一种基于几何力学的机械臂末端规划算法
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摘要
在几何力学框架下提出了开链机械臂末端实时追踪避障算法.首先,将回转力引入机械臂末端的自然运动方程,可以在工作空间获得光滑的避障轨迹;其次,利用阻尼最小二乘法求解相应的逆运动学问题,得到关节空间的平滑运动轨迹;最后,通过6自由度机械臂的仿真,并与经典的RRT算法作对比,验证了所提算法的有效性.
An online algorithm of real-time collision avoidance and trajectory tracking for the manipulator end-effector is proposed in the framework of geometric mechanics in this paper. First,the gyroscopic force is introduced in the motion of end-effector to generate its collision-free smooth trajectory in work space. Next,the corresponding smooth trajectories in the joint space are obtained by solving the inverse kinematics problem with the damped least square method. Finally,through the comparison with the classical RRT algorithm,the effectiveness of the proposed algorithm is illustrated by numerical simulations of a 6 DOF manipulator.
An online algorithm of real-time collision avoidance and trajectory tracking for the manipulator end-effector is proposed in the framework of geometric mechanics in this paper. First,the gyroscopic force is introduced in the motion of end-effector to generate its collision-free smooth trajectory in work space. Next,the corresponding smooth trajectories in the joint space are obtained by solving the inverse kinematics problem with the damped least square method. Finally,through the comparison with the classical RRT algorithm,the effectiveness of the proposed algorithm is illustrated by numerical simulations of a 6 DOF manipulator.
引文
1 Luo R C,Ko M C,Chung Y T.Repulsive reaction vector generator for whole-arm collision avoidance of 7-Do F redundant robot manipulator.In:IEEE/ASME International Conference on Advanced Intelligent Mechatronics,Besacon,France,2014:1036~1041
2 Kuffner J J,Steven M L.RRT-connect:An efficient approach to single-query path planning.In:International Conference on Robotics and Automation,San Francisco,USA,2000:995~1001
3 Karaman S,Emilio F.Sampling-based algorithms for optimal motion planning.The International Journal of Robotics Research,2011,30(7):846~894
4 Gerdts M,Henrion R,H9mberg D,et al.Path planning and collision avoidance for robots.Numerical Algebra Control and Optimization,2012,2(3):437~463
5 Khatib O.Real-time obstacle avoidance for manipulators and mobile robots.The International Journal of Robotics Research,1986,5(1):90~98
6 Chang D E,Marsden J E.Gyroscopic forces and collision avoidance with convex obstacles.In:New trends in nonlinear dynamics and control and their applications,New York:Springer-Verlag,2003:145~159
7 Garimella G,Sheckells M,Kobilarov M.A stabilizing gyroscopic obstacle avoidance controller for underactuated systems.In:The 55th IEEE Conference on Decision and Control,Las Vegas,USA,2016:5010~5016
8 Abraham R,Marsden J E,Ratiu T.Foundations of mechanics,2nd ed.Boston:Addison-Wesley Publishing Company,1985
9郭永新,罗绍凯,梅凤翔.非完整约束系统几何动力学研究进展:Lagrange理论及其它.力学进展,2004,34(4):477~492(Guo Y X,Luo S K,Mei F X.Progress of geometric dynamics of non-holonomic constrained mechanical systems:Lagrange theory and others.Advances in Mechanics,2004,34(4):477~492(in Chinese))
10高强,钟万勰.非完整约束动力系统的离散积分方法.动力学与控制学报,2012,10(3):193~198(Gao Q,Zhong W X.Numerical algorithms for dynamic system with non-holonomic constrains.Journal of Dynamics and Control,2012,10(3):193~198(in Chinese))
11冯康,秦孟兆.哈密尔顿系统的辛几何算法.杭州:浙江科学技术出版社,2003(Feng K,Qin M Z.Symplectic geometric algorithm for Hamiltonian system.Hangzhou:Zhejiang Science and Technology Press,2003(in Chinese))
12胡伟鹏,邓子辰.无限维动力学系统的保结构分析方法.西安:西北工业大学出版社,2015(Hu W P,Deng Z C.Structure-preserving analysis methods for infinite-dimension dynamical system.Xi'an:Northwestern Polytechnical University Press,2015(in Chinese))
13 Bullo F,Murray R M.Tracking for fully actuated mechanical systems:A geometric framework.Automatica,1999,35(1):17~34
14 Aristidou A,Lasenby J.Inverse kinematics:a review of existing techniques and introduction of a new fast iterative solver.Technical Report,University of Cambridge,2009:12~17
15 Selig J M.Cayley maps for SE(3).In:The 12th International Federation for the Promotion of Mechanism and Machine Science World Congress,Besan9on,France,2007
16 Zang X Z,Yu W T,Zhang L,et al.Path planning based on BI-RRT algorithm for redundant manipulator.In:International Conference of Electrical,Automation and Mechanical Engineering,Phuket,Thailand,2015:189~191
17 Weghe M V,Ferguson D,Srinivasa S S.Randomized path planning for redundant manipulators without inverse kinematics.In:The 7th IEEE-RAS International Conference on Humanoid Robots,Pittsburgh,USA,2007:477~482
18 Kuffner J J.Effective sampling and distance metrics for 3Drigid body path planning.In:International Conference on Robotics and Automation,New Orleans,USA,2004:3993~3998
19 Murray R M,Li Z X,Sastry S S.A mathematical introduction to robotic manipulation.Boca Raton:CRC press,1994:81~142
2 Kuffner J J,Steven M L.RRT-connect:An efficient approach to single-query path planning.In:International Conference on Robotics and Automation,San Francisco,USA,2000:995~1001
3 Karaman S,Emilio F.Sampling-based algorithms for optimal motion planning.The International Journal of Robotics Research,2011,30(7):846~894
4 Gerdts M,Henrion R,H9mberg D,et al.Path planning and collision avoidance for robots.Numerical Algebra Control and Optimization,2012,2(3):437~463
5 Khatib O.Real-time obstacle avoidance for manipulators and mobile robots.The International Journal of Robotics Research,1986,5(1):90~98
6 Chang D E,Marsden J E.Gyroscopic forces and collision avoidance with convex obstacles.In:New trends in nonlinear dynamics and control and their applications,New York:Springer-Verlag,2003:145~159
7 Garimella G,Sheckells M,Kobilarov M.A stabilizing gyroscopic obstacle avoidance controller for underactuated systems.In:The 55th IEEE Conference on Decision and Control,Las Vegas,USA,2016:5010~5016
8 Abraham R,Marsden J E,Ratiu T.Foundations of mechanics,2nd ed.Boston:Addison-Wesley Publishing Company,1985
9郭永新,罗绍凯,梅凤翔.非完整约束系统几何动力学研究进展:Lagrange理论及其它.力学进展,2004,34(4):477~492(Guo Y X,Luo S K,Mei F X.Progress of geometric dynamics of non-holonomic constrained mechanical systems:Lagrange theory and others.Advances in Mechanics,2004,34(4):477~492(in Chinese))
10高强,钟万勰.非完整约束动力系统的离散积分方法.动力学与控制学报,2012,10(3):193~198(Gao Q,Zhong W X.Numerical algorithms for dynamic system with non-holonomic constrains.Journal of Dynamics and Control,2012,10(3):193~198(in Chinese))
11冯康,秦孟兆.哈密尔顿系统的辛几何算法.杭州:浙江科学技术出版社,2003(Feng K,Qin M Z.Symplectic geometric algorithm for Hamiltonian system.Hangzhou:Zhejiang Science and Technology Press,2003(in Chinese))
12胡伟鹏,邓子辰.无限维动力学系统的保结构分析方法.西安:西北工业大学出版社,2015(Hu W P,Deng Z C.Structure-preserving analysis methods for infinite-dimension dynamical system.Xi'an:Northwestern Polytechnical University Press,2015(in Chinese))
13 Bullo F,Murray R M.Tracking for fully actuated mechanical systems:A geometric framework.Automatica,1999,35(1):17~34
14 Aristidou A,Lasenby J.Inverse kinematics:a review of existing techniques and introduction of a new fast iterative solver.Technical Report,University of Cambridge,2009:12~17
15 Selig J M.Cayley maps for SE(3).In:The 12th International Federation for the Promotion of Mechanism and Machine Science World Congress,Besan9on,France,2007
16 Zang X Z,Yu W T,Zhang L,et al.Path planning based on BI-RRT algorithm for redundant manipulator.In:International Conference of Electrical,Automation and Mechanical Engineering,Phuket,Thailand,2015:189~191
17 Weghe M V,Ferguson D,Srinivasa S S.Randomized path planning for redundant manipulators without inverse kinematics.In:The 7th IEEE-RAS International Conference on Humanoid Robots,Pittsburgh,USA,2007:477~482
18 Kuffner J J.Effective sampling and distance metrics for 3Drigid body path planning.In:International Conference on Robotics and Automation,New Orleans,USA,2004:3993~3998
19 Murray R M,Li Z X,Sastry S S.A mathematical introduction to robotic manipulation.Boca Raton:CRC press,1994:81~142