22 Zesch, R.Buechi, A.Codourey, R.Siegwart. Inertial drives for micro- and nanorobots: two novel mechanisms. The International Society for Optical Engineering, Philadelphia, PA, USA, SPIE, 1995, 2593: 80~88
23 Agnes Bonvilain, Nicolas Chaillet.Fabrication and Experiment of Microlegs for an Insect-Like Microrobot. Microrobotics and Microassembly III, Bradley J. Nelson, Jean-Marc Breguet, Editors,Proceedings of SPIE Vol. 4568 (2001) ? 2001 SPIE·0277-786X/01
24陈西平,杨志刚,程光明,曾平.双弯曲振子型压电式管内移动机构的试验研究.压电与声光. 2002, 24(4): 323~326
25陈西平,杨志刚,程光明,曾平.谐振型压电式管内移动机构.吉林大学学报(工学版). 2002, 32(1): 28~32
26贺红林,金家楣,赵淳生.一种基于压电驱动的小型移动机器人的研究.压电与声光. 2006, 28(5):520~523
27 Gregory Fischer, Adam G. Cox, Michael Gogola, M. Kurt Gordon. Elastodynamic locomotion in mesoscale robotic insects. Part of the SPIE Conference on Electroactive Polymer Actuators 362 and Devices Newport Beach, California ? March 1999:362~368
28 M.F.A.Azeez, A.F.Vakakis. Proper orthogonal decomposition(POD) of a class of vibroimpact oscillations. Journal of sound and vibration. 2001, 240(5): 859~889
29 M.John, J.Boyle, B.Bharat. Vibration modeling of magnetic tape with vibr-impact of tape-guide contact. Journal of sound and vibration. 2006, 289: 632~655
30 D.J.Wagg, S.F.Bishop. Application of non-smooth modeling techniques to the dynamics of a flexible impacting beam. Journal of sound and vibration. 2002, 256(5): 803~820
31 K.L.Johnson.接触力学.徐秉业译.高等教育出版社. 1992: 103~122
32 S.Dubowsky, T.N.Gardner. Dynamic interactions of link elasticity and cleatance connections in planar mechanical systems. Journal of engineering for industry. 1975, 97B(2): 652~661
33 Walter Sextro.Dynamical contact problems with friction.Springer2002:53~58
34汪盛.基于粘滑原理的摩擦力驱动机理研究与建模.哈尔滨工业大学硕士学位论文. 2006:13~15
35刘强,尔联洁,刘金琨.摩擦非线性环节的特性、建模与控制补偿综述. 2002,24(11):45~50
36刘秉正,彭建华.非线性动力学.高等教育出版社.2005:14~15
37张伟,霍拳忠,李骊.非线性振动系统的异宿轨道分叉、次谐分叉和混沌.应用数学和力学.1992,13(3):199~208
38龙运佳.混沌振动研究.清华大学出版社.1997:7~12
39韩维.斜碰撞振动系统动力学研究.南京航空航天大学博士学位论文. 2003: 39~40
40黄润生,黄浩.混沌及其应用.第二版.武汉大学出版社, 2005:170~178
2张永顺,李海亮.超磁致伸缩薄膜驱动仿生游动微型机器人.机器人. 2006年3月:170~176
3李明东,奚汉达,储金荻,马培荪,程君实.一种形状记忆合金驱动的微小型六足机器人.上海交通大学学报. 2000, 34(10): 1425~1429
4梅涛,陈永.铁磁橡胶执行器与微型游泳机器人的尺度效应.光学精密工程.第9卷第6期. 2001年12月:523~526
5宋晓峰,谈士力.微型机器人的发展和研究现状.机床与液压.2004.8:1~2
6周群,何斌,岳继光.仿生微型机器人的研究与发展.机床与液压.2007.4: 225~228
7 G. Caprari, P. Balmer, R. Piguet, R. Siegwart.The Autonomous Micro Robot "Alice": a platform for scientific and commercial applications.1998 INTERNATIONAL SYMPOSIUM ON MICROMECHATRONICS AND HUMAN SCIENCE 0-7803-5131-4/98 01998 IEEE.
8李江昊,李振波,陈佳品.毫米级全方位移动微型装配机器人设计、运动学分析与控制.机器人, 2008, 30(1): 63~69
9李江昊,李振波,陈佳品.一种用于微型工厂的毫米级全方位移动微机器人设计与分析.机器人. 2007, 29(5): 423~427
10李江昊,陈佳品,李振波.毫米级全方位微机器人结构设计与控制对运动精度的影响.光学精密工程. 2008, 16(6): 1056~1062
11 H.Aoyama, O.Fuchiwaki, D.Misaki, T.Usuda. Desktop micro machining system by multiple micro robots. IEEE Conference on Robotics, Automation and Mechatronics, Bangkok, Thailand, IEEE, 2006: 4018735
12 O.Fuchiwaki, C.Kanomori, H.Aoyama, D.Misaki. Development of the orthogonal micro robot for accurate microscopic operations. IEEE International Conference on Mechatronics and Automation, Harbin, China, IEEE, 2007, 416~421
13 O.Fuchiwaki, A.Ito, D.Misaki, H.Aoyama. Multi-axial micromanipulation organized by versatile micro robots and micro tweezers. IEEE International Conference on Robotics and Automation, Pasadena, CA, United States, IEEE, 2008, 893~898
14 D.Misaki, S.Kayano, Y.Wakikaido, O.Fuchiwaki, H.Aoyama. Precise automatic guiding and positioning of micro robots with a fine tool for microscopic operations. IEEE/RSJ International Conference on Intelligent Robots and Systems, Sendai, Japan, IEEE, 2004, 1: 218~223
15 Young Pyo Lee, Byungkyu Kim, Moon Gu Lee and Jong-Oh Park.Locomotive Mechanism Design and Fabrication of Biomimetic Micro Robot Using Shape Memory Alloy.Proceedings of the 2004 IEEE International Conference on Robotics &Automation New Orleans, LA Aprll2004
16 H.W?rn, J.Seyfried, S.Fahlbusch, A.Bürkle, F.Schmoeckel. Flexible Microrobots for Micro Assembly Tasks. International Symposium on Micromechatronics and Human Science, United states, 2000, Institute of Electrical and Electronics Engineers Inc.: 135-143
17 H.Worn, F.Schmoeckel, A.Buerkle, J.Samitier, M.Puig-Vidal, S.Johansson, U.Simu, J.U.Meyer, M.Biehl. From decimeter- to centimeter-sized mobile microrobots - The development of the MINIMAN system. The International Society for Optical Engineering, Newton, MA, United states, SPIE, 2001, 4568: 175~186
18 S.Fatikow, J.Seyfried, S.Fahlbusch, A.Bürkle, F.Schmoeckel. Development of a Microrobot-based Microassembly Station, International Conference on Advanced Robotics, Tokyo, 1999: 205~210
19 S.Fatikow, J.Seyfried, S.Fahlbusch, A.Bürkle, F.Schmoeckel, H.W?rn. Intelligent Microrobotic System for Microassembly Tasks. International Conference on Mechatronics and Robotics, 2000
20 Walter Driesen, Thierry Varidel.Flexible micro manipulation platform based on tethered cm3-sized mobile micro robots.2005 IEEE international conference on robotics and biomimetics
21 Y.Nomura, H.Aoyama. Development of inertia driven micro robot with nano tilting stage for SEM operation. Microsystem Technologies. 2007, 13(8-10):1347~1352
22 Zesch, R.Buechi, A.Codourey, R.Siegwart. Inertial drives for micro- and nanorobots: two novel mechanisms. The International Society for Optical Engineering, Philadelphia, PA, USA, SPIE, 1995, 2593: 80~88
23 Agnes Bonvilain, Nicolas Chaillet.Fabrication and Experiment of Microlegs for an Insect-Like Microrobot. Microrobotics and Microassembly III, Bradley J. Nelson, Jean-Marc Breguet, Editors,Proceedings of SPIE Vol. 4568 (2001) ? 2001 SPIE·0277-786X/01
24陈西平,杨志刚,程光明,曾平.双弯曲振子型压电式管内移动机构的试验研究.压电与声光. 2002, 24(4): 323~326
25陈西平,杨志刚,程光明,曾平.谐振型压电式管内移动机构.吉林大学学报(工学版). 2002, 32(1): 28~32
26贺红林,金家楣,赵淳生.一种基于压电驱动的小型移动机器人的研究.压电与声光. 2006, 28(5):520~523
27 Gregory Fischer, Adam G. Cox, Michael Gogola, M. Kurt Gordon. Elastodynamic locomotion in mesoscale robotic insects. Part of the SPIE Conference on Electroactive Polymer Actuators 362 and Devices Newport Beach, California ? March 1999:362~368
28 M.F.A.Azeez, A.F.Vakakis. Proper orthogonal decomposition(POD) of a class of vibroimpact oscillations. Journal of sound and vibration. 2001, 240(5): 859~889
29 M.John, J.Boyle, B.Bharat. Vibration modeling of magnetic tape with vibr-impact of tape-guide contact. Journal of sound and vibration. 2006, 289: 632~655
30 D.J.Wagg, S.F.Bishop. Application of non-smooth modeling techniques to the dynamics of a flexible impacting beam. Journal of sound and vibration. 2002, 256(5): 803~820
31 K.L.Johnson.接触力学.徐秉业译.高等教育出版社. 1992: 103~122
32 S.Dubowsky, T.N.Gardner. Dynamic interactions of link elasticity and cleatance connections in planar mechanical systems. Journal of engineering for industry. 1975, 97B(2): 652~661
33 Walter Sextro.Dynamical contact problems with friction.Springer2002:53~58
34汪盛.基于粘滑原理的摩擦力驱动机理研究与建模.哈尔滨工业大学硕士学位论文. 2006:13~15
35刘强,尔联洁,刘金琨.摩擦非线性环节的特性、建模与控制补偿综述. 2002,24(11):45~50
36刘秉正,彭建华.非线性动力学.高等教育出版社.2005:14~15
37张伟,霍拳忠,李骊.非线性振动系统的异宿轨道分叉、次谐分叉和混沌.应用数学和力学.1992,13(3):199~208
38龙运佳.混沌振动研究.清华大学出版社.1997:7~12
39韩维.斜碰撞振动系统动力学研究.南京航空航天大学博士学位论文. 2003: 39~40
40黄润生,黄浩.混沌及其应用.第二版.武汉大学出版社, 2005:170~178