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多体系统轨迹跟踪的瞬时最优控制保辛方法

彭海军 李飞 高强 陈飙松 吴志刚 钟万勰

彭海军, 李飞, 高强, 陈飙松, 吴志刚, 钟万勰. 多体系统轨迹跟踪的瞬时最优控制保辛方法[J]. 力学学报, 2016, 48(4): 784-791. doi: 10.6052/0459-1879-16-164
引用本文: 彭海军, 李飞, 高强, 陈飙松, 吴志刚, 钟万勰. 多体系统轨迹跟踪的瞬时最优控制保辛方法[J]. 力学学报, 2016, 48(4): 784-791. doi: 10.6052/0459-1879-16-164
Peng Haijun, Li Fei, Gao Qiang, Chen Biaosong, Wu Zhigang, Zhong Wanxie. SYMPLECTIC METHOD FOR INSTANTANEOUS OPTIMAL CONTROL OF MULTIBODY SYSTEM TRAJECTORY TRACKING[J]. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(4): 784-791. doi: 10.6052/0459-1879-16-164
Citation: Peng Haijun, Li Fei, Gao Qiang, Chen Biaosong, Wu Zhigang, Zhong Wanxie. SYMPLECTIC METHOD FOR INSTANTANEOUS OPTIMAL CONTROL OF MULTIBODY SYSTEM TRAJECTORY TRACKING[J]. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(4): 784-791. doi: 10.6052/0459-1879-16-164

多体系统轨迹跟踪的瞬时最优控制保辛方法

doi: 10.6052/0459-1879-16-164
基金项目: 国家自然科学基金资助项目(11472069, 11472067, 11432010).
详细信息
    通讯作者:

    钟万勰,教授,主要研究方向:工程与计算力学,动力学与控制.E-mail:wxzhong@dlut.edu.cn

  • 中图分类号: O313.7

SYMPLECTIC METHOD FOR INSTANTANEOUS OPTIMAL CONTROL OF MULTIBODY SYSTEM TRAJECTORY TRACKING

  • 摘要: 随着近年来机器人在各行业领域的广泛应用,对机器人的动力学与控制性能不断提出新的要求,特别是对设计越来越复杂、操作越来越灵巧的智能机器人,要求其能够对目标轨迹实现高精度跟踪以满足实际工作需求. 因此,针对机器人多体系统对目标轨迹跟踪的任务需求,基于微分代数方程提出瞬时最优控制保辛方法. 首先,采用多体动力学绝对坐标建模方法建立机器人系统的普适动力学方程,即微分代数方程;然后,采用保辛方法将连续时间域内的微分代数方程进行离散化,进而得到以当前位置、速度和拉式乘子为未知量的非线性代数方程组;其次,通过引入对目标轨迹跟踪以及对控制加权的瞬时最优性能指标,根据瞬时最优控制理论获得当前最优控制输入;最后,通过离散时间步的更新完成对目标轨迹的跟踪任务. 为了验证本文方法的有效性,以双摆轨迹跟踪控制为例进行了数值仿真,结果表明:针对机器人轨迹跟踪任务所提出的瞬时最优控制保辛方法能够实现对目标轨迹的高精度跟踪,且瞬时最优控制由受控微分代数方程推导获得,更具一般性,能够适应其他复杂多体系统的轨迹跟踪控制问题.

     

  • 1 Flores-Abad A, Ma O, Pham K, et al. A review of space robotics technologies for on-orbit servicing. Progress in Aerospace Sciences, 2014, 68: 1-26  
    2 谭民, 王硕. 机器人技术研究进展. 自动化学报, 2013, 39(7): 963-972 (Tan Min, Wang Shuo. Research progress on robotics. Acta Automatica Sinica, 2013, 39(7): 963-972 (in Chinese))
    3 曹玉君, 尚建忠, 梁科山等. 软体机器人研究现状综述. 机械工程学报, 2012, 48(3): 25-33 (Cao Yujun, Shang Jianjun, Liang Keshan, et al. Review of soft-bodied robots. Journal of Mechanical Engineering, 2012, 48(3): 25-33 (in Chinese))
    4 Hong Y, Xu Y, Huang J. Finite-time control for robot manipulators. Systems & Control Letters, 2002, 46(4): 243-253  
    5 Parhi DR, Pradhan SK, Panda AK, et al. The stable and precise motion control for multiple mobile robots. Applied Soft Computing, 2009, 9(2): 477-487  
    6 Lee TC, Tsai CY, Song KT. Fast parking control of mobile robots: a motion planning approach with experimental validation. IEEE Transactions on Control Systems Technology, 2004, 12(5): 661-676.  
    7 Galicki M. Finite-time control of robotic manipulators. Automatica, 2015, 51: 49-54  
    8 Galicki M. Finite-time trajectory tracking control in a task space of robotic manipulators, Automatica, 2016, 67: 165-170
    9 Kim CJ, Sung SK, Yang CD, et al. Rotorcraft trajectory tracking using the state-dependent Riccati equation controller. Transactions of the Japan Society for Aeronautical and Space Sciences, 2008, 51(173): 184-192  
    10 Korayem MH, Zehfroosh A, Tourajizadeh H, et al. Optimal motion planning of non-linear dynamic systems in the presence of obstacles and moving boundaries using SDRE: application on cablesuspended robot. Nonlinear Dynamics, 2014, 76(2): 1423-1441  
    11 Scaglia G, Serrano E, Rosales A, et al. Linear interpolation based controller design for trajectory tracking under uncertainties: Application to mobile robots. Control Engineering Practice, 2015, 45: 123-132  
    12 陈罡, 高婷婷, 贾庆伟等. 带有未知参数和有界干扰的移动机器人轨迹跟踪控制. 控制理论与应用, 2015, 32(4): 491-496(Chen Gang, Gao Tingting, Jia Qingwei, et al. Trajectory tracking control for nonholonomic mobile robots with unknown parameters and bounded disturbance. Control Theory & Applications, 2015, 32(4): 491-496(in Chinese))
    13 杨俊友, 白殿春, 王硕玉等. 全方位轮式下肢康复训练机器人轨迹跟踪控制. 机器人, 2011, 33(3): 314-318(Yang Junyou, Bai Dianchun, Wang Shuoyu, et al. Trajectory tracking control of omnidirectional wheeled robot for lower limbs rehabilitative training. Robot, 2011, 33(3): 314-318(in Chinese))
    14 Gattringer H, Johannes G. Multibody System Dynamics, Robotics and Control. Springer Science & Business Media, 2013
    15 Jain A. Robot and Multibody Dynamics: Analysis and Algorithms. Springer Science & Business Media, 2010
    16 马秀腾, 翟彦博, 罗书强. 基于 1 方法的多体动力学数值算法研究. 力学学报, 2011, 43(5): 931-937(Ma Xiuteng, Zhai Yanbo, Luo Shuqiang. Numerical method of multibody dynamics based on 1 method. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(5): 931-937 (in Chinese))
    17 刘铖, 田强, 胡海岩. 基于绝对节点坐标的多柔体系统动力学高效计算方法. 力学学报, 2010, 42(6): 1197-1205 (Liu Cheng, Tian Qiang, Hu Haiyan. Efficient computational method for dynamics of flexible multibody systems based on absolute nodal coordinate. Chinese Journal of Theoretical and Applied Mechanics, 2010, 42(6): 1197-1205 (in Chinese))
    18 Antos P, Ambrósio JAC. A control strategy for vehicle trajectory tracking using multibody models. Multibody System Dynamics, 2004, 11: 365-394
    19 Liu C, Tian Q, Hu H. Dynamics and control of a spatial rigid-flexible multibody system with multiple cylindrical clearance joints. Mechanism and Machine Theory, 2012, 52: 106-129  
    20 Bottasso CL, Chang CS, Croce A, et al. Adaptive planning and tracking of trajectories for the simulation of maneuvers with multibody models. Computer Methods in Applied Mechanics and Engineering, 2006, 195: 7052-7072  
    21 Büskens C, Knauer M. Higher order real-time approximations in optimal control of multibody-systems for industrial robots. Multibody System Dynamics, 2006, 15(1): 85-106  
    22 钟万勰, 高强. 约束动力系统的分析结构力学积分. 动力学与控制学报, 2006, 4(3): 193-199 (Zhong Wanxie, Gao Qiang. Integration of constrained dynamical system via analytical structural mechanics. Journal of Dynamics and Control, 2006, 4(3): 193-199 (in Chinese))
    23 吴锋, 高强, 钟万勰. 基于祖冲之类方法的多体动力学方程保能量保约束积分. 计算机辅助工程, 2014, 23(1): 64-68 (Wu Feng, Gao Qiang, Zhong Wanxie. Energy and constraint preservation integration for multibody equations based on Zu Chongzhi method. Computer Aided Engineering, 2014, 23(1): 64-68 (in Chinese))
    24 彭海军, 高强, 吴志刚等. 非线性轨迹优化问题的保辛自适应求解方法. 应用力学学报,2010, 27(4): 732-739(Peng Haijun, Gao Qiang, Wu Zhigang, et al. Symplectic adaptive algorithm for solving nonlinear trajectory optimization problem. Chinese Journal of Applied Mechanics, 2010, 27(4): 732-739 (in Chinese))
    25 Peng HJ, Gao Q, Wu ZG, et al. Symplectic adaptive algorithm for solving nonlinear two-point boundary value problems in astrodynamics. Celestial Mechanics and Dynamical Astronomy, 2011, 110(4): 319-342  
    26 钟万勰, 高强, 彭海军. 经典力学辛讲. 大连:大连理工大学出版社, 2013 (Zhong Wanxie, Gao Qiang, Peng Haijun. Classical Mechanics: Its Symplectic Description. Dalian: Dalian University of Technology Press, 2013 (in Chinese))
    27 Shabana AA. Dynamics of Multibody Systems. Cambridge University Press, 2013
    28 Hairer E, Wanner G. Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems, Springer-Verlag Berlin Heidelberg, 1996
    29 Yang JN, Akbarpour A, Ghaemmaghami P. New optimal control algorithms for structural control. Journal of Engineering Mechanics, 1987, 113(9): 1369-1386  
    30 Yang JN, Li Z, Liu SC. Stable controllers for instantaneous optimal control. Journal of Engineering Mechanics, 1992, 118(8): 1612-1630  
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出版历程
  • 收稿日期:  2016-06-06
  • 修回日期:  2016-06-13
  • 刊出日期:  2016-07-18

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