摘要
球形移动机器人(简称球形机器人)是一种拥有球形外壳的全封闭机器人,它通过质心偏移或者动量守恒等原理来实现运动。该类机器人具有良好的密封性,平衡性强且运动灵活性高,不存在侧翻问题,因此球形机器人在星球探索、危险环境探测等领域具有较大优势和广泛应用前景。然而球形机器人具有非完整约束、欠驱动、非链式等特点,导致其运动控制问题非常复杂且常规控制方法无法应用到它的运动控制上,阻碍了球形机器人的应用和发展。对国内外在球形机器人的机构设计、运动学和动力学建模方法以及控制方法等方面的研究进展进行回顾、综述与分析,其中也包括作者所在实验室对BHQ系列球形机器人研究工作的全面回顾;按照驱动方式对球形机器人进行归纳分类,并从运动学建模、动力学建模、开环控制和闭环控制四个方面介绍球形机器人研究的关键技术和发展趋势;最后针对球形机器人的研究进展和发展趋势给出五点结论。
Spherical mobile robot(spherical robot in short) is a fully enclosed robot with a ball-shaped outer shell, which can move by shifting its gravity center or through the principle of momentum conservation. Spherical robot has the characteristics of good sealability, high moving flexibility and strong stability as a roly-poly. Thus spherical robot has big advantages and wide future applications in the exploration of outer planets and the detection of dangerous environments. However, spherical robot is a special type of nonholonomic, under-actuated and unchained system, which makes its motion equations very complicated and the conventional methods cannot be applied to control it. This hinders the development and application of spherical robots. Review,summary and analysis of spherical robots' research progress on mechanism design, kinematics modeling, dynamics modeling, control methods and so on are given, including the comprehensive review of the BHQ series spherical robots developed by the authors' laboratory. The spherical robots are classified according to the driving modes. The key technologies and development trends of the research on spherical robots are introduced from four aspects: kinematics modeling, dynamic modeling, open-loop control and closed-loop control. At last, five conclusions about the research progress and development trend are given.
引文
[1]HALME A,SCHONBERG T,WANG Y.Motion control of a spherical mobile robot[C]//4th IEEE International Workshop on Advanced Motion Control,March 18-21,1996,Mie University,Mie,Japan.IEEE,1996:259-264.
[2]BICCHI A,BALLUCHI A,PRATTICHIZZO D,et al.Introducing the“SPHERICLE”:An experimental testbed for research and teaching in nonholonomy[C]//IEEEInternational Conference on Robotics and Automation,April 25-25,1997,Albuquerque,New Mexico.IEEE,1997:2620-2625.
[3]Sphero|Connected Toys[EB/OL].[2018-02-03].http://www.sphero.com/.
[4]KARAVAEV Y L,KILIN A A.The dynamics and control of a spherical robot with an internal omniwheel platform[J].Regular&Chaotic Dynamics,2015,20(2):134-152.
[5]CHEMEL B,MUTSCHLER E,SCHEMPF H.Cyclops:Miniature robotic reconnaissance system[C]//IEEEInternational Conference on Robotics and Automation,May 10-15,1999,Marriott Hotel,Renaissance Center,Detroit,Michigan.IEEE,1999:2298-2302.
[6]MUKHERJEE R,MINOR M A,PUKRUSHPAN J T.Simple motion planning strategies for spherobot:Aspherical mobile robot[C]//IEEE Conference on Decision and Control,December 7-10,1999,Phoenix,Arizona.IEEE,1999:2132-2137.
[7]TOMIK F,NUDEHI S,FLYNN L L,et al.Design,fabrication and control of spherobot:A spherical mobile robot[J].Journal of Intelligent&Robotic Systems,2012,67(2):117-131.
[8]AMIR H J A,MOJABI P.Introducing August:A novel strategy for an omnidirectional spherical rolling robot[C]//IEEE International Conference on Robotics and Automation,April 26-May 1,2004,Hilton New Orleans Riverside,New Orleans,Los Angeles.IEEE,2004:3527-3533.
[9]BHATTACHARYA S,AGRAWAL S K.Spherical rolling robot:A design and motion planning studies[J].IEEE Transactions on Robotics&Automation,2000,16(6):835-839.
[10]JOSHI V A,BANAVAR R N.Motion analysis of a spherical mobile robot[J].Robotica,2009,27(3):343-353.
[11]JOSHI V A,BANAVAR R N,HIPPALGAONKAR R.Design and analysis of a spherical mobile robot[J].Mechanism&Machine Theory,2010,45(2):130-136.
[12]MURALIDHARAN V,MAHINDRAKAR A D.Geometric controllability and stabilization of spherical robot dynamics[J].IEEE Transactions on Automatic Control,2015,60(10):2762-2767.
[13]SUGIYAMA Y,SHIOTSU A,YAMANAKA M,et al.Circular/spherical robots for crawling and jumping[C]//IEEE International Conference on Robotics and Automation,May 15-19,2006,Hilton in Walt Disney World Resort,Orlando,Florida.IEEE,2006:3595-3600.
[14]WAIT K W,JACKSON P J,SMOOT L S.Selflocomotion of a spherical rolling robot using a novel deformable pneumatic method[C]//IEEE International Conference on Robotics and Automation,May 4-8,2010,Anchorage,Alaska.IEEE,2010:3757-3762.
[15]OTANI T,URAKUBO T,MAEKAWA S,et al.Position and attitude control of a spherical rolling robot equipped with a gyro[C]//IEEE International Workshop on Advanced Motion Control,March 27-29,2006,Istanbul,Turkey.IEEE,2006:416-421.
[16]URAKUBO T,OSAWA M,TAMAKI H,et al.Development of a spherical rolling robot equipped with a gyro[C]//IEEE International Conference on Mechatronics and Automation,August 5-10,2012,Chengdu,China.IEEE,2012:1602-1607.
[17]URAKUBO T,MONNO M,MAEKAWA S,et al.Dynamic modeling and controller design for a spherical rolling robot equipped with a gyro[J].IEEE Transactions on Control Systems Technology,2016,24(5):1669-1679.
[18]Rotundus[EB/OL].[2018-02-03].http://www.rotundus.se/.
[19]ERKAN K,BAYRAKTAROGLU Z Y,WOUTER S.Modeling and control of a spherical rolling robot:Adecoupled dynamics approach[J].Robotica,2012,30(4):671-680.
[20]KAYACAN E,KAYACAN E,RAMON H,et al.Adaptive neuro-fuzzy control of a spherical rolling robot using sliding-mode-control-theory-based online learning algorithm[J].IEEE Transactions on Cybernetics,2013,43(1):170.
[21]ROOZEGAR M,MAHJOOB M J,JAHROMI M.DP-based path planning of a spherical mobile robot in an environment with obstacles[J].Journal of the Franklin Institute,2014,351(10):4923-4938.
[22]ROOZEGAR M,MAHJOOB M J,JAHROMI M.Optimal motion planning and control of a nonholonomic spherical robot using dynamic programming approach:Simulation and experimental results[J].Mechatronics,2016,39:174-184.
[23]BELLMAN R.Dynamic programming and modern control theory[J].Proc.International Congress Math,1965,37(1):65-82.
[24]ROOZEGAR M,MAHJOOB M J,ESFANDYARI M J,et al.XCS-based reinforcement learning algorithm for motion planning of a spherical mobile robot[J].Applied Intelligence,2016,45(3):1-11.
[25]ROOZEGAR M,MAHJOOB M J.Modelling and control of a non-holonomic pendulum-driven spherical robot moving on an inclined plane:Simulation and experimental results[J].IET Control Theory&Applications,2017,11(4):541-549.
[26]GAJBHIYE S,BANAVAR R N.Geometric modeling and local controllability of a spherical mobile robot actuated by an internal pendulum[J].International Journal of Robust&Nonlinear Control,2016,26(11):2436-2454.
[27]SHEN J,SCHNEIDER D A,BLOCH A M.Controllability and motion planning of a multibody Chaplygin's sphere and Chaplygin’s top[J].International Journal of Robust&Nonlinear Control,2008,18(9):905-945.
[28]SHEN J,MCCLAMROCH N H,BLOCH A M.Local equilibrium controllability of multibody systems controlled via shape change[J].IEEE Transactions on Automatic Control,2004,49(4):506-520.
[29]LIN X,GUO S.Development of a spherical underwater robot equipped with multiple vectored water-jet-based thrusters[J].Journal of Intelligent&Robotic Systems,2012,67(3-4):307-321.
[30]LI Y,GUO S,YUE C.Preliminary concept of a novel spherical underwater robot[J].International Journal of Mechatronics&Automation,2015,5(1):11-21.
[31]MAHBOUBI S,FAKHRABADI M M S,GHANBARI A.Design and implementation of a novel spherical mobile robot[J].Journal of Intelligent&Robotic Systems,2013,71(1):43-64.
[32]HOGAN F R,FORBES J R.Modeling of spherical robots rolling on generic surfaces[J].Multibody System Dynamics,2015,35(1):91-109.
[33]DEJONG B P,KARADOGAN E,YELAMARTHI K,et al.Design and analysis of a four-pendulum omnidirectional spherical robot[J].Journal of Intelligent&Robotic Systems,2017,86(1):1-13.
[34]复杂机构与智能控制实验室[EB/OL].[2018-02-03].http://cmic.buaa.edu.cn/.Complex Mechanism and Intelligent Control Laboratory[EB/OL].[2018-02-03].http://cmic.buaa.edu.cn/.
[35]战强.一种新型的月球探测车运动机构[C]//第二届月球探测技术研讨会,2001.北京:清华大学出版社,2001:328-330.ZHAN Qiang.A novel moving mechanism for moon exploring vehicles[C]//The 2nd Workshop on Moon Exploring Technology,Beijing:Tsinghua University Press,2001:328-330.
[36]战强,贾川,马晓辉,等.一种球形移动机器人的运动性能分析[J].北京航空航天大学学报,2005,31(7):744-747.ZHAN Qiang,JIA Chuan,MA Xiaohui,et al.Analysis of moving capability of a spherical mobile robot[J].Journal of Beijing University of Aeronautics and Astronautics,2005,31(7):744-747.
[37]ZHAN Qiang,JIA Chuan,MA Xiaohui,et al.Mechanism design and motion analysis of a spherical mobile robot[J].Chinese Journal of Mechanical Engineering,2005,18(4):542-545.
[38]战强,蔡三龙,刘增波.一种球形探测机器人的电机控制研究[J].材料科学与工艺,2006,14(增刊):96-100.ZHAN Qiang,CAI Sanlong,LIU Zengbo.Research on motor control of a spherical mobile robot for exploration[J].Materials Science&Technology,2006,14(Suppl.):96-100.
[39]ZHAN Qiang,ZHOU Tingzhi,CHEN Ming,et al.Dynamic trajectory planning of a spherical mobile robot[C]//IEEE Conference on Robotics,Automation and Mechatronics,June 7-9,2006,The Twin Towers Hotel,Bangkok,Thailand.IEEE,2006:1-6.
[40]CHEN Ming,ZHAN Qiang,LIU Zengbo,et al.Optimal trajectory planning based on Hamiltonian function of a spherical mobile robot[J].High Technology Letters,2008,14(3):289-293.
[41]刘增波,战强,蔡尧.一种环境探测球形移动机器人的运动控制[J].航空学报,2008,29(6):1673-1679.LIU Zengbo,ZHAN Qiang,CAI Yao.Motion control of a spherical mobile robot for environment exploration[J].Acta Aeronautica Et Astronautica Sinica,2008,29(6):1673-1679.
[42]ZHAN Qiang,CAI Yao,LIU Zengbo.Near-optimal trajectory planning of a spherical mobile robot for environment exploration[C]//IEEE Conference on Robotics,Automation and Mechatronics,September21-24,2008,Chengdu,China.IEEE,2008:84-89.
[43]ZHAN Qiang,LIU Zengbo,CAI Yao.A back-stepping based trajectory tracking controller for a non-chained nonholonomic spherical robot[J].Chinese Journal of Aeronautics,2008,21(5):472-480.
[44]CAI Yao,ZHAN Qiang,XI Xi,et al.Inverse kinematics identification of a spherical robot based on BP neural networks[C]//IEEE Conference on Industrial Electronics and Applications,June 21-23,2011,Beijing,China.IEEE,2011:2114-2119.
[45]CAI Yao,ZHAN Qiang,YAN Caixia.Two-state trajectory tracking control of a spherical robot using neurodynamics[J].Robotica,2012,30(2):195-203.
[46]CAI Yao,ZHAN Qiang,XI Xi.Neural network control for the linear motion of a spherical mobile robot[J].International Journal of Advanced Robotic Systems,2011,8(4):79-87.
[47]ZHAN Qiang,CHI Xing,XI Xi.Linear motion control of an underactuated spherical mobile robot[J].Applied Mechanics&Materials,2014,644-650,351-355.
[48]CAI Yao,ZHAN Qiang,XI Xi.Path tracking control of a spherical mobile robot[J].Mechanism&Machine Theory,2012,51(5):58-73.
[49]ZHENG Minghui,ZHAN Qiang,LIU Jinkun,et al.Control of a spherical robot:Path following based on nonholonomic kinematics and dynamics[J].Chinese Journal of Aeronautics,2011,24(3):337-345.
[50]ZHENG Minghui,ZHAN Qiang,LIU Jinkun,et al.Trajectory tracking of a spherical robot based on an RBFneural network[J].Advanced Materials Research,2012,383-390,631-637.
[51]ZHAN Qiang,CAI Yao,YAN Caixia.Design,analysis and experiments of an omni-directional spherical robot[C]//IEEE International Conference on Robotics and Automation,May 9-13,2011,Shanghai,China.IEEE,2011:4921-4926.
[52]ZHAN Qiang,LIU Zening.A deformable spherical mobile robot[J].Applied Mechanics&Materials,2014,590(590):422-426.
[53]战强,刘泽宁,张超.一种可变形球形探测机器人:中国,CN104002886A[P].2014-08-27.ZHAN Qiang,LIU Zening,ZHANG Chao.A deformable spherical mobile robot for exploration:China,CN104002886A[P].2014-08-27.
[54]肖爱平,孙汉旭,廖启征,等.一种球形机器人的设计与原理分析[J].机电产品开发与创新,2004,17(1):14-16.XIAO Aiping,SUN Hanxu,LIAO Qizheng,et al.Design and principle analysis of a spherical robot[J].DeveIopment&Innovation of Machinery&Electrical Products,2004,17(1):14-16.
[55]孙汉旭,肖爱平,贾庆轩,等.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.SUN Hanxu,XIAO Aiping,JIA Qingxuan,et al.Omnidirectional kinematics analysis on bi-driver spherical robot[J].Journal of Beijing University of Aeronautics and Astronautics,2005,31(7):735-739.
[56]王亮清,孙汉旭,贾庆轩.球形机器人的爬坡与弹跳能力[J].北京邮电大学学报,2007,30(2):11-14.WANG Qingliang,SUN Hanxu,JIA Qingxuan.Research on the climbing and jumping of a spherical rolling robot[J].Journal of Beijing University of Posts and Telecommunications,2007,30(2):11-14.
[57]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.WANG Qingliang,SUN Hanxu,JIA Qingxuan.Circle motion analysis on a spherical robot[J].Robot,2007,29(1):56-60.
[58]LIU Daliang,SUN Hanxu,JIA Qingxuan,et al.Motion control of a spherical mobile robot by feedback linearization[C]//World Congress on Intelligent Control and Automation,June 25-27,2008,Chongqing,China.2008:965-970.
[59]孙汉旭,王亮清,贾庆轩,等.BYQ-3球形机器人的动力学模型[J].机械工程学报,2009,45(10):8-14.SUN Hanxu,WANG Qingliang,JIA Qingxuan,et al.Dynamic model of the BYQ-3 spherical robot[J].Journal of Mechanical Engineering,2009,45(10):8-14.
[60]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(自然科学版),2007,34(1):29-33.LI Tuanjie,ZHANG Xuefeng,CHEN Yongqin.Motion analysis and trajectory planning of a spherical omnidirectional rolling robot[J].Journal of Xidian University,2007,34(1):29-33.
[61]李团结,严天宏,张学锋.一种全向滚动球形机器人的动力学分析与仿真[J].西安电子科技大学学报,2007,34(3):4239-4242.LI Tuanjie,YAN Tianhong,ZHANG Xuefeng.Dynamic analysis and simulation of a spherical omnidirectional rolling robot[J].Journal of Xidian University,2007,34(3):4239-4242.
[62]岳明,邓宗全.基于状态观测器的球形机器人状态反馈控制系统设计[J].光学精密工程,2007,15(6):878-883.YUE Ming,DENG Zongquan.Design of state feedback control system for spherical robot based on state observer[J].Optics and Precision Engineering,2007,15(6):878-883.
[63]YUE Ming,LIU Baoyin,AN Cong,et al.Extended state observer-based adaptive hierarchical sliding mode control for longitudinal movement of a spherical robot[J].Nonlinear Dynamics,2014,78(2):1233-1244.
[64]赵勃,王鹏飞,孙立宁,等.双偏心质量块驱动球形机器人的直线运动控制[J].机械工程学报,2011,47(11):1-6.ZHAO Bo,WANG Pengfei,SUN Lining,et al.Linear motion control of two-pendulums-driven spherical robot[J].Journal of Mechanical Engineering,2011,47(11):1-6.
[65]杨伟,李健,肖起阳,等.球形机器人的仿真与实验测试分析[J].制造业自动化,2017,39(8):26-29.YANG Wei,LI Jian,XIAO Qiyang,et al.The simulation and experimental analysis of a spherical robot[J].Manufacturing Automation,2017,39(8):26-29.
[66]兰晓娟,孙汉旭,贾庆轩.水下球形机器人BYSQ-2的原理与动力学分析[J].北京邮电大学学报,2010,33(3):20-23.LAN Xiaojuan,SUN Hanxu,JIA Qingxuan.Principle and dynamic analysis of a new-type spherical underwater vehicle[J].Journal of Beijing University of Posts and Telecommunications,2010,33(3):20-23.
[67]李艳生,孙汉旭,贾庆轩,等.一种摆式球形水下机器人水底滚动特性分析[J].中南大学学报,2016,47(11):3664-3669.LI Yansheng,SUN Hanxu,JIA Qingxuan,et al.Analysis of rolling characteristics at water bottom for spherical robot with heavy pendulums[J].Journal of Central South University,2016,47(11):3664-3669.
[68]CHEN W H,CHEN C P,TSAI J S,et al.Design and implementation of a ball-driven omnidirectional spherical robot[J].Mechanism&Machine Theory,2013,68(68):35-48.
[69]叶平,韩亮亮,张天石,等.具有立体视觉的球形机器人及其运动控制[J].机械工程学报,2013,49(11):8-15.YE Ping,HAN Liangliang,ZHANG Tianshi,et al.Design and motion control of ball-shaped robot with stereo vision[J].Journal of Mechanical Engineering,2013,49(11):8-15.
[70]YE Ping,SUN Hanxu,QIU Zhongjiang,et al.Design and motion control of a spherical robot with stereovision[C]//Industrial Electronics and Applications,5-7 June,2016,Hefei,China.IEEE,2016:1276-1282.