基于遗传算法的二层优化在喷漆机器人轨迹规划中的研究
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摘要
机器人的轨迹规划在机器人的控制中具有重要的地位。本文首先介绍了国内外机器人的轨迹规划的研究现状及意义,分析了各种关于机器人轨迹规划的规划算法,指出了它们的优点和存在的不足。
本文的规划主要是在操作空间中,依据喷漆机器人喷漆面积和约束的要求来进行规划的。通过对机器人操作臂的轨迹规划的具体分析、基于运动学寻轨迹算法的模拟实现、关节空间的轨迹优化,喷漆面积的优化等方面的全过程的研究,阐述了喷漆机器人轨迹规划的一般规律。
论文中根据喷漆机器人轨迹规划的要求和约束,提出一种新的机器人轨迹规划的方法——二层轨迹规划问题(BLTOPP)。研究出的规划方法可以很好解决在喷漆机器人工作时的喷漆质量,实时性和精确性的矛盾,以及关节空间中的时间最小优化问题。
在基于喷漆机器人的运动学的轨迹规划下,为了增加机械臂的运动范围。提高喷漆效率。本文采用了依据机械臂的运动要求而改变安装在机械臂末段的喷嘴与被喷涂部件的距离的方法。由于需要同时满足两个不同的要求:机械臂运行的最佳位姿和喷漆质量(重复覆盖面积最小且不能有空隙),并且两者的变量是相互耦合的,所以属于二层规划。文中对于下层函数(时间最小)选用的是最优时间轨迹规划方法(MTTP)优化求解中间结点,增加了机器人的动力学的约束,使得结果更加精确。在对于上层函数(喷漆质量的优化)上层选用的是遗传算法(GA)优化,通过遗传机制优化的到全局最优解,使得两者都达到最好的优化,最后在MATLAB平台上进行离线编程和仿真,并在机器人实验室进行了试验,达到了预期的结果,论证了方法的可行性。
Robotic trajectory planning plays a very important role in robotic control domain. This thesis is presented the milestone and necessarily of robotic trajectory planning firstly. Then analyses several different types of robotic trajectory planning algorithm, the strong points of these algorithms are reviewed, the weak points are highlighted as well.
This thesis is devoted to the study of generating a trajectory under the painting coverage area and the constraints. By the researching processes of concrete analysis of trajectory planning on robotic manipulator arm, imitation of trajectory based on kinematics and optimization of trajectory in the articulation space, this paper formulizes general regularity of trajectory planning.
A novel approach is employed to generate this trajectory based on the requirements and constraints of spray robot-----Bi-level Trajectory Optimal Planning Problem(BLTOPP). The method researched resolves contradiction between real-time and accuracy in the operation space, and problem of minimal optimization about time.
In order to increase the flexibility of robot arm to improved the productivity of paint spray. Thus, the changeable stream length method is employed in this thesis. The coverage area is changed with the stream length. Due to the influence of robot pose selection, coverage quality (minimum overlap area and no bank area) and coupled parameters, this optimal problem is a bi-level problem. In process of the trajectory planning depending on robotic inverse and forward kinematics, MTTP is adopted to optimal the middle nodal point. Due to the constraint of robotic dynamic is enhanced, the results is more accuracy. Genetic algorithm is employed to optimal the painting quality. In the end of this thesis, the simulation is conducted by MATLAB, and experiment is conducted on the real-world robot. The method is provided reasonable by results.
本文的规划主要是在操作空间中,依据喷漆机器人喷漆面积和约束的要求来进行规划的。通过对机器人操作臂的轨迹规划的具体分析、基于运动学寻轨迹算法的模拟实现、关节空间的轨迹优化,喷漆面积的优化等方面的全过程的研究,阐述了喷漆机器人轨迹规划的一般规律。
论文中根据喷漆机器人轨迹规划的要求和约束,提出一种新的机器人轨迹规划的方法——二层轨迹规划问题(BLTOPP)。研究出的规划方法可以很好解决在喷漆机器人工作时的喷漆质量,实时性和精确性的矛盾,以及关节空间中的时间最小优化问题。
在基于喷漆机器人的运动学的轨迹规划下,为了增加机械臂的运动范围。提高喷漆效率。本文采用了依据机械臂的运动要求而改变安装在机械臂末段的喷嘴与被喷涂部件的距离的方法。由于需要同时满足两个不同的要求:机械臂运行的最佳位姿和喷漆质量(重复覆盖面积最小且不能有空隙),并且两者的变量是相互耦合的,所以属于二层规划。文中对于下层函数(时间最小)选用的是最优时间轨迹规划方法(MTTP)优化求解中间结点,增加了机器人的动力学的约束,使得结果更加精确。在对于上层函数(喷漆质量的优化)上层选用的是遗传算法(GA)优化,通过遗传机制优化的到全局最优解,使得两者都达到最好的优化,最后在MATLAB平台上进行离线编程和仿真,并在机器人实验室进行了试验,达到了预期的结果,论证了方法的可行性。
Robotic trajectory planning plays a very important role in robotic control domain. This thesis is presented the milestone and necessarily of robotic trajectory planning firstly. Then analyses several different types of robotic trajectory planning algorithm, the strong points of these algorithms are reviewed, the weak points are highlighted as well.
This thesis is devoted to the study of generating a trajectory under the painting coverage area and the constraints. By the researching processes of concrete analysis of trajectory planning on robotic manipulator arm, imitation of trajectory based on kinematics and optimization of trajectory in the articulation space, this paper formulizes general regularity of trajectory planning.
A novel approach is employed to generate this trajectory based on the requirements and constraints of spray robot-----Bi-level Trajectory Optimal Planning Problem(BLTOPP). The method researched resolves contradiction between real-time and accuracy in the operation space, and problem of minimal optimization about time.
In order to increase the flexibility of robot arm to improved the productivity of paint spray. Thus, the changeable stream length method is employed in this thesis. The coverage area is changed with the stream length. Due to the influence of robot pose selection, coverage quality (minimum overlap area and no bank area) and coupled parameters, this optimal problem is a bi-level problem. In process of the trajectory planning depending on robotic inverse and forward kinematics, MTTP is adopted to optimal the middle nodal point. Due to the constraint of robotic dynamic is enhanced, the results is more accuracy. Genetic algorithm is employed to optimal the painting quality. In the end of this thesis, the simulation is conducted by MATLAB, and experiment is conducted on the real-world robot. The method is provided reasonable by results.
引文
[1]熊有伦主编,机器人技术基础[M],武汉:华中科技大学出版社,1996.
[2]蔡自兴,徐光枯.人工智能及其应用:研究生用书(第三版).清华大学出版社,2004
[3]孙增沂.智能控制理论与技术.清华大学出版社.2003.
[4]付京逊,冈萨雷斯RC,CSG李.机器人学控制、传感技术、视觉、智能.北京:中国科学技术出版社,1989.10.
[5]Lin,C.-S.,Chang,P.-R.,and Lu.H,J.,1983,Formulation and optimisation of cubic polynomial joint trajectories for industrial robots.IEEE Transactions on Automatic Control,28,1066-1074.
[6]Tondu B,Zorkany H E.Identification of a trajectory generator model for the PUMA-560 robot.Journal of Robotic Systems,1994,11(2):77-90.
[7]Bazaz S A,Tondu B.Optimization of a robotic manipulator joint trajectory time with velocity and acceleration constraints.Proceedings of the 1997 travel International Symposium on Assembly and Task Planning,Los Angeles,California,USA,August 7-9,1997,1-6.
[8]Choi Y K,Park J H,Kim H S,mode control for robots using 423-428.et al.Optimal trajectory planning andevolution strategy.Robotica,2000,sliding 18(4):.
[9]Garg D P,Kumar M.Optimization techniques applied to multiple manipulators for path planning and torque minimization.Engineering Applications of Artificial Intelligence,2002,15(3-4):241-252.
[10]杨国军,崔平远.机械手时间最优轨迹规划方法研究.中国机械工程,2002.13(20):1715-1717.
[11]王建滨,马培荪,徐军,等.基于超冗余度机械臂动力学的时间最优轨迹规划.上海交通大学学报,2002,36(9):1360-1364.
[12]王焱,赵德安等.喷漆机器人喷枪最优轨迹规划的研究.江苏理工大学学报.2001(5):55-59.
[13]王幼民,徐蔚鸿.机器人关节空间B样条轨迹优化设计[J].机电工程,2000,17(4):57-60.
[14]王幼民,徐蔚鸿.机器人连续轨迹控制中的B样条轨迹优化设计[J].机械设计,2000,10(10):33-35.
[15]Craig,J.J.,Introduction to Robotics:Mechanics and Control,1989.
[16]玄光男,程润伟著;于欲杰,周根贵译.遗传算法与工程优化.北京:清华大学出版社,2004
[17]雷英杰,张善文等,遗传算法工具箱及应用[M],西安:西安电子科技大学出版社,2005.
[18]王先甲,冯尚友,二层系统最优化理论[M],北京:科学出版社,1995.
[19]W.Bialas and M.Karwan,"Two-level linear programming," Management Science,1984,vol.30,pp.1004-1020.
[20]H.Tuy,A.Migdalas,and P.Varbrand,"A global optimization approach for the linear two-level program," Journal of Global Optimization,1993,vol.3,pp.1-23.
[21]Judice,J.J.and A.M.Faustino,"A Sequential LCP Method for Bi-level Linear Programming," Annals of Operations Research,1992.34(1-4):p.89-106.
[22]Bard,J.F.and J.T.Moore,"A Branch and Bound Algorithm for the Bi-level Programming Problem," SIAM Journal of Scientific and Statistical Computing,1990.11(2):p.281-292.
[23]T.Edmunds and J.F.Bard,"Algorithms for nonlinear bi-level mathematical programs," IEEE transactions on Systems,Man,and Cybernetics,1991,vol.21,no.1,pp.83-89.
[24]F.A.Al-Khayal,R.Horst,and P.M.Pardalos,"Global optimization of concave functions subject to quadratic constraints:An application in nonlinear bi-level programming," Annals of Operations Research,1992,vol.34,pp.125-147.
[25]杜文,黄崇超.求解二层规划问题的遗传算法.数学杂志 2005 25 21:167.
[26]周明,孙树栋,彭炎午.使用遗传算法规划机器人路径[J].西北工业大学学报,1998,16(4):581-583.
[27]R.Mathieu,L.Pittard,and G.Anandalingam,"Genetic Algorithm Based Approach to Bi-level," Linear Programming Operations Research,1994,28(1):p.1-21.
[28]Y.Yin,"Genetic Algorithm based approach for bi-level programming models,"Journal of Transportation Engineering,2000,126(2):p.115-120.
[29]S.R.Hejazi,A.Memariani,G.Jahanshanloo,M.M.Sepehri,"Bi-level Programming Solution by Genetic Algorithms," In Pro.The First National Industrial Engineering Conference,2001.
[30]H.P.Cheng,N.Xi,W.H.Sheng,M.M.Song,and Y.F.Chen,"CAD-based Automated Robot Trajectory Planning for Spray Painting of Free-form Surfaces,"Industrial Robot,2002,pp.426-433.
[31]S.Meguerdichian,F.Koushanfar,M.Potkonjak and M.B.Srivastava,"Coverage problems in wireless ad-hoc sensor networks," in:Proc.of the 20th IEEE INFOCOM,2001,pp.1380-1387.
[32]X.Y.Li,P.J.Wan,and O.Frieder,"Coverage in wireless ad-hoc sensor networks",IEEE Trans.Comput.52(2003)1-11.
[33]X.R.Wang,G.L.Xing,Y.F.Zhang,C.Y.Lu,R.Pless,C.Gill,"Integrated coverage and connectivity configuration in wireless sensor networks," in:Proc.of the Ist ACM Conf on Embedded networked sensor systems,2003
[34]J.K.Antonio,"Optimal Trajectory Planning for Spray Coating," in Proc.IEEE Int.Conf Robotics and Automation,May,1994,pp.2570-2576
[35]Z.Bi,P.H.Calamai,and A.R.Conn,"Anexact penalty function approach for the nonlinear bi-level programming problem," Technical Report No,180-0-170591,Department of Systems Design Engineering,University of Waterloo,1991.
[36]Z.Bi,P.H.Calamai,and A.R.Conn,"An exact penalty function approach for the linear bi-level programming problem," Technical Report No.167-0-310789,Department of Systems Design Engineering,University of Waterloo,1989.
[37]K.Shimizu and E.Aiyoshi,"A new computational method for Stackelberg and min-max problems by use of a penalty method," IEEE Transactions on Automatic Control,1981,vol.26,pp.460-466.
[38]S.H.Suh,I.K.Woo,and S.K.Noh,"Develpoment of an Automatic Trajectory Planning System(ATPS)for Spray Painting Robots," in Proc.IEEE Int.Conf Robotics and Automation,1991,pp.1948-1955.
[39]Shen,Y.,H"uper.K.,Optimal Trajectory Planning of Manipulators Subject to Motion Constraints.Proceeding of IEEE international conference on Advanced Robotics,2005,pp.9-16
[40]Bianco,C.G.L.,and Piazzi,A Minimum-time trajectory planning of mechanical manipulators under dynamic constraints,International Journal of Control,2002,75,967-980
[41]J.K.Antonio,"Optimal Trajectory Planning for Spray Coating," in Proc.IEEE Int.Conf Robotics and Automation,May,1994,pp.2570-2576
[42]Y.Ishizuka and E.Aiyoshi,"Double penalty method for bi-level optimization problems," Annals of Operations Research,1992,vol.34,pp.73-88.
[43]L.M.Case,An l_1 Penalty Function Approach to the Nonlinear Bi-level Programming Problem,PhD thesis,University of Waterloo:Ontario,Canada,1999.
[44]J.K.Antonio,R.Rbhadran,and T.L.Ling,"A Frame Work for Optimal Trajectory Planning for Automated Spray Coating," Int.J.Robot.Automat.1997,vol.12,no.4,pp.124-134.
[45]G.M.Wang,Z.P.Wan,and X.J.Wang,"Genetic Algorithm for Solving Convex Quadratic Bi-level Programming Problem,"
[46]J.E.Falk and J.Liu,"On bi-level programming,Part Ⅰ:general nonlinear cases,"Mathematical Programming,1995,vol.70,no.1,pp.47-72.
[47]G.Savard and J.Gauvin,"The steepest descent direction for the nonlinear bilevel programming problem," Operations Research Letters,1994,vol.15,pp.265-272
[48]W.H.Sheng,H.P.Cheng,N.Xi,and Y.F.Chen,"Tool Path Planning for Compound Surface in Spray Forming Process," Automation Science and Engineering,2005,pp.240-248.
[49]W.H.Sheng,H.P.Cheng,N.Xi,J.D.Tan,and Y.F.Chen,"Optimal Tool Path Planning for Compound Surface in Spray Forming Process," in Porc.IEEE Int.ConfRobotics and Automation,Apr.2004,pp.45-50.
[50]N.Asakawa and Y.Takeuchi,"Teaching less Spray-painting of Sculptured Surface by an Industrial Robot," in Proc.IEEE Int.ConfRobotics and Automation,Albuquerque,NM,Apr.1997,pp.1875-1879.
[2]蔡自兴,徐光枯.人工智能及其应用:研究生用书(第三版).清华大学出版社,2004
[3]孙增沂.智能控制理论与技术.清华大学出版社.2003.
[4]付京逊,冈萨雷斯RC,CSG李.机器人学控制、传感技术、视觉、智能.北京:中国科学技术出版社,1989.10.
[5]Lin,C.-S.,Chang,P.-R.,and Lu.H,J.,1983,Formulation and optimisation of cubic polynomial joint trajectories for industrial robots.IEEE Transactions on Automatic Control,28,1066-1074.
[6]Tondu B,Zorkany H E.Identification of a trajectory generator model for the PUMA-560 robot.Journal of Robotic Systems,1994,11(2):77-90.
[7]Bazaz S A,Tondu B.Optimization of a robotic manipulator joint trajectory time with velocity and acceleration constraints.Proceedings of the 1997 travel International Symposium on Assembly and Task Planning,Los Angeles,California,USA,August 7-9,1997,1-6.
[8]Choi Y K,Park J H,Kim H S,mode control for robots using 423-428.et al.Optimal trajectory planning andevolution strategy.Robotica,2000,sliding 18(4):.
[9]Garg D P,Kumar M.Optimization techniques applied to multiple manipulators for path planning and torque minimization.Engineering Applications of Artificial Intelligence,2002,15(3-4):241-252.
[10]杨国军,崔平远.机械手时间最优轨迹规划方法研究.中国机械工程,2002.13(20):1715-1717.
[11]王建滨,马培荪,徐军,等.基于超冗余度机械臂动力学的时间最优轨迹规划.上海交通大学学报,2002,36(9):1360-1364.
[12]王焱,赵德安等.喷漆机器人喷枪最优轨迹规划的研究.江苏理工大学学报.2001(5):55-59.
[13]王幼民,徐蔚鸿.机器人关节空间B样条轨迹优化设计[J].机电工程,2000,17(4):57-60.
[14]王幼民,徐蔚鸿.机器人连续轨迹控制中的B样条轨迹优化设计[J].机械设计,2000,10(10):33-35.
[15]Craig,J.J.,Introduction to Robotics:Mechanics and Control,1989.
[16]玄光男,程润伟著;于欲杰,周根贵译.遗传算法与工程优化.北京:清华大学出版社,2004
[17]雷英杰,张善文等,遗传算法工具箱及应用[M],西安:西安电子科技大学出版社,2005.
[18]王先甲,冯尚友,二层系统最优化理论[M],北京:科学出版社,1995.
[19]W.Bialas and M.Karwan,"Two-level linear programming," Management Science,1984,vol.30,pp.1004-1020.
[20]H.Tuy,A.Migdalas,and P.Varbrand,"A global optimization approach for the linear two-level program," Journal of Global Optimization,1993,vol.3,pp.1-23.
[21]Judice,J.J.and A.M.Faustino,"A Sequential LCP Method for Bi-level Linear Programming," Annals of Operations Research,1992.34(1-4):p.89-106.
[22]Bard,J.F.and J.T.Moore,"A Branch and Bound Algorithm for the Bi-level Programming Problem," SIAM Journal of Scientific and Statistical Computing,1990.11(2):p.281-292.
[23]T.Edmunds and J.F.Bard,"Algorithms for nonlinear bi-level mathematical programs," IEEE transactions on Systems,Man,and Cybernetics,1991,vol.21,no.1,pp.83-89.
[24]F.A.Al-Khayal,R.Horst,and P.M.Pardalos,"Global optimization of concave functions subject to quadratic constraints:An application in nonlinear bi-level programming," Annals of Operations Research,1992,vol.34,pp.125-147.
[25]杜文,黄崇超.求解二层规划问题的遗传算法.数学杂志 2005 25 21:167.
[26]周明,孙树栋,彭炎午.使用遗传算法规划机器人路径[J].西北工业大学学报,1998,16(4):581-583.
[27]R.Mathieu,L.Pittard,and G.Anandalingam,"Genetic Algorithm Based Approach to Bi-level," Linear Programming Operations Research,1994,28(1):p.1-21.
[28]Y.Yin,"Genetic Algorithm based approach for bi-level programming models,"Journal of Transportation Engineering,2000,126(2):p.115-120.
[29]S.R.Hejazi,A.Memariani,G.Jahanshanloo,M.M.Sepehri,"Bi-level Programming Solution by Genetic Algorithms," In Pro.The First National Industrial Engineering Conference,2001.
[30]H.P.Cheng,N.Xi,W.H.Sheng,M.M.Song,and Y.F.Chen,"CAD-based Automated Robot Trajectory Planning for Spray Painting of Free-form Surfaces,"Industrial Robot,2002,pp.426-433.
[31]S.Meguerdichian,F.Koushanfar,M.Potkonjak and M.B.Srivastava,"Coverage problems in wireless ad-hoc sensor networks," in:Proc.of the 20th IEEE INFOCOM,2001,pp.1380-1387.
[32]X.Y.Li,P.J.Wan,and O.Frieder,"Coverage in wireless ad-hoc sensor networks",IEEE Trans.Comput.52(2003)1-11.
[33]X.R.Wang,G.L.Xing,Y.F.Zhang,C.Y.Lu,R.Pless,C.Gill,"Integrated coverage and connectivity configuration in wireless sensor networks," in:Proc.of the Ist ACM Conf on Embedded networked sensor systems,2003
[34]J.K.Antonio,"Optimal Trajectory Planning for Spray Coating," in Proc.IEEE Int.Conf Robotics and Automation,May,1994,pp.2570-2576
[35]Z.Bi,P.H.Calamai,and A.R.Conn,"Anexact penalty function approach for the nonlinear bi-level programming problem," Technical Report No,180-0-170591,Department of Systems Design Engineering,University of Waterloo,1991.
[36]Z.Bi,P.H.Calamai,and A.R.Conn,"An exact penalty function approach for the linear bi-level programming problem," Technical Report No.167-0-310789,Department of Systems Design Engineering,University of Waterloo,1989.
[37]K.Shimizu and E.Aiyoshi,"A new computational method for Stackelberg and min-max problems by use of a penalty method," IEEE Transactions on Automatic Control,1981,vol.26,pp.460-466.
[38]S.H.Suh,I.K.Woo,and S.K.Noh,"Develpoment of an Automatic Trajectory Planning System(ATPS)for Spray Painting Robots," in Proc.IEEE Int.Conf Robotics and Automation,1991,pp.1948-1955.
[39]Shen,Y.,H"uper.K.,Optimal Trajectory Planning of Manipulators Subject to Motion Constraints.Proceeding of IEEE international conference on Advanced Robotics,2005,pp.9-16
[40]Bianco,C.G.L.,and Piazzi,A Minimum-time trajectory planning of mechanical manipulators under dynamic constraints,International Journal of Control,2002,75,967-980
[41]J.K.Antonio,"Optimal Trajectory Planning for Spray Coating," in Proc.IEEE Int.Conf Robotics and Automation,May,1994,pp.2570-2576
[42]Y.Ishizuka and E.Aiyoshi,"Double penalty method for bi-level optimization problems," Annals of Operations Research,1992,vol.34,pp.73-88.
[43]L.M.Case,An l_1 Penalty Function Approach to the Nonlinear Bi-level Programming Problem,PhD thesis,University of Waterloo:Ontario,Canada,1999.
[44]J.K.Antonio,R.Rbhadran,and T.L.Ling,"A Frame Work for Optimal Trajectory Planning for Automated Spray Coating," Int.J.Robot.Automat.1997,vol.12,no.4,pp.124-134.
[45]G.M.Wang,Z.P.Wan,and X.J.Wang,"Genetic Algorithm for Solving Convex Quadratic Bi-level Programming Problem,"
[46]J.E.Falk and J.Liu,"On bi-level programming,Part Ⅰ:general nonlinear cases,"Mathematical Programming,1995,vol.70,no.1,pp.47-72.
[47]G.Savard and J.Gauvin,"The steepest descent direction for the nonlinear bilevel programming problem," Operations Research Letters,1994,vol.15,pp.265-272
[48]W.H.Sheng,H.P.Cheng,N.Xi,and Y.F.Chen,"Tool Path Planning for Compound Surface in Spray Forming Process," Automation Science and Engineering,2005,pp.240-248.
[49]W.H.Sheng,H.P.Cheng,N.Xi,J.D.Tan,and Y.F.Chen,"Optimal Tool Path Planning for Compound Surface in Spray Forming Process," in Porc.IEEE Int.ConfRobotics and Automation,Apr.2004,pp.45-50.
[50]N.Asakawa and Y.Takeuchi,"Teaching less Spray-painting of Sculptured Surface by an Industrial Robot," in Proc.IEEE Int.ConfRobotics and Automation,Albuquerque,NM,Apr.1997,pp.1875-1879.