内外驱动兼备的球形机器人运动学及动力学研究
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摘要
球形机器人是一种新型的移动机器人,具有球形外壳,能够在失稳后获得最大的稳定性,不怕翻倒,可以实现全向滚动,转弯更加灵活。球形机器人是传统机器人运动方式的突破,是移动机器人研究领域的热点问题之一。
目前的球形机器人大多为内部驱动,很难解决能源供给问题。为此,本文提出了一种内外驱动兼备的球形机器人,并对其进行了结构设计、越障性能分析、运动学和动力学分析方面的研究。
首先介绍了球形机器人的发展现状,给出了目前球形机器人研究中遇到的主要问题。通过应用机器人重心偏移力偶驱动的方法,设计了一种内外驱动兼备的球形机器人装置。该球形机器人以外部风能驱动为主,以球体内部电机驱动为辅。运用空气动力学和静力学理论建立了机器人的静力学平衡方程,根据力矩平衡原理建立了描述该球形机器人越障运动性能的约束方程,得出了风速、地形倾角、障碍物高度、球体尺寸及重量等各物理参数之间的函数关系。基于广义欧拉角描述球形机器人的坐标变换,运用系统的动量矩定理,建立了球形机器人的运动模型。基于Lagrange-Routh方程和非完整约束理论,建立了该机器人平面运动的动力学模型,推导出了机器人的动力学运动微分方程。编制了运动分析程序,并进行了计算机仿真分析。最后,制作了内外驱动兼备的球形机器人的样机,通过样机测试,得到了一些实验数据,对机器人运动模型的正确性进行了验证。
Spherical robots are a new type of mobile robots with a global shell, and it can obtain the great steady ability after being imposed a disturbance, achieve the omnidirectional rolling, swerve agilely and never overturn. Being a breakthrough of the motion modes of traditional robots, spherical robots are one of the sbjects in great demand for the mobile robots' research.
At present, much of spherical robots are driven by inside drive units that are difficult to solve the problem of supplying the enough power source for the robots system. In this paper, a kind of internal and external driven spherical robot is presented and its structural design, performance of overcoming obstacles, kinematics and dynamics analysis are mainly studied.
At the beginning, the status in quo of the research on spherical robots was stated and the existing main problems followed. Then the internal and external driven spherical robot was chosen as the studied object. The spherical robot was designed based on the method of applying the robot-driven force couple caused by offseting the gravity center. And, it was driven mainly by the external wind force and had the internal motor as its sub-drive impetus. Using the theory of aerodynamics and statics, the static equilibrium equation of the spherical robot was built. According to the theory of moment balance, the constraint equations that described the performance of overcoming obstacles for the spherical robot was developed. With these equations, wind velocity, the slope angle of the terrain, the height of obstacles, the size and weight of the sphere and the ball-ground contact area were determined to be associated each other by some functions. Moreover, basing on the spherical robot's coordinate conversion described by the generalized Euler angles, its motion model was developed by using of the theorem of momentum moment. The dynamics model of the robot on a plane were established by using the theory of nonholonomic constraints and Lagrange-Routh equations. From this, the differential equations of dynamics for the robot motioning were deduced and the motion analysis programmes were composed. Several typical motion cases of the robot were illustrated and simulated by computer. Finally, the prototype of the internal and external driven spherical robot was produced. Several tests were made and obtained some experimental data. So, the correctness of the robot's motion model has been verified.
目前的球形机器人大多为内部驱动,很难解决能源供给问题。为此,本文提出了一种内外驱动兼备的球形机器人,并对其进行了结构设计、越障性能分析、运动学和动力学分析方面的研究。
首先介绍了球形机器人的发展现状,给出了目前球形机器人研究中遇到的主要问题。通过应用机器人重心偏移力偶驱动的方法,设计了一种内外驱动兼备的球形机器人装置。该球形机器人以外部风能驱动为主,以球体内部电机驱动为辅。运用空气动力学和静力学理论建立了机器人的静力学平衡方程,根据力矩平衡原理建立了描述该球形机器人越障运动性能的约束方程,得出了风速、地形倾角、障碍物高度、球体尺寸及重量等各物理参数之间的函数关系。基于广义欧拉角描述球形机器人的坐标变换,运用系统的动量矩定理,建立了球形机器人的运动模型。基于Lagrange-Routh方程和非完整约束理论,建立了该机器人平面运动的动力学模型,推导出了机器人的动力学运动微分方程。编制了运动分析程序,并进行了计算机仿真分析。最后,制作了内外驱动兼备的球形机器人的样机,通过样机测试,得到了一些实验数据,对机器人运动模型的正确性进行了验证。
Spherical robots are a new type of mobile robots with a global shell, and it can obtain the great steady ability after being imposed a disturbance, achieve the omnidirectional rolling, swerve agilely and never overturn. Being a breakthrough of the motion modes of traditional robots, spherical robots are one of the sbjects in great demand for the mobile robots' research.
At present, much of spherical robots are driven by inside drive units that are difficult to solve the problem of supplying the enough power source for the robots system. In this paper, a kind of internal and external driven spherical robot is presented and its structural design, performance of overcoming obstacles, kinematics and dynamics analysis are mainly studied.
At the beginning, the status in quo of the research on spherical robots was stated and the existing main problems followed. Then the internal and external driven spherical robot was chosen as the studied object. The spherical robot was designed based on the method of applying the robot-driven force couple caused by offseting the gravity center. And, it was driven mainly by the external wind force and had the internal motor as its sub-drive impetus. Using the theory of aerodynamics and statics, the static equilibrium equation of the spherical robot was built. According to the theory of moment balance, the constraint equations that described the performance of overcoming obstacles for the spherical robot was developed. With these equations, wind velocity, the slope angle of the terrain, the height of obstacles, the size and weight of the sphere and the ball-ground contact area were determined to be associated each other by some functions. Moreover, basing on the spherical robot's coordinate conversion described by the generalized Euler angles, its motion model was developed by using of the theorem of momentum moment. The dynamics model of the robot on a plane were established by using the theory of nonholonomic constraints and Lagrange-Routh equations. From this, the differential equations of dynamics for the robot motioning were deduced and the motion analysis programmes were composed. Several typical motion cases of the robot were illustrated and simulated by computer. Finally, the prototype of the internal and external driven spherical robot was produced. Several tests were made and obtained some experimental data. So, the correctness of the robot's motion model has been verified.
引文
[1]朱超.具有稳定平台的全向滚动机器人的研究[D].西安电子科技大学,2006.
[2]张学锋.一种球形机器人的动力学分析和轨迹规划研究[D].西安电子科技大学,2007.
[3]孙汉旭,肖爱平,贾庆轩.二驱动球形机器人的全方位运动特性分析[J].北京航空航天大学学报,2005,31(7):735-739.
[4]邓宗全,岳明.球形机器人的发展概况综述[J].机器人技术与应用,2006,(3):27-31.
[5]李团结,朱超.一种具有稳定平台可全向滚动的球形机器人设计与分析[J].西安电子科技大学学报,2006,33(1):53-56.
[6]王亮清,孙汉旭,贾庆轩.球形机器人的圆周运动分析[J].机器人,2007,29(1):56-60.
[7]林杰,芮延年,周国梁,任芸丹,陈慧萍.一种全方位球形机器人的运动学分析[J].苏州大学学报,2005,25(4):71-73.
[8]李团结,张学锋,陈永琴.一种全向滚动球形机器人的运动分析与轨迹规划[J].西安电子科技大学学报,2007,34(1):29-33.
[9]Jeffrey Antol,Philip Calhoun,John Flick,and Gregory Hajos.Low Cost Mars Surface Exploration:The Mars Tumbleweed.National Aeronautics and Space Administration.NASA/TM-2003-212411.
[10]Jeffrey Antol.A New Vehicle for Planetary Surface Exploration:The Mars Tumbleweed.1st Space Exploration Conference:Continuing the Voyage of Discovery31 January-1 February 2005,Orlando,Florida.
[11]John J.Flick and Matthew D.Toniolo.Preliminary Dynamic Feasibility and Analysis of a Spherical,Wind-Driven(Tumbleweed),Martian Rover.43rd AIAA Aerospace Sciences Meeting and Exhibit 10-13 January 2005,Reno,Nevada.
[12]H.Wang,B.Yang and J.A.Jones.Mobility Analysis of an Inflated Tumbleweed Ball under Wind Loads.43rd AIAA/ASME/ASCE/AHS/ASC Structures,Structural Dynamics,and Materials Con 22-25 April 2002,Denver,Colorado.
[13]Behzad Raiszadeh and Phillip Calhoun.Mars Tumbleweed Simulation Using Singular Perturbation Theory.AIAA Modeling and Simulation Technologies Conference and Exhibit 15-18 August 2005,San Francisco,California.
[14]Scott E.Rose,Cody B.Moody,Darryl L.James and Alan A.Barhorst.Drag Measurement and Dynamic Simulation of Martian Wind Driven Sensor Platform Concepts.43rd AIAA Aerospace Sciences Meeting and Exhibit 10-13 January 2005,Reno,Nevada.
[15]Alan A.Barhorst and Darryl L.James.Elasto-dynamic Model of a Segmented Martian Tumblweed Concept.44th AIAA Aerospace Sciences Meeting and Exhibit 9-12 January 2006,Reno,Nevada.
[16]Richard M.Kolacinski and Roger D.Quinn.Numerical Simulation of a Bouncing,Rolling and Sliding Tumbleweed Rover.43rd AIAA Aerospace Sciences Meeting and Exhibit 10-13 January 2005,Reno,Nevada.
[17]Tomi Ylikorpi,Aarne Halme and Jussi Suomela.Comparison Between Wind-Propelled Thistle and Motor-Driven Un-Balanced Thistle.44th AIAA Aerospace Sciences Meeting and Exhibit 9-12 January 2006,Reno,Nevada.
[18]Jamie L.Wilson,Alex E.Hartl,Andre Mazzoleni and Fred DeJarnette.Dynamics Modeling of a Mars Tumbleweed Rover.44th AIAA Aerospace Sciences Meeting and Exhibit 9-12 January 2006,Reno,Nevada.
[19]Lori Southard,Thomas M.Hoeg,Daniel W.Palmer,Jeffrey Antol,Richard M.Kolacinski,Roger D.Exploring Mars Using a Group of Tumbleweed Rovers.2007 IEEE International Conference on Robotics and Automation Roma,Italy,10-14 April 2007:775-780.
[20]苏翼林.材料力学[M].天津:天津大学出版社,2001.65-109.
[21]毛谦德,李振清.袖珍机械设计师手册(第3版)[M].北京:机械工业出版社,2006.528-558.
[22]刘鸿文.材料力学(上册)[M].北京:高等教育出版社,1992.136-229.
[23]徐华舫.空气动力学基础(上)[M].北京:北京航空学院出版社,1987.
[24]强元棨.经典力学[M].北京:科学出版社,2003.
[25]叶尚辉,李在贵.天线结构设计[M].西安:西北电讯工程学院出版社,1986.89-115.
[26][英]J.E.艾伦著,黄志澄,张如清译.空气动力学——运动空气的科学[M].北京:国防工业出版社,1987.
[27]卓勇志.边界层中双栋并排矩形建筑之表面风压量测[D].国立中央大学(台湾),2001.12-35.
[28][苏]к.я.康德拉捷夫,A.M.布那果娃著,王跃山译.火星气象学[M].北京:科学出版社,1978.7-20.
[29][苏]В.и.列凡托夫斯基著,凌福根等译.宇宙飞行力学基础[M].北京:国防工业出版社,1979.197-209.
[30]第612研究所.航空机械设计手册[M].内部发行,1979.274,542-550.
[31]过崇伟.航空航天技术概论[M].北京:北京航空航天大学出版社,1992.17-37.
[32]崔桂香,张兆顺.流体力学[M].北京:清华大学出版社,1999.
[33]Granger,R.A.,"Fluid Mechanics",Dover Edition,Dover Publications Inc.New York,1995.
[34]Home,W.B.,Trafford,W.L.,"Influence of Tire Tread Pattern and Runway Surface Condition on Braking Friction and Rolling Resistance of a Modem Aircraft Tire," NASA TN-D-1376,1962.
[35]陈乐生,王以伦.多刚体动力学基础[M].哈尔滨:哈尔滨工程大学出版社,1995.16-68.
[36]蒋伟.机械动力学分析[M].北京:中国传媒大学出版社,2005.3-131.
[37]Saeed B.Niku著,孙富春等译.机器人学导论[M].北京:电子工业出版社,2004.
[38]Jussi Suomela and Tomi Ylikorpi.Ball-Shaped Robots..An Historical Overview and Recent Developments at TKK.P.Corke and S.Sukkarieh(Eds.):Field and Service Robotics,STAR 25,pp.343-354,2006.
[39]梅凤翔.非完整系统力学基础[M].北京:北京工业学院出版社,1985.81-299.
[40]边宇虹.分析力学与多刚体动力学基础[M].北京:机械工业出版社,1998.
[41]陈强顺.分析力学导论[M].上海:同济大学出版社出版,1997.21-100.
[42]Jeffrey Antol,Philip C.Calhoun,John J.Flick,Gregory A.Hajos,Jennifer P.Keyes,Frederic H.Stillwagen,Shawn A.Krizan,Christopher V.Strickland,Rachel Owens and Michael Wisniewski.Mars Tumbleweed..FY2003 Conceptual Design Assessment.National Aeronautics and Space Administration.NASA/TM-2005-213527.
[43]陈永春.MATLAB M语言高级编程[M].北京:清华大学出版社,2004.
[44]黄忠霖,黄京.MATLAB符号运算及其应用[M].北京:国防工业出版社,2004.
[45]邱秉权.分析力学[M].北京:中国铁道出版社,1998.130-156.
[46]孙江宏.Pro/ENGINEER Wildfire 3.0中文版参数化建模与案例分析[M].北京:清华大学出版社.2007.
[47]卞毓麟,余伟才.火星——红色的行星[M].北京:科学出版社,1987.64-222.
[48]吴宗泽.机械结构设计[M].北京:机械工业出版社.1988.65-73.
[49]郭应征,周志红.理论力学[M].北京:清华大学出版社,2005.
[2]张学锋.一种球形机器人的动力学分析和轨迹规划研究[D].西安电子科技大学,2007.
[3]孙汉旭,肖爱平,贾庆轩.二驱动球形机器人的全方位运动特性分析[J].北京航空航天大学学报,2005,31(7):735-739.
[4]邓宗全,岳明.球形机器人的发展概况综述[J].机器人技术与应用,2006,(3):27-31.
[5]李团结,朱超.一种具有稳定平台可全向滚动的球形机器人设计与分析[J].西安电子科技大学学报,2006,33(1):53-56.
[6]王亮清,孙汉旭,贾庆轩.球形机器人的圆周运动分析[J].机器人,2007,29(1):56-60.
[7]林杰,芮延年,周国梁,任芸丹,陈慧萍.一种全方位球形机器人的运动学分析[J].苏州大学学报,2005,25(4):71-73.
[8]李团结,张学锋,陈永琴.一种全向滚动球形机器人的运动分析与轨迹规划[J].西安电子科技大学学报,2007,34(1):29-33.
[9]Jeffrey Antol,Philip Calhoun,John Flick,and Gregory Hajos.Low Cost Mars Surface Exploration:The Mars Tumbleweed.National Aeronautics and Space Administration.NASA/TM-2003-212411.
[10]Jeffrey Antol.A New Vehicle for Planetary Surface Exploration:The Mars Tumbleweed.1st Space Exploration Conference:Continuing the Voyage of Discovery31 January-1 February 2005,Orlando,Florida.
[11]John J.Flick and Matthew D.Toniolo.Preliminary Dynamic Feasibility and Analysis of a Spherical,Wind-Driven(Tumbleweed),Martian Rover.43rd AIAA Aerospace Sciences Meeting and Exhibit 10-13 January 2005,Reno,Nevada.
[12]H.Wang,B.Yang and J.A.Jones.Mobility Analysis of an Inflated Tumbleweed Ball under Wind Loads.43rd AIAA/ASME/ASCE/AHS/ASC Structures,Structural Dynamics,and Materials Con 22-25 April 2002,Denver,Colorado.
[13]Behzad Raiszadeh and Phillip Calhoun.Mars Tumbleweed Simulation Using Singular Perturbation Theory.AIAA Modeling and Simulation Technologies Conference and Exhibit 15-18 August 2005,San Francisco,California.
[14]Scott E.Rose,Cody B.Moody,Darryl L.James and Alan A.Barhorst.Drag Measurement and Dynamic Simulation of Martian Wind Driven Sensor Platform Concepts.43rd AIAA Aerospace Sciences Meeting and Exhibit 10-13 January 2005,Reno,Nevada.
[15]Alan A.Barhorst and Darryl L.James.Elasto-dynamic Model of a Segmented Martian Tumblweed Concept.44th AIAA Aerospace Sciences Meeting and Exhibit 9-12 January 2006,Reno,Nevada.
[16]Richard M.Kolacinski and Roger D.Quinn.Numerical Simulation of a Bouncing,Rolling and Sliding Tumbleweed Rover.43rd AIAA Aerospace Sciences Meeting and Exhibit 10-13 January 2005,Reno,Nevada.
[17]Tomi Ylikorpi,Aarne Halme and Jussi Suomela.Comparison Between Wind-Propelled Thistle and Motor-Driven Un-Balanced Thistle.44th AIAA Aerospace Sciences Meeting and Exhibit 9-12 January 2006,Reno,Nevada.
[18]Jamie L.Wilson,Alex E.Hartl,Andre Mazzoleni and Fred DeJarnette.Dynamics Modeling of a Mars Tumbleweed Rover.44th AIAA Aerospace Sciences Meeting and Exhibit 9-12 January 2006,Reno,Nevada.
[19]Lori Southard,Thomas M.Hoeg,Daniel W.Palmer,Jeffrey Antol,Richard M.Kolacinski,Roger D.Exploring Mars Using a Group of Tumbleweed Rovers.2007 IEEE International Conference on Robotics and Automation Roma,Italy,10-14 April 2007:775-780.
[20]苏翼林.材料力学[M].天津:天津大学出版社,2001.65-109.
[21]毛谦德,李振清.袖珍机械设计师手册(第3版)[M].北京:机械工业出版社,2006.528-558.
[22]刘鸿文.材料力学(上册)[M].北京:高等教育出版社,1992.136-229.
[23]徐华舫.空气动力学基础(上)[M].北京:北京航空学院出版社,1987.
[24]强元棨.经典力学[M].北京:科学出版社,2003.
[25]叶尚辉,李在贵.天线结构设计[M].西安:西北电讯工程学院出版社,1986.89-115.
[26][英]J.E.艾伦著,黄志澄,张如清译.空气动力学——运动空气的科学[M].北京:国防工业出版社,1987.
[27]卓勇志.边界层中双栋并排矩形建筑之表面风压量测[D].国立中央大学(台湾),2001.12-35.
[28][苏]к.я.康德拉捷夫,A.M.布那果娃著,王跃山译.火星气象学[M].北京:科学出版社,1978.7-20.
[29][苏]В.и.列凡托夫斯基著,凌福根等译.宇宙飞行力学基础[M].北京:国防工业出版社,1979.197-209.
[30]第612研究所.航空机械设计手册[M].内部发行,1979.274,542-550.
[31]过崇伟.航空航天技术概论[M].北京:北京航空航天大学出版社,1992.17-37.
[32]崔桂香,张兆顺.流体力学[M].北京:清华大学出版社,1999.
[33]Granger,R.A.,"Fluid Mechanics",Dover Edition,Dover Publications Inc.New York,1995.
[34]Home,W.B.,Trafford,W.L.,"Influence of Tire Tread Pattern and Runway Surface Condition on Braking Friction and Rolling Resistance of a Modem Aircraft Tire," NASA TN-D-1376,1962.
[35]陈乐生,王以伦.多刚体动力学基础[M].哈尔滨:哈尔滨工程大学出版社,1995.16-68.
[36]蒋伟.机械动力学分析[M].北京:中国传媒大学出版社,2005.3-131.
[37]Saeed B.Niku著,孙富春等译.机器人学导论[M].北京:电子工业出版社,2004.
[38]Jussi Suomela and Tomi Ylikorpi.Ball-Shaped Robots..An Historical Overview and Recent Developments at TKK.P.Corke and S.Sukkarieh(Eds.):Field and Service Robotics,STAR 25,pp.343-354,2006.
[39]梅凤翔.非完整系统力学基础[M].北京:北京工业学院出版社,1985.81-299.
[40]边宇虹.分析力学与多刚体动力学基础[M].北京:机械工业出版社,1998.
[41]陈强顺.分析力学导论[M].上海:同济大学出版社出版,1997.21-100.
[42]Jeffrey Antol,Philip C.Calhoun,John J.Flick,Gregory A.Hajos,Jennifer P.Keyes,Frederic H.Stillwagen,Shawn A.Krizan,Christopher V.Strickland,Rachel Owens and Michael Wisniewski.Mars Tumbleweed..FY2003 Conceptual Design Assessment.National Aeronautics and Space Administration.NASA/TM-2005-213527.
[43]陈永春.MATLAB M语言高级编程[M].北京:清华大学出版社,2004.
[44]黄忠霖,黄京.MATLAB符号运算及其应用[M].北京:国防工业出版社,2004.
[45]邱秉权.分析力学[M].北京:中国铁道出版社,1998.130-156.
[46]孙江宏.Pro/ENGINEER Wildfire 3.0中文版参数化建模与案例分析[M].北京:清华大学出版社.2007.
[47]卞毓麟,余伟才.火星——红色的行星[M].北京:科学出版社,1987.64-222.
[48]吴宗泽.机械结构设计[M].北京:机械工业出版社.1988.65-73.
[49]郭应征,周志红.理论力学[M].北京:清华大学出版社,2005.