树型刚柔机械多体系统递推动力学与广义―α求解算法
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摘要
研究树型柔性航天器动力学高效率建模和高精度广义―α的数值求解算法。利用拓扑结构和连接矩阵的方法描述树型机械多体系统,采用图论的方法将树型系统分解为多条链式系统;对系统中铰的驱动情况分别定义为主动铰和被动铰,通过铰链的类型以及判断是刚性体或者柔性体,基于空间算子代数理论建立树型系统的动力学模型;采用广义―α算法求解加速度约束的动力学微分—代数方程组。最后通过软件编制仿真验证本研究内容的正确性和高效性。
Generalized efficient recursive dynamics model of a kind of flexible spacecraft with appendages system was built.The flexible spacecraft system was described by the topology method and the lower body array.The method of describing the under-actuated rigid-flexible multibody system based on Spatial Operator Algebra(SOA)theory was proposed.The generalized flexible spacecraft was described in according to the type of the joint(active or passive),and the rigid body or the flexible body;then the generalized articulated inertia-matrix,the residual forces and the generalized acceleration and torque were computed through twice tip-to-base recursive and once base-to-tip recursive;the generalized torque and the acceleration was linear added at the branch,at last generalized-αmethod is presented for stiff dynamic equations of multibody systems based on the constraints projection method.Simulations results show that the dynamic modeling and fast integration techniques proposed in this paper are very useful.
Generalized efficient recursive dynamics model of a kind of flexible spacecraft with appendages system was built.The flexible spacecraft system was described by the topology method and the lower body array.The method of describing the under-actuated rigid-flexible multibody system based on Spatial Operator Algebra(SOA)theory was proposed.The generalized flexible spacecraft was described in according to the type of the joint(active or passive),and the rigid body or the flexible body;then the generalized articulated inertia-matrix,the residual forces and the generalized acceleration and torque were computed through twice tip-to-base recursive and once base-to-tip recursive;the generalized torque and the acceleration was linear added at the branch,at last generalized-αmethod is presented for stiff dynamic equations of multibody systems based on the constraints projection method.Simulations results show that the dynamic modeling and fast integration techniques proposed in this paper are very useful.
引文
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[14]田富洋,吴洪涛,赵大旭,等.空间柔性机器人动力学分析的快速积分算法[J].山东大学学报(工学版),2009,39(3):94~98.Tian Fuyang,Wu Hongtao,Zhao Daxu,et al.Fast integration algorithms for dynamic of flexible space robots system[J].Journal of Shandong University(Engineering Science),2009,39(3):94~98.
[15]丁洁玉,潘振宽.多体系统动力学刚性方程广义―α投影法[J].中国科学(物理学力学天文学),2013,43(4):572~578.Ding Jieyu,Pan Zhenkuan.Generalized-αprojection method for stiff dynamic equations of multibody systems[J].Scientia Sinica(Physica,Mechanica&Astronomica),2013,43(4):572~578.
[2]Shang W,Cong S,Jiang S.Dynamic model based nonlinear tracking control of a planar parallel manipulator[J].Nonlinear Dynamics,2010,60(4):597~606.
[3]Müller A,Hufnagel T.Model-based control of redundantly actuated parallel manipulators in redundant coordinates[J].Robotics and Autonomous Systems,2012,60(4):563~571.
[4]Featherstone R.Efficient factorization of the joint-space inertia matrix for branched kinematic trees[J].The International Journal of Robotics Research,2005,24(6):487~500.
[5]Wensing P,Featherstone R,Orin D E.A reduced-order recursive algorithm for the computation of the operational—space inertia matrix[C]//Robotics and Automation(ICRA),2012IEEE International Conference on.IEEE,2012:4911~4917.
[6]Jain A.Robot and Multibody dynamics:analysis and algorithms[M].Springer Science&Business Media,2010.
[7]刘云平,顾和军,吴洪涛.空间操作臂的高效率动力学建模方法[J].华中科技大学学报(自然科学版).2011,39(6):75~78.Liu Yunping,Gu Hejun,Wu Hongtao.High effective dynamics modeling for space manipulator[J].Journal of Huazhong University of Science and Technology(Natural Science Edition),2011,39(6):75~78.
[8]赵大旭,陈柏,吴洪涛,等.潜游式管道机器人动力学分析[J].华南理工大学学报,2010,38(8):65~71.Zhao Daxu,Chen Bai,Wu hongtao,et al.Dynamic analysis of submersible in-pipe robot[J].Journal of South China University of Technology,2010,38(8):65~71.
[9]方喜峰,吴洪涛,刘云平,等.基于空间算子代数理论计算多体系统动力学建模[J].机械工程学报,2009,(1):66~72.Fang Xifeng,Wu Hongtao Liu Yunping,Lu Yuping,et al.Computational dynamics of multi-body system modeling based on spatial operator algebra theory[J].Chinese Journal of Mechanical Engineering,2009,(1):66~72.
[10]孙宏丽,吴洪涛,田富洋,等.空间算子代数刚柔耦合系统动力学软件流程[J].华中科技大学学报,2009,37(12):107~111.Sun Hongli,Wu Hongtao,Tian Fuyang,et al.Dynamic software flow of the rigid-flexible coupling system based on spatial operator algebra theory[J].Journal of Huazhong University of Science and Technology,2009,37(12):107~111.
[11]田富洋,吴洪涛,赵大旭,等.一类柔性宏刚性微空间机器人广义动力学建模研究[J].宇航学报,2010,31(3):687~694.Tian Fuyang,Wu Hongtao,Zhao Daxu,et al.Research on generalized efficient recursive dynamics of flexible macro-micro space robots system[J].Journal of Astronautics,2010,31(3):687~694.
[12]田富洋,吴洪涛,邵兵,等.柔性多体系统混合递推动力学建模及实时仿真研究[J].中国机械工程,2010,21(1):6~12.Tian Fuyang,Wu Hongtao,Shao Bing,et al.Hybrid dynamics of flexible multibody system and real time simulation[J].China Mechanical Engineering,2010,21(1):6~12.
[13]魏承,赵阳.基于空间算子代数的空间多体系统动力学递推计算[J].宇航学报,2009,30(6):2105~2110.Wei Cheng,Zhao Yang.Recursive computation of space multibody dynamics using spatial operator algebra[J].Journal of Astronautics,2009,30(6):2105~2110.
[14]田富洋,吴洪涛,赵大旭,等.空间柔性机器人动力学分析的快速积分算法[J].山东大学学报(工学版),2009,39(3):94~98.Tian Fuyang,Wu Hongtao,Zhao Daxu,et al.Fast integration algorithms for dynamic of flexible space robots system[J].Journal of Shandong University(Engineering Science),2009,39(3):94~98.
[15]丁洁玉,潘振宽.多体系统动力学刚性方程广义―α投影法[J].中国科学(物理学力学天文学),2013,43(4):572~578.Ding Jieyu,Pan Zhenkuan.Generalized-αprojection method for stiff dynamic equations of multibody systems[J].Scientia Sinica(Physica,Mechanica&Astronomica),2013,43(4):572~578.