在轨服务空间机器人机械多体系统动力学高效率建模研究
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摘要
近年来,随着空间科学技术的发展,空间机器人机械多体系统的动力学建模获得了广泛的研究。根据现实工程需要,目前空间机器人是自由度较多、结构复杂的航天装备,以及随着空间机器人构件的轻质、柔性化,利用空间刚性机器人的建模理论已经不能解决柔性机器人的动力学建模问题,因而大型空间机器人系统的高效率动力学建模与实时仿真已成为一个新的热点问题。由于大型在轨服务空间机器人的结构复杂性,以及机器人本体的质量随着载荷及燃料的消耗而发生变化等因素,在地面上很难实施全尺寸的动力学参数辨识试验,这就需要开展在轨空间机器人参数辨识技术研究。因此,针对自由浮动空间机器人的动力学高效率建模、实时仿真以及参数辨识问题开展了研究工作,以期为在轨航天器实时控制获得坚实的基础。
本文对机械多体系统动力学建模的数学基础理论、描述多体系统体间关系的拓扑结构、旋量表示以及基本空间算子等理论进行了详细的介绍;根据Lagrang建立多体系统动力学模型的理论,研究了空间机器人机械多体系统动力学的一般符号推导过程;得到了机械多体系统符号动力学建模算法;利用有限元方法对柔性体的物理模型进行离散,得到了柔性体的质量矩阵和刚度矩阵,由此建立多柔体系统的动力学方程。
在空间算子代数理论的基础上,将根据空间算子描述的刚性多体系统、柔性多体系统推广到一般的机械多体系统动力学建模应用中进行递推计算。该机械多体系统既可以包含有柔体又包含有刚体,既可以是链式系统又可以是树型多体系统。利用Huston理论的低序体阵列方法描述了一般多体系统的拓扑结构,然后根据判断相邻两体是刚体或者柔体,利用空间算子代数理论建立一般多体系统动力学模型。
进一步发展了空间算子代数理论体系,采用空间算子描述了机械多体系统广义动力学高效率建模问题。根据系统中铰的驱动情况分别对铰链定义为主动铰和被动铰,通过判断铰链的类型分别按照两次从系统的顶端到基座的顺序、一次从基座到顶端的顺序进行了系统铰接体惯量的递推、系统冗余力的递推和广义加速度和广义主动力的递推。通过上述三种方式的递推过程建立了在轨服务空间机器人系统广义递推动力学模型,实现了高效率O(n)次的计算效率,该算法可以应用于一般机械多体系统(包括刚性多体系统、柔性多体系统、欠驱动系统),求解反向动力学、正向动力学和混合动力学递推。
基于翟婉明提出的新型积分校正算法,通过将二次微分方程逐步降阶成代数方程,利用违约校正逐次求解出方程的离散值。并且进一步发展了线性多步积分算法高效率的求解大型微分(微分-代数)方程组。全面介绍了机械多体系统动力学的直接数值方法,重点论述了求解微分方程和微分代数方程组的线性多步积分算法。
分析并解决了利用动量守恒方法进行参数辨识过程中的线性方程组奇异性问题,并且研究了机器人的各类参数等因素对辨识研究的影响。研究了空间刚性机器人(单臂和双臂)本体和操作臂抓取未知目标卫星的参数辨识问题。根据机器人本体携带的测速敏感器测得本体质心的线速度及角速度,通过依次使不同的铰具有初始速度的方法,基于线动量及角动量守恒即可分别对双臂空间机器人本体和未知目标卫星进行未知参数的辨识。
根据上述理论成果,完成了机械多体系统符号动力学软件编制。该软件有强大的功能模块,运用Mathematica符号软件开发的。软件包括机械多体系统动力学建模、数值积分算法、有限元处理、可视化输出以及控制等模块。软件能实现机械多体系统的动力学符号与数值仿真分析,并可以获得系统的拓扑结构、约束信息以及系统各机械参数的描述,可以输出如仿真运行时间、SOA算子、运动、受力等,并以表格、曲线和动画的形式表现出来。
最后在以上理论和方法的基础上,对航天工程实例进行了仿真计算验证。对本文提出的理论方法的可行性以及有效性在地面实验室中得到验证。
At present, with the development of the space science and technology, the space robots are becoming imperative to understand their distinctive dynamics. Flexible space robots, as well as large flexible space structures in general, have unveiled a new and challenging field of dynamics and control. The dynamics model of the space flexible robots is very complex. So the high O(n) recursive dynamic method and real time simulation to solve large space robots system become very important. The parameter identification is necessary for precise control because the payload changes the kinematics of the system together with the dynamics. Two methods are proposed under the condition that the robot is free to translate and rotate. The kinematics, recursive dynamics, real time simulation and parameter identification of space robot system have been discussed in this thesis.
Based on the mathematical basic theory of the multibody system dynamics, the topological structure, screw theory and Spatial Operator Algebra were discussed. The dynamics equation of space robots multibody system was derived based on Lagrange equation. The model of the flexible body was discrete used finite element method, and the mass matrix and stiffness matrix were gained. The dynamic equation of flexible multibody system was gained.
The recursive dynamics of the general multibody system, which contain rigid body and flexible body, was discussed. The topology of the general multibody system was described used Huston’s Lower-body-array theory, then recursive dynamics was researched according to the feature (flexible or rigid) based on SOA theory.
The hybrid recursive dynamics base on the spatial operator algebra theory and real time simulation of the generalized flexible multibody was presented in this paper. the generalized flexible multibody was described in according to the type of the joint (active or passive); 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; at last the O(n) hybrid dynamic was gained. Next the real time solver for the large differential-algebra equation was studied based on the linear multi-step method in this paper. Simulations results show that the dynamic modeling and fast integration techniques proposed in this paper are very useful.
With the parameter identification methods for inertial parameters of the base and unknown object handled by manipulators on a free-floating space robot was concerned in this paper. Firstly, kinematic model of robots based on spatial operator algebra theory was gained. Next, parameter identification of the base was studied based on the conservation principle of linear and angular momentum, then parameter identification of the unknown object handled by manipulators is considered based on the parameter of base. Al last the effect of the parameter of robots to parameter identification was considered.
Numerical integration method based linear muti-step numerical method was researched. Various numerical methods for dynamics of multibody systems are discussed. A new method for solving the differential-algebra equation and differential equation are discussed. This method was proposed by professor Zhai-Wanming based on Newmark-βmethod. The correct value of the dynamics equation was gained by translates the differential-algebra equation or differential equation to algebra equation by constraint stabilization.
This chapter has laid the foundation for software module programming. It has studied the multibody system mark dynamics programming. It uses the Mathematica software platform. And it is a visualization contact surface, so the user can easily describe the topology, the restraint information, and information acquisition of the multibody systems which is for simulation analysis. And it also gives the result like simulation run time, the SOA operator, the movement, the stress and so on with the form of the curve and the animation formal expression and so on.
At last, engineering problems were simulated on computer according to the above theories.The feasibility of the parameter identification methods is demonstrated by a hardware experiment on the ground as well as numerical simulation.
本文对机械多体系统动力学建模的数学基础理论、描述多体系统体间关系的拓扑结构、旋量表示以及基本空间算子等理论进行了详细的介绍;根据Lagrang建立多体系统动力学模型的理论,研究了空间机器人机械多体系统动力学的一般符号推导过程;得到了机械多体系统符号动力学建模算法;利用有限元方法对柔性体的物理模型进行离散,得到了柔性体的质量矩阵和刚度矩阵,由此建立多柔体系统的动力学方程。
在空间算子代数理论的基础上,将根据空间算子描述的刚性多体系统、柔性多体系统推广到一般的机械多体系统动力学建模应用中进行递推计算。该机械多体系统既可以包含有柔体又包含有刚体,既可以是链式系统又可以是树型多体系统。利用Huston理论的低序体阵列方法描述了一般多体系统的拓扑结构,然后根据判断相邻两体是刚体或者柔体,利用空间算子代数理论建立一般多体系统动力学模型。
进一步发展了空间算子代数理论体系,采用空间算子描述了机械多体系统广义动力学高效率建模问题。根据系统中铰的驱动情况分别对铰链定义为主动铰和被动铰,通过判断铰链的类型分别按照两次从系统的顶端到基座的顺序、一次从基座到顶端的顺序进行了系统铰接体惯量的递推、系统冗余力的递推和广义加速度和广义主动力的递推。通过上述三种方式的递推过程建立了在轨服务空间机器人系统广义递推动力学模型,实现了高效率O(n)次的计算效率,该算法可以应用于一般机械多体系统(包括刚性多体系统、柔性多体系统、欠驱动系统),求解反向动力学、正向动力学和混合动力学递推。
基于翟婉明提出的新型积分校正算法,通过将二次微分方程逐步降阶成代数方程,利用违约校正逐次求解出方程的离散值。并且进一步发展了线性多步积分算法高效率的求解大型微分(微分-代数)方程组。全面介绍了机械多体系统动力学的直接数值方法,重点论述了求解微分方程和微分代数方程组的线性多步积分算法。
分析并解决了利用动量守恒方法进行参数辨识过程中的线性方程组奇异性问题,并且研究了机器人的各类参数等因素对辨识研究的影响。研究了空间刚性机器人(单臂和双臂)本体和操作臂抓取未知目标卫星的参数辨识问题。根据机器人本体携带的测速敏感器测得本体质心的线速度及角速度,通过依次使不同的铰具有初始速度的方法,基于线动量及角动量守恒即可分别对双臂空间机器人本体和未知目标卫星进行未知参数的辨识。
根据上述理论成果,完成了机械多体系统符号动力学软件编制。该软件有强大的功能模块,运用Mathematica符号软件开发的。软件包括机械多体系统动力学建模、数值积分算法、有限元处理、可视化输出以及控制等模块。软件能实现机械多体系统的动力学符号与数值仿真分析,并可以获得系统的拓扑结构、约束信息以及系统各机械参数的描述,可以输出如仿真运行时间、SOA算子、运动、受力等,并以表格、曲线和动画的形式表现出来。
最后在以上理论和方法的基础上,对航天工程实例进行了仿真计算验证。对本文提出的理论方法的可行性以及有效性在地面实验室中得到验证。
At present, with the development of the space science and technology, the space robots are becoming imperative to understand their distinctive dynamics. Flexible space robots, as well as large flexible space structures in general, have unveiled a new and challenging field of dynamics and control. The dynamics model of the space flexible robots is very complex. So the high O(n) recursive dynamic method and real time simulation to solve large space robots system become very important. The parameter identification is necessary for precise control because the payload changes the kinematics of the system together with the dynamics. Two methods are proposed under the condition that the robot is free to translate and rotate. The kinematics, recursive dynamics, real time simulation and parameter identification of space robot system have been discussed in this thesis.
Based on the mathematical basic theory of the multibody system dynamics, the topological structure, screw theory and Spatial Operator Algebra were discussed. The dynamics equation of space robots multibody system was derived based on Lagrange equation. The model of the flexible body was discrete used finite element method, and the mass matrix and stiffness matrix were gained. The dynamic equation of flexible multibody system was gained.
The recursive dynamics of the general multibody system, which contain rigid body and flexible body, was discussed. The topology of the general multibody system was described used Huston’s Lower-body-array theory, then recursive dynamics was researched according to the feature (flexible or rigid) based on SOA theory.
The hybrid recursive dynamics base on the spatial operator algebra theory and real time simulation of the generalized flexible multibody was presented in this paper. the generalized flexible multibody was described in according to the type of the joint (active or passive); 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; at last the O(n) hybrid dynamic was gained. Next the real time solver for the large differential-algebra equation was studied based on the linear multi-step method in this paper. Simulations results show that the dynamic modeling and fast integration techniques proposed in this paper are very useful.
With the parameter identification methods for inertial parameters of the base and unknown object handled by manipulators on a free-floating space robot was concerned in this paper. Firstly, kinematic model of robots based on spatial operator algebra theory was gained. Next, parameter identification of the base was studied based on the conservation principle of linear and angular momentum, then parameter identification of the unknown object handled by manipulators is considered based on the parameter of base. Al last the effect of the parameter of robots to parameter identification was considered.
Numerical integration method based linear muti-step numerical method was researched. Various numerical methods for dynamics of multibody systems are discussed. A new method for solving the differential-algebra equation and differential equation are discussed. This method was proposed by professor Zhai-Wanming based on Newmark-βmethod. The correct value of the dynamics equation was gained by translates the differential-algebra equation or differential equation to algebra equation by constraint stabilization.
This chapter has laid the foundation for software module programming. It has studied the multibody system mark dynamics programming. It uses the Mathematica software platform. And it is a visualization contact surface, so the user can easily describe the topology, the restraint information, and information acquisition of the multibody systems which is for simulation analysis. And it also gives the result like simulation run time, the SOA operator, the movement, the stress and so on with the form of the curve and the animation formal expression and so on.
At last, engineering problems were simulated on computer according to the above theories.The feasibility of the parameter identification methods is demonstrated by a hardware experiment on the ground as well as numerical simulation.
引文
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