仿人型乒乓球机械手运动学及动力学控制方法研究
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摘要
仿人型乒乓球机械手是模拟人手臂结构设计制造、用来击打乒乓球的机械手臂,具有6个以上自由度,可以灵活地实现绝大部分人手臂可以实现的动作。这类手臂是链式旋转关节机械手,与传统机械手臂相比,具有结构小巧、重量轻、速度快、控制灵活等特点。除了在手臂终端安装乒乓球拍完成击打乒乓球的任务以外,还可以安装各种夹具、灵巧手指等机构,完成各种演示、抓取等任务。其控制方法具有可扩展性,容易应用于焊接、喷涂、教学等机械手臂的控制中。该控制方法的研究也为家庭服务型机器人领域的机械手臂应用奠定坚实的基础。
本实验室设计制造的仿人型乒乓球机械手臂为7自由度手臂,三个版本的机械手臂都可以在位置、速度和电流三种控制模式下运行。位置模式对应的控制指令为各关节角度转换成的码盘读数,电机控制中的速度和力矩环由电机控制盒实现。速度模式也被称为运动学控制,对应的控制指令为各关节角速度,力矩控制环由控制盒实现。由于直流伺服电机电流与力矩成正比关系,因此电流模式也称为力矩模式,对应手臂动力学控制。该模式对应的控制指令为电机电流,控制盒使实际电机电流跟踪指令电流。本文的研究包含参数识别、运动学和动力学控制方法,主要研究内容包括：
1)针对机械手臂加工、组装等环节的不精确导致的手臂DH模型参数(也称为运动学参数、几何参数)不准问题,提出了一种使用Leica三维激光测量装置、基于大量测量数据的参数标定方法。通过标定得到DH模型参数的修正值,大幅提高了手臂终端的三维空间定位精度。对于动力学模型参数的识别,提出了一种基于二次优化的动力学参数识别方法。并针对识别参数构成的惯性矩阵非正定的问题,提出一种特征值调整使惯性矩阵正定化的方法,使得最终获得的动力学参数满足惯性矩阵正定化的条件。同时,本文给出了基于Solidworks三维建模的动力学参数估计方法。
2)提出一种针对点到点任务的冗余化方法,将传统的非冗余6维点到点任务投影到低维空间实现,使障碍避免等次任务可以通过冗余控制方法实现。同时本文给出了低维投影的示例以及投影函数需满足的数学条件。
3)针对冗余机械手臂多任务控制问题,提出一种扩展最小二乘方法,将关节限制以外的其他次任务转化为虚拟关节的关节限制问题,再应用加权最小二乘方法解决。并通过直接设定权重矩阵的逆矩阵和一步预测的方法设定其中加权矩阵的权值,实现冗余机械手臂在较多次任务约束情形下的控制问题。只要同时到达限制阈值的次任务数目不多于手臂的冗余自由度数目,该方法可同时保证主任务跟踪精度和多于手臂自由度数目的次任务的实现。
4)给出了仿人型机械手臂的动力学控制方法。针对动态LuGre摩擦力补偿问题,提出一种使用简化观测器观测鬃毛偏折状态的方法,并结合自适应控制律,使用Lyapunov方法分析了使用简化观测器的自适应控制的稳定性。单关节和多关节情形下的实验结果证明(?)该方法在动态摩擦力补偿中的优越性。
5)提出了一种适用于动力学参数中含有一定不确定性的机械手臂的碰撞检测算法。该算法基于动量守恒推导而出,构造一个扰动观测器观测手臂受到外部作用力的大小,并根据该观测器的结果判断是否与外部物体发生碰撞。在是否发生碰撞的判定中使用了观测器结果和其相邻周期变化量作为共同指标,并使用一个高通滤波器滤除观测结果中的低频分量,以减少不确定动力学参数带来的影响。该方法可有效的检测到外部碰撞的发生,并控制机械手臂远离碰撞区域,保证机械手臂与人的安全。
Humanoid pingpong manipulator, imitating the mechanical structure of human arm, is built to play pingpong, with 6 or more degrees of freedom. It can move with dexterity like a human arm. The humanoid pingpong manipulator is a kind of traditional serial link manipulator with rotational joints. It is more compact in structure, lighter in weight, faster and more dexterous in moving than the normal industrial robots. Besides the pingpong playing task, the grasping task could be fulfilled if the pingpong pat at the end of the manipulator is replaced with gripper or dexterous robotic fingers. The control methods for pingpong manipulator could be adopted to welding, spaying or educational robots. The study on the control law of pingpong manipulator offers technical help to the widespread use of humanoid manipulators in the service robot field.
The three editions of humanoid pingpong manipulators we built could run at position mode, velocity mode and current mode. The control mode is divided into three based on the input of the servo amplifier which drives the motor of the joint. The input of amplifier is the joint angles when the manipulator is running at position mode. Velocity mode means that the input is joint velocities and current mode corresponds to motor currents. The current mode is called torque mode, since the current of DC servo is in direct proportion to the motor torque. The major research works and contributions of this thesis include:
1) In order to handle the uncertainty of DH parameters which is lead by imprecisely manufac-ture and assembly, a kinematic calibration method is presented. The Leica Geosystems Absolute Tracker is used to get the exact position of the manipulator end-effector. The kinematic errors are determined by least-norm calculation of numbers of measuring data. The position accuracy of the end-effector is approved with the compensation kinematic errors. And, a dynamic parameter identification method is proposed, which is based on quadratic programming. A new method to make the inertia matrix positive definite is developed via doing quadratic programming twice. The dynamic parameters estimation based on the Solidworks model is also given.
2) A lower dimensional task function method for point-to-point tasks of non-redundant manip- ulator is developed in this thesis. A series of mapping functions which map the six-dimensional point-to-point task to a lower dimensional task space are given. In the lower dimensional task space the manipulator is changed to redundant one and redundant control laws could be adopted for the subtasks. And the conditions that the mapping function should satisfy are also given.
3) A generalize-weighted least-norm method for the control of redundant manipulator with multi subtasks is developed. This method maintains the advantage of weighted least norm method which has fantastic ability to avoid joint limits. With a new concept of virtual joints, the subtasks performance criterions are changed to the virtual joints limits problem and solved by weighted (?)t norm method. With this generalized method, the number of subtasks to be deal with could be larger than the number of joints of the manipulator.
4) An adaptive dynamic friction compensation method is developed in this thesis. With the dy-namic LuGre friction compensation, obtaining the internal bristle-deflection state is the most important in the control design. A simple nonlinear observer, which is a simplification of De Wit's nonlinear observer, is developed in this paper. The stability of the adaptive control is an-alyzed using the second Lyapunov theory. A low-pass filter is added to remove the influence of the high frequency noise of joint velocities measurements. The experiments on single joint or multiple joints verify the advantage of this method on the dynamic compensation of friction.
5) For the collision safety problem of manipulator with inertia parameter uncertainties, a new collision detection algorithm is presented. A disturbance observer which is deduced from preser-vation of momentum is designed to evaluate the influence of the collision force. The variation of the observed results is added into the collision detection thresholds. For the damage limiting of the robot or the safety of the human body, two different safe reaction methods for velocity mode and torque mode control are also presented. The experiments demonstrate that the collision could be detected and the safety of the manipulator and human are guaranteed with this method.
本实验室设计制造的仿人型乒乓球机械手臂为7自由度手臂,三个版本的机械手臂都可以在位置、速度和电流三种控制模式下运行。位置模式对应的控制指令为各关节角度转换成的码盘读数,电机控制中的速度和力矩环由电机控制盒实现。速度模式也被称为运动学控制,对应的控制指令为各关节角速度,力矩控制环由控制盒实现。由于直流伺服电机电流与力矩成正比关系,因此电流模式也称为力矩模式,对应手臂动力学控制。该模式对应的控制指令为电机电流,控制盒使实际电机电流跟踪指令电流。本文的研究包含参数识别、运动学和动力学控制方法,主要研究内容包括：
1)针对机械手臂加工、组装等环节的不精确导致的手臂DH模型参数(也称为运动学参数、几何参数)不准问题,提出了一种使用Leica三维激光测量装置、基于大量测量数据的参数标定方法。通过标定得到DH模型参数的修正值,大幅提高了手臂终端的三维空间定位精度。对于动力学模型参数的识别,提出了一种基于二次优化的动力学参数识别方法。并针对识别参数构成的惯性矩阵非正定的问题,提出一种特征值调整使惯性矩阵正定化的方法,使得最终获得的动力学参数满足惯性矩阵正定化的条件。同时,本文给出了基于Solidworks三维建模的动力学参数估计方法。
2)提出一种针对点到点任务的冗余化方法,将传统的非冗余6维点到点任务投影到低维空间实现,使障碍避免等次任务可以通过冗余控制方法实现。同时本文给出了低维投影的示例以及投影函数需满足的数学条件。
3)针对冗余机械手臂多任务控制问题,提出一种扩展最小二乘方法,将关节限制以外的其他次任务转化为虚拟关节的关节限制问题,再应用加权最小二乘方法解决。并通过直接设定权重矩阵的逆矩阵和一步预测的方法设定其中加权矩阵的权值,实现冗余机械手臂在较多次任务约束情形下的控制问题。只要同时到达限制阈值的次任务数目不多于手臂的冗余自由度数目,该方法可同时保证主任务跟踪精度和多于手臂自由度数目的次任务的实现。
4)给出了仿人型机械手臂的动力学控制方法。针对动态LuGre摩擦力补偿问题,提出一种使用简化观测器观测鬃毛偏折状态的方法,并结合自适应控制律,使用Lyapunov方法分析了使用简化观测器的自适应控制的稳定性。单关节和多关节情形下的实验结果证明(?)该方法在动态摩擦力补偿中的优越性。
5)提出了一种适用于动力学参数中含有一定不确定性的机械手臂的碰撞检测算法。该算法基于动量守恒推导而出,构造一个扰动观测器观测手臂受到外部作用力的大小,并根据该观测器的结果判断是否与外部物体发生碰撞。在是否发生碰撞的判定中使用了观测器结果和其相邻周期变化量作为共同指标,并使用一个高通滤波器滤除观测结果中的低频分量,以减少不确定动力学参数带来的影响。该方法可有效的检测到外部碰撞的发生,并控制机械手臂远离碰撞区域,保证机械手臂与人的安全。
Humanoid pingpong manipulator, imitating the mechanical structure of human arm, is built to play pingpong, with 6 or more degrees of freedom. It can move with dexterity like a human arm. The humanoid pingpong manipulator is a kind of traditional serial link manipulator with rotational joints. It is more compact in structure, lighter in weight, faster and more dexterous in moving than the normal industrial robots. Besides the pingpong playing task, the grasping task could be fulfilled if the pingpong pat at the end of the manipulator is replaced with gripper or dexterous robotic fingers. The control methods for pingpong manipulator could be adopted to welding, spaying or educational robots. The study on the control law of pingpong manipulator offers technical help to the widespread use of humanoid manipulators in the service robot field.
The three editions of humanoid pingpong manipulators we built could run at position mode, velocity mode and current mode. The control mode is divided into three based on the input of the servo amplifier which drives the motor of the joint. The input of amplifier is the joint angles when the manipulator is running at position mode. Velocity mode means that the input is joint velocities and current mode corresponds to motor currents. The current mode is called torque mode, since the current of DC servo is in direct proportion to the motor torque. The major research works and contributions of this thesis include:
1) In order to handle the uncertainty of DH parameters which is lead by imprecisely manufac-ture and assembly, a kinematic calibration method is presented. The Leica Geosystems Absolute Tracker is used to get the exact position of the manipulator end-effector. The kinematic errors are determined by least-norm calculation of numbers of measuring data. The position accuracy of the end-effector is approved with the compensation kinematic errors. And, a dynamic parameter identification method is proposed, which is based on quadratic programming. A new method to make the inertia matrix positive definite is developed via doing quadratic programming twice. The dynamic parameters estimation based on the Solidworks model is also given.
2) A lower dimensional task function method for point-to-point tasks of non-redundant manip- ulator is developed in this thesis. A series of mapping functions which map the six-dimensional point-to-point task to a lower dimensional task space are given. In the lower dimensional task space the manipulator is changed to redundant one and redundant control laws could be adopted for the subtasks. And the conditions that the mapping function should satisfy are also given.
3) A generalize-weighted least-norm method for the control of redundant manipulator with multi subtasks is developed. This method maintains the advantage of weighted least norm method which has fantastic ability to avoid joint limits. With a new concept of virtual joints, the subtasks performance criterions are changed to the virtual joints limits problem and solved by weighted (?)t norm method. With this generalized method, the number of subtasks to be deal with could be larger than the number of joints of the manipulator.
4) An adaptive dynamic friction compensation method is developed in this thesis. With the dy-namic LuGre friction compensation, obtaining the internal bristle-deflection state is the most important in the control design. A simple nonlinear observer, which is a simplification of De Wit's nonlinear observer, is developed in this paper. The stability of the adaptive control is an-alyzed using the second Lyapunov theory. A low-pass filter is added to remove the influence of the high frequency noise of joint velocities measurements. The experiments on single joint or multiple joints verify the advantage of this method on the dynamic compensation of friction.
5) For the collision safety problem of manipulator with inertia parameter uncertainties, a new collision detection algorithm is presented. A disturbance observer which is deduced from preser-vation of momentum is designed to evaluate the influence of the collision force. The variation of the observed results is added into the collision detection thresholds. For the damage limiting of the robot or the safety of the human body, two different safe reaction methods for velocity mode and torque mode control are also presented. The experiments demonstrate that the collision could be detected and the safety of the manipulator and human are guaranteed with this method.
引文
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