刚体姿态控制及其在机器人控制中的应用研究
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摘要
机器人研究体现了人类复制自身的愿望，是最高意义上的机械仿生学，是当代众多高技术领域成果的综合体现。机器人智能主要来自机器人控制系统，而机器人的底层控制问题是机械臂和末端执行器的运动控制。因此，当将机械臂和末端执行器近似看作刚体时，机器人的底层控制问题实际上是刚体运动的控制问题。
基于这样的认识，本文在国家自然科学基金项目“刚体姿态控制的几何方法”(基金代号：69774010)、航空科学基金项目“航空火控系统中的姿态控制问题”(基金代号：97D53040)和国家973重大基础研究项目“复杂大系统过程优化与高性能软件”(项目代号：G1988030417)的资助下，对刚体姿态控制及其在机器人控制中的应用进行了较为系统的研究。本文的主要工作和贡献有以下几点：
(1) 系统地研究了刚体姿态的参数化描述方法，给出了描述刚体姿态的姿态矩阵、欧拉角、四元数和Rodrigues参数的相互转换关系，建立了基于四元数和Rodrigues参数的刚体姿态调节控制模型，和基于误差四元数和误差Rodrigues参数的刚体姿态跟踪控制模型。
(2) 系统地研究了刚体姿态控制系统的输出反馈控制问题。目前的姿态控制系统中，基本上都要用到全部状态信息，即姿态和角速率信息。但角速率信息通常很难获取，或带有严重的噪声。针对这种情况，本文利用刚体姿态控制系统中固有的无源性，设计了无需角速率测量值的刚体姿态控制器。
(3) 刚体姿态控制系统中一般存在两类不确定性：惯性矩阵含有的不确定性和控制矩阵含有的不确定性。现有的刚体姿态鲁棒控制器都只是针对惯性矩阵的不确定性。本文首次针对控制矩阵中的不确定性，采用自适应控制方法，得到了一种对上述两种不确定性都具有鲁棒性的自适应鲁棒控制器。
(4) 系统地研究了刚体机器人控制系统的输出反馈控制问题。利用机器人控制系统固有的无源性，在作业空间中，采用Rodrigues参数描述末端执行器的姿态，设计了用于机器人末端执行器位姿控制的输出反馈控制律，消除了控制器中的广义速度。目前的动态输出反馈控制器都采用7阶无源网络，而本文的无源网络是由6阶平方线性系统实现的。另外，在关节空间中，我们利用机器人控制系统固有的无源性，设计了无需测量关节速度的PD控制律。
西北工业大学博士学位论文
（5）针对机器人控制系统中的精确重力补偿问题，给出了可以用平衡点的
常数重力补偿项来实现精确重力补偿的条件，大大地简化了机器人控制系统中
的精确重力补偿问题。
（6）改进了现有的弹性关节机器人控制律，利用无源性方法，给出了仅需要
作动器位置测量的输出反馈控制器。
（7）基于线性化假设，研究了基于Internet的机器人控制系统的稳定性分
析和镇定控制器设计问题，给出了一种时滞系统稳定性新判据，并据此设计了。
””’”’””“‘“’”‘”“””’‘””’”““”’”“’“”””“”“’“””““““”“’““”””’“f
镇定控制器。
Robotics research is the embodiment of man's long-standing and deep desire to create something like himself,and robot is the highest form of the achievements in mechanical bionics. Now robot is the integration of many high and new technologies.
As is well-known,the intelligence of a robot is derived from its control system,and the basic problem of a robot control system is the manipulation of the robot arm and its end-effector. When the robot arm and its end-effector is treated as a rigid body,as is quite reasonable in most cases,the motion control,especially attitude control,of a rigid body becomes the basic problem of robot control.
Based on the above perception,we carried out systematic research on attitude control of a rigid body and its application to robot control. Our research is supported partly by the National Natural Science Foundation of China (Grant No. 69774010),Aeronautical Science Foundation of China (Grant No. 97D53040) and the National 973 Fundamental Research Program of China ( Grant No. G1988030417).
The main contributions of this dissertation are as follows:
(1) Four kinds of parameters for representing the attitude of a rigid body are studied. They are attitude matrix,Euler angles,quaternion,and Rodrigues parameters. Formulas are given for changing from any kind of parameters to the other three kinds of parameters. The model for attitude stabilization is established using quaternion or Rodrigues parameters,and the model for attitude tracking is established using error quaternion or error Rodrigues parameters.
(2) Attitude stabilization and attitude tracking are then studied. As is known,the existing control laws require full state information,including attitude parameters and angular velocities. Usually,angular velocities are difficult to oh tain,or even if they can be obtained,they are usually contaminated by noises. To
solve this problem,we propose an output feedback control law without angular velocities by making use of the inherent passivity of the attitude control system.
(3) Usually,there are two kinds of unknown external disturbances and/or modeling uncertainties:one in the inertial matrix,and the other in the control matrix. The existing robust attitude controllers can only deal with disturbances and/ or uncertaities in the inertial matrix. In this paper,we for the first time present an adaptive robust attitude controller which is robust to the disturbances and/or uncertaities in both the inertial matrix and the control matrix.
(4) Output feedback controllers are proposed for eliminating velocity measurement in robot control systems. In the task space,the attitude space of the robot end-effector is parameterized by Rodrigues parameters,and an output feedback controller without the generalized velocity is designed for controlling the position and attitude of the end-effector of a rigid robot. The existing dynamic output feedback schemes use a seven-order passive network,but our dynamic controller is realized by a six-order square linear system. In the joint space,proportional plus derivative (PD) controllers without joint velocity measurement are designed by making use of the inherent passivity of the robot control system.
(5) In the existing robot controller,the gravity compensation item needs to be computed for each joint state,it is quite a burden for real-time control. We proved in this paper that under a certain condition the gravity compensation item can be replaced by the constant gravity compensation item at the equilibrium point,thus greatly reducing the computation overhead.
(6) We also improved the existing controllers for elastic joint robot by the passivity approach,and an output feedback controller is designed,which only requires the measurement of the actuator position.
(7) Finally,based on the linearization of the robot control system,we studied the stability criterion of an Internet-based robot control system which is a linear system with multiple time-delays. A new and less conservative stability criterion is given,and a controller for
基于这样的认识，本文在国家自然科学基金项目“刚体姿态控制的几何方法”(基金代号：69774010)、航空科学基金项目“航空火控系统中的姿态控制问题”(基金代号：97D53040)和国家973重大基础研究项目“复杂大系统过程优化与高性能软件”(项目代号：G1988030417)的资助下，对刚体姿态控制及其在机器人控制中的应用进行了较为系统的研究。本文的主要工作和贡献有以下几点：
(1) 系统地研究了刚体姿态的参数化描述方法，给出了描述刚体姿态的姿态矩阵、欧拉角、四元数和Rodrigues参数的相互转换关系，建立了基于四元数和Rodrigues参数的刚体姿态调节控制模型，和基于误差四元数和误差Rodrigues参数的刚体姿态跟踪控制模型。
(2) 系统地研究了刚体姿态控制系统的输出反馈控制问题。目前的姿态控制系统中，基本上都要用到全部状态信息，即姿态和角速率信息。但角速率信息通常很难获取，或带有严重的噪声。针对这种情况，本文利用刚体姿态控制系统中固有的无源性，设计了无需角速率测量值的刚体姿态控制器。
(3) 刚体姿态控制系统中一般存在两类不确定性：惯性矩阵含有的不确定性和控制矩阵含有的不确定性。现有的刚体姿态鲁棒控制器都只是针对惯性矩阵的不确定性。本文首次针对控制矩阵中的不确定性，采用自适应控制方法，得到了一种对上述两种不确定性都具有鲁棒性的自适应鲁棒控制器。
(4) 系统地研究了刚体机器人控制系统的输出反馈控制问题。利用机器人控制系统固有的无源性，在作业空间中，采用Rodrigues参数描述末端执行器的姿态，设计了用于机器人末端执行器位姿控制的输出反馈控制律，消除了控制器中的广义速度。目前的动态输出反馈控制器都采用7阶无源网络，而本文的无源网络是由6阶平方线性系统实现的。另外，在关节空间中，我们利用机器人控制系统固有的无源性，设计了无需测量关节速度的PD控制律。
西北工业大学博士学位论文
（5）针对机器人控制系统中的精确重力补偿问题，给出了可以用平衡点的
常数重力补偿项来实现精确重力补偿的条件，大大地简化了机器人控制系统中
的精确重力补偿问题。
（6）改进了现有的弹性关节机器人控制律，利用无源性方法，给出了仅需要
作动器位置测量的输出反馈控制器。
（7）基于线性化假设，研究了基于Internet的机器人控制系统的稳定性分
析和镇定控制器设计问题，给出了一种时滞系统稳定性新判据，并据此设计了。
””’”’””“‘“’”‘”“””’‘””’”““”’”“’“”””“”“’“””““““”“’““”””’“f
镇定控制器。
Robotics research is the embodiment of man's long-standing and deep desire to create something like himself,and robot is the highest form of the achievements in mechanical bionics. Now robot is the integration of many high and new technologies.
As is well-known,the intelligence of a robot is derived from its control system,and the basic problem of a robot control system is the manipulation of the robot arm and its end-effector. When the robot arm and its end-effector is treated as a rigid body,as is quite reasonable in most cases,the motion control,especially attitude control,of a rigid body becomes the basic problem of robot control.
Based on the above perception,we carried out systematic research on attitude control of a rigid body and its application to robot control. Our research is supported partly by the National Natural Science Foundation of China (Grant No. 69774010),Aeronautical Science Foundation of China (Grant No. 97D53040) and the National 973 Fundamental Research Program of China ( Grant No. G1988030417).
The main contributions of this dissertation are as follows:
(1) Four kinds of parameters for representing the attitude of a rigid body are studied. They are attitude matrix,Euler angles,quaternion,and Rodrigues parameters. Formulas are given for changing from any kind of parameters to the other three kinds of parameters. The model for attitude stabilization is established using quaternion or Rodrigues parameters,and the model for attitude tracking is established using error quaternion or error Rodrigues parameters.
(2) Attitude stabilization and attitude tracking are then studied. As is known,the existing control laws require full state information,including attitude parameters and angular velocities. Usually,angular velocities are difficult to oh tain,or even if they can be obtained,they are usually contaminated by noises. To
solve this problem,we propose an output feedback control law without angular velocities by making use of the inherent passivity of the attitude control system.
(3) Usually,there are two kinds of unknown external disturbances and/or modeling uncertainties:one in the inertial matrix,and the other in the control matrix. The existing robust attitude controllers can only deal with disturbances and/ or uncertaities in the inertial matrix. In this paper,we for the first time present an adaptive robust attitude controller which is robust to the disturbances and/or uncertaities in both the inertial matrix and the control matrix.
(4) Output feedback controllers are proposed for eliminating velocity measurement in robot control systems. In the task space,the attitude space of the robot end-effector is parameterized by Rodrigues parameters,and an output feedback controller without the generalized velocity is designed for controlling the position and attitude of the end-effector of a rigid robot. The existing dynamic output feedback schemes use a seven-order passive network,but our dynamic controller is realized by a six-order square linear system. In the joint space,proportional plus derivative (PD) controllers without joint velocity measurement are designed by making use of the inherent passivity of the robot control system.
(5) In the existing robot controller,the gravity compensation item needs to be computed for each joint state,it is quite a burden for real-time control. We proved in this paper that under a certain condition the gravity compensation item can be replaced by the constant gravity compensation item at the equilibrium point,thus greatly reducing the computation overhead.
(6) We also improved the existing controllers for elastic joint robot by the passivity approach,and an output feedback controller is designed,which only requires the measurement of the actuator position.
(7) Finally,based on the linearization of the robot control system,we studied the stability criterion of an Internet-based robot control system which is a linear system with multiple time-delays. A new and less conservative stability criterion is given,and a controller for
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