柔性机器人协调操作的运动学和动力学研究
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摘要
机器人协调操作和柔性机器人的研究是机器人领域中的两个前沿课题。
到目前为止，国内外在机器人协调操作这一领域的研究中，绝大多数局限于
刚性机器人协调操作方面。相对于刚性机器人而言，柔性机器人能够满足未
来机器人在高速、精密、大承载和轻量化等方面的要求，因而越来越受到各
国学者的重视，但目前大多是针对单个柔性臂的研究。多柔性机器人的协调
操作则能综合柔性机器人和协调机器人两方面的优势，克服单柔性机器人变
形误差大、振动剧烈等缺点，使机器人系统的性能进一步提高，是柔性机器
人发展的必然趋势。因此，已开始引起国外学者的兴趣，目前的研究尚在初
期阶段。
本文将柔性机器人和机器人协调操作两个领域加以融合，以柔性机器人
协调操作系统为对象，在柔性机器人协调操作刚性负载的动力学建模、逆动
力学分析及仿真、系统的操作性能分析、操作精度控制等方面进行系统深入
的研究。
首先，通过分析认识到，柔性机器人协调操作区别于刚性机器人协调操作
的两个本质特性是：1）柔性机器人协调操作的名义刚性位形不一定满足相应
的刚性机器人协调操作的运动协调约束条件；2）柔性机器人协调操作的运动
学分析和动力学分析之间存在相互耦合，运动学分析不能脱离动力学分析而
单独进行。相应地采用有限元模型，定义了柔性机器人的名义刚性位形、刚
性位形和实际位形，分别给出了柔性机器人协调操作零自由度刚性负载、单
自出度开链刚性负载的运动协调约束条件和动力协调约束条件，并利用这些
约束条件，导出了既不显含系统内力又不显含系统外部无功约束力的系统动
力学方程，给出了相应逆动力学的求解方法。文中还通过仿真算例就不同基
解位形对操作结果的影响进行了比较。
其次，利用闭链刚性机构内部各杆件之间的运动微分关系，导出了柔性
机器人协调操作单自由度闭链刚性机构的运动协调约束条件和动力协调约束
条件，从而得到了系统动力学方程。而后，又对柔性机器人协调操作多环多
自由度闭链刚性负载进行了研究，通过多环多自由度闭链刚性负载内部的运
动微分关系，建立了基于标准目标任务的系统动力学通用模型，该模型具有
结构化特性，有利于建立此类系统的虚拟样机，编制通用化、参数化的计算
机仿真软件。
然后，利用柔性机器人协调抓取的几何微分约束和力平衡约束，通过深
入分析系统在静态位形时其内部各运动参量和力参量之间的关系，定义了系
统的操作刚度，从两个方面对系统的操作性能进行了分析：1）操作空间中，基
os
于系统操作刚度的全局特性；2）在一定约束的条件下，系统操作力矢端可达 二
边界的局部特性。
最后，在前面分析的基础上，提出了柔性机器人协调操作的位姿动态校
正控制策略，并以两柔性机器人协调操作零自由度刚性负载CP轨迹作业为目
标任务，将在线求得（或测得）的被操作负载位姿误差经过变换动态反馈至输入
端，以规划各关节的校正输入，从而提高系统的位姿操作精度。文中还通过
仿真算例分析了系统前向通道增益对控制稳定性和控制结果的影响。
以上几方面研究形成了系统的理论和方法，为柔性机器人协调操作这一
新领域研究的全面开展奠定了基础。
The coordination of robots and flexible manipulators are advanced topics in the robotics research. In the field of robot cooperation, most of works were limited in rigid robots so far. Compared with rigid ones, flexible robots are provided with the advantages of high speed, heavy payload and light weight. However, the large error, elastic vibration and other drawbacks due to the elastic deformation of flexible links can not be neglected in flexible robots. The coordination of flexible robots present the way to overcome these disadvantages, which has abstracted some attention and is being developed in recent years.
In this dissertation, on the integration of flexible manipulator and coordinated robots, the cooperation of flexible manipulators manipulating rigid loads is studied in such aspects as system dynamic modeling. system inverse dynamics, numerical simulation, manipulability and control schemes.
Firstly, two characteristics of flexible coordinated robot system have been recognized different from the coordinated system of rigid robots, i.e.
i) The kinematic coordination constraints in the cooperation system of rigid robots will not hold true for that of flexible ones;
ii) There exists coupling effect between the kinematics and dynamics of flexible cooperative system.
Based on these properties, the nominal rigid configuration, rigid configuration and actual configuration have been defined, respectively. By applying the Finite Element Model, the kinematic and dynamic coordination constraints are then derived for coordinated flexible manipulators manipulating the rigid load with zero d.o.f. and the open-loop rigid load with one d.o.f., respectively. The dynamic equations of system have been established and the inverse dynamic algorithm has been presented. The influences of different basic configurations of solution have also been discussed through numerical simulation.
Secondly, the kinematic and dynamic constraints of coordinated flexible manipulators manipulating a rigid four-bar linkage have been derived from the differential relationships of kinematics within the internal links of linkage. The dynamic equations of system have been governed consequently. Based on the
iii
standard assignment, the general dynamic equations have been then obtained for the coordinated flexible manipulators manipulating multi-loop rigid load with multid.o.f., which is useful to establishing the virtual prototype and designing simulation software of such system.
Thirdly, based on the geometrical differential constraints and force balancing constraints of the coordinated flexible manipulators, the mutual relationships between the kinematic and dynamic parameters in static configuration have been presented. The manipulation stiffness of the coordinated system has also been proposed. The manipulability of the flexible robot system has been then analyzed in two aspects:
i) The global characteristics in the manipulation workspace based on the manipulation stiffness;
ii) The local property of the reachable boundary of generalized forces.
A simulation of two coordinated manipulators manipulating a rigid load is presented as an example.
Finally, the dynamic control scheme for compensating the position and orientation errors of the grasped load has been developed to complete the assignment of CP trace for two coordinated flexible manipulators manipulating a rigid load. The improvement on manipulating precision of grasped load has been achieved by feeding back the transformation of position and orientation errors of the grasped load to scheme the compensative input angle of each joint. The effect of the gain in forward channel on the stability and result of control scheme have also been illustrated by numerical simulation.
A comprehensive study has been completed in this thesis, which paves the way to the further development of flexible cooperating robots.
到目前为止，国内外在机器人协调操作这一领域的研究中，绝大多数局限于
刚性机器人协调操作方面。相对于刚性机器人而言，柔性机器人能够满足未
来机器人在高速、精密、大承载和轻量化等方面的要求，因而越来越受到各
国学者的重视，但目前大多是针对单个柔性臂的研究。多柔性机器人的协调
操作则能综合柔性机器人和协调机器人两方面的优势，克服单柔性机器人变
形误差大、振动剧烈等缺点，使机器人系统的性能进一步提高，是柔性机器
人发展的必然趋势。因此，已开始引起国外学者的兴趣，目前的研究尚在初
期阶段。
本文将柔性机器人和机器人协调操作两个领域加以融合，以柔性机器人
协调操作系统为对象，在柔性机器人协调操作刚性负载的动力学建模、逆动
力学分析及仿真、系统的操作性能分析、操作精度控制等方面进行系统深入
的研究。
首先，通过分析认识到，柔性机器人协调操作区别于刚性机器人协调操作
的两个本质特性是：1）柔性机器人协调操作的名义刚性位形不一定满足相应
的刚性机器人协调操作的运动协调约束条件；2）柔性机器人协调操作的运动
学分析和动力学分析之间存在相互耦合，运动学分析不能脱离动力学分析而
单独进行。相应地采用有限元模型，定义了柔性机器人的名义刚性位形、刚
性位形和实际位形，分别给出了柔性机器人协调操作零自由度刚性负载、单
自出度开链刚性负载的运动协调约束条件和动力协调约束条件，并利用这些
约束条件，导出了既不显含系统内力又不显含系统外部无功约束力的系统动
力学方程，给出了相应逆动力学的求解方法。文中还通过仿真算例就不同基
解位形对操作结果的影响进行了比较。
其次，利用闭链刚性机构内部各杆件之间的运动微分关系，导出了柔性
机器人协调操作单自由度闭链刚性机构的运动协调约束条件和动力协调约束
条件，从而得到了系统动力学方程。而后，又对柔性机器人协调操作多环多
自由度闭链刚性负载进行了研究，通过多环多自由度闭链刚性负载内部的运
动微分关系，建立了基于标准目标任务的系统动力学通用模型，该模型具有
结构化特性，有利于建立此类系统的虚拟样机，编制通用化、参数化的计算
机仿真软件。
然后，利用柔性机器人协调抓取的几何微分约束和力平衡约束，通过深
入分析系统在静态位形时其内部各运动参量和力参量之间的关系，定义了系
统的操作刚度，从两个方面对系统的操作性能进行了分析：1）操作空间中，基
os
于系统操作刚度的全局特性；2）在一定约束的条件下，系统操作力矢端可达 二
边界的局部特性。
最后，在前面分析的基础上，提出了柔性机器人协调操作的位姿动态校
正控制策略，并以两柔性机器人协调操作零自由度刚性负载CP轨迹作业为目
标任务，将在线求得（或测得）的被操作负载位姿误差经过变换动态反馈至输入
端，以规划各关节的校正输入，从而提高系统的位姿操作精度。文中还通过
仿真算例分析了系统前向通道增益对控制稳定性和控制结果的影响。
以上几方面研究形成了系统的理论和方法，为柔性机器人协调操作这一
新领域研究的全面开展奠定了基础。
The coordination of robots and flexible manipulators are advanced topics in the robotics research. In the field of robot cooperation, most of works were limited in rigid robots so far. Compared with rigid ones, flexible robots are provided with the advantages of high speed, heavy payload and light weight. However, the large error, elastic vibration and other drawbacks due to the elastic deformation of flexible links can not be neglected in flexible robots. The coordination of flexible robots present the way to overcome these disadvantages, which has abstracted some attention and is being developed in recent years.
In this dissertation, on the integration of flexible manipulator and coordinated robots, the cooperation of flexible manipulators manipulating rigid loads is studied in such aspects as system dynamic modeling. system inverse dynamics, numerical simulation, manipulability and control schemes.
Firstly, two characteristics of flexible coordinated robot system have been recognized different from the coordinated system of rigid robots, i.e.
i) The kinematic coordination constraints in the cooperation system of rigid robots will not hold true for that of flexible ones;
ii) There exists coupling effect between the kinematics and dynamics of flexible cooperative system.
Based on these properties, the nominal rigid configuration, rigid configuration and actual configuration have been defined, respectively. By applying the Finite Element Model, the kinematic and dynamic coordination constraints are then derived for coordinated flexible manipulators manipulating the rigid load with zero d.o.f. and the open-loop rigid load with one d.o.f., respectively. The dynamic equations of system have been established and the inverse dynamic algorithm has been presented. The influences of different basic configurations of solution have also been discussed through numerical simulation.
Secondly, the kinematic and dynamic constraints of coordinated flexible manipulators manipulating a rigid four-bar linkage have been derived from the differential relationships of kinematics within the internal links of linkage. The dynamic equations of system have been governed consequently. Based on the
iii
standard assignment, the general dynamic equations have been then obtained for the coordinated flexible manipulators manipulating multi-loop rigid load with multid.o.f., which is useful to establishing the virtual prototype and designing simulation software of such system.
Thirdly, based on the geometrical differential constraints and force balancing constraints of the coordinated flexible manipulators, the mutual relationships between the kinematic and dynamic parameters in static configuration have been presented. The manipulation stiffness of the coordinated system has also been proposed. The manipulability of the flexible robot system has been then analyzed in two aspects:
i) The global characteristics in the manipulation workspace based on the manipulation stiffness;
ii) The local property of the reachable boundary of generalized forces.
A simulation of two coordinated manipulators manipulating a rigid load is presented as an example.
Finally, the dynamic control scheme for compensating the position and orientation errors of the grasped load has been developed to complete the assignment of CP trace for two coordinated flexible manipulators manipulating a rigid load. The improvement on manipulating precision of grasped load has been achieved by feeding back the transformation of position and orientation errors of the grasped load to scheme the compensative input angle of each joint. The effect of the gain in forward channel on the stability and result of control scheme have also been illustrated by numerical simulation.
A comprehensive study has been completed in this thesis, which paves the way to the further development of flexible cooperating robots.
引文
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