六自由度串联机器人运动优化与轨迹跟踪控制研究
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摘要
1954年,第一台电子可编程机器人在美国诞生,从此,机器人不再是捷克小说家的科学幻想,而成为众多科学家和工程师奋斗终生的目标。历经50多年的发展,国外的机器人技术和应用逐渐成熟,并造就了安川、松下、KUKA、ABB、iRobot等一批著名的机器人公司。如今,机器人已成为自动化生产线、柔性制造系统中必不可少的单元,2004年底全球在役的工业机器人超过100万台,2005年增长率达到创记录的30%,其中亚洲机器人增长幅度高达43%,2007年全球新安装工业机器人的数量超过十万套。机器人的研究和应用远没有停止,而是以日新月异的速度向智能化、模块化和系统化的方向发展,其应用领域也从传统的制造业向建筑、农业、防灾、医疗、宇宙、海洋开发等领域,甚至是娱乐、家庭服务等与人类活动密切相关的领域拓展。
然而,机器人技术是集机构学、电子技术、计算机技术、传感技术、控制论、人工智能和仿生学等多学科于一体的高新技术。由于基础制造技术、多学科交叉融合以及产业化推动等诸多因素的影响,我国虽在1972年即开始研制工业机器人,但至今没有形成品牌,国内的工业机器人装备也主要依赖进口。因此,无论是在理论和技术上跟踪国际先进水平,还是在应用上服务国内制造业,进一步研究机器人的关键共性理论和技术,找到制约机器人国产化的核心问题和解决方案,都具有非常重要的意义。
本文以自主研制的钱江Ⅰ号焊接机器人作为载体,通过理论研究和实验验证相结合的方式,系统深入地研究了六自由度串联机器人的实时逆运动学、轨迹规划与优化、动力学耦合特性和高精度轨迹跟踪控制问题,旨在找到工业机器人国产化的受限因素,并为串联机器人的开发应用提供一套有效的理论和技术解决方案。
本文的研究共分为七章,各章内容概括如下:
第一章,调研分析国内外串联机器人的发展历程及应用现状,以工业机器人为重点指出串联机器人的核心理论和技术问题,结合国内工业机器人研究和产业现状,阐明本课题的研究意义、研究难点和研究内容。
第二章,建立机器人连杆坐标系并获得D-H参数,推导机器人正运动学和逆运动学计算公式。由于任务空间的位姿变量和关节空间的关节变量具有一对多关系,因此重点解决逆运动学算法的实时性和稳定性问题。将机器人的几何结构从满足Pieper准则拓展到一般几何结构,提出一种基于矩阵分解的一般6R机器人实时逆运动学算法,结合封闭解法、牛顿-拉夫森迭代算法,得到一套可以解决各类几何结构六自由度串联机器人逆运动学问题的高效算法。采用C++实现整套算法,使其可以用于6R机器人实时控制系统。
第三章,建立机器人任务空间和关节空间轨迹构造方法。推导三维空间直线、圆弧、样条曲线构造方程。为实现机器人作业的柔顺性,采用三次样条曲线构造任务空间平滑位置轨迹,采用四元数球面立体插值方法构造任务空间平滑姿态轨迹。由于机器人各关节驱动和传动部件具有输出力矩限制和运动平滑性要求,因此,提出一种考虑运动学约束的平滑轨迹规划方法,采用B样条曲线构造关节轨迹,使关节速度、加速度、加加速度均连续,且轨迹的起始和终止位置的速度、加速度和加加速度可以任意配置。为提高机器人的作业效率,研究时间最优轨迹规划,以轨迹执行时间作为优化目标,将运动学约束转化为B样条曲线控制顶点约束,采用序列二次规划算法搜索最优时间节点,进而规划出时间最优且加加速度连续的轨迹。将加加速度累积效果作为优化目标,采用类似的轨迹构造方法和寻优方法,规划出最优平滑轨迹。该套轨迹规划与优化算法为机器人快速平稳地执行作业任务奠定了基础。
第四章,讨论自主研制的钱江Ⅰ号焊接机器人及其关键技术,包括系统架构、机器人本体、嵌入式示教盒软硬件、主控制器及主控软件、运动控制器及运动控制软件、手动焊机数字化转接模块。采用拉格朗日功能平衡法推导六自由度串联机器人的动力学方程,代入钱江Ⅰ号焊接机器人的结构参数,分析其惯量特性、哥氏力和离心力特性、重力矩特性,为机械结构的优化设计和驱动传动部件的合理选型提供理论依据,为关节控制器和轨迹跟踪控制器的研究设计提供动力学模型。
第五章,首先分析电机驱动的机器人单关节控制模型。在Matlab中建立交流伺服电机PID控制模型,以单关节阶跃响应的瞬态性能和稳态性能作为优化指标,采用序列二次规划方法分别在单关节最大惯量和最小惯量处对速度闭环PI控制参数和位置闭环PID控制参数进行寻优。然后,考虑机器人六关节联动时的动态、耦合和非线性特性,分别采用模糊自适应PID控制策略和有重力补偿的PID控制策略提高轨迹跟踪精度,研究模糊自适应PID控制器对于提高轨迹跟踪精度的效果,研究完全重力补偿PID控制器应用于串联机器人的可行性和有效性。
第六章,针对工业机器人执行的作业任务具有重复性的特点,引入迭代学习控制技术,用于适应工业机器人重复执行作业任务时重复出现的动态特性,包括惯量耦合、力矩耦合、摩擦力、噪声干扰等。提出一种自适应迭代学习轨迹跟踪控制器,根据轨迹跟踪的误差和误差导数得到学习量,用于修正PD控制器的输出,从而提高轨迹跟踪精度。提出一种输入型迭代学习控制策略,在不改变控制器模型和参数的条件下,通过修正输入参考轨迹达到提高期望轨迹跟踪精度的目的。在钱江Ⅰ号焊接机器人系统上进行控制实验,结果验证了输入迭代学习策略的有效性。
第七章,总结归纳了本文的主要研究工作、研究结论和创新点,针对串联机器人的国产化和前沿研究作出展望,为后续研发工作提供参考。
In 1954, the first electronic programmable robot was born in the U.S. Since then, robot is no long a science fiction of Czech novelist, but the life-long goal struggled by many scientists and engineers. After 50 years of development, foreign technology and application of robots gradually matured, and a number of well-known companies such as Yaskawa, Panasonic, KUKA, ABB and iRobot were brought up. Today, robot has become an essential unit of automatic production lines and flexible manufacturing systems. At the end of 2004, totoal number of the world's industrial robots was more than one million, and the annual growth rate in 2005 was 30 percent, which created a new record, and the growth rate in Asia was up to 43%. In 2007, the world's newly installed industrial robots were more than one million sets. Research and application of robot is far from stopped, but developing day by day with the trend of intelligent, modular and systematic. Its applications are expanding from traditional field of manufacturing to new fileds of architecture, agriculture, disaster prevention, medical care, the universe, the ocean, and even the fields closely related to human activities such as entertainment, home service.
However, robotics is a high-tech technology which integrating the electronics technology, computer technology, sensor technology, control theory, artificial intelligence and bionics, etc. For the reasons of basic manufacturing technology, multi-disciplinary integration, promotion of industrialization and many other factors, although the research and development of robot began in 1972 in our country, but so far there is no successful domestic branch of robot, so the robots demanded still rely on imports. Therefore, whether for tracking the international advanced theory and technology, or for suppling services of robot application for domestic manufacturing, further research of key and common theories and technologies in robotics, and discovery of problems and solutions of domestic robot industrialization, are of great importance.
In this paper, an arc welding robot named Qianjiang I is designed, theoretical research and experimental verification are carried out systematicly and deeply on serial robot, especially serial robot with six degrees of freedom. The research focuses on real-time inverse kinematics, trajectory planning, trajectory optimizing, dynamics coupling characteristics and high-precision tracking control, and aims to finding the constraints on domestic robot industrialization, as well as obtaining an effective solution of theory and technology for the development and application of serial robots.
The thesis is divided into seven chapters, each chapter is summarized as follows:
In the first chapter, development and application of serial robots at home and abroad are investigated and analyesed. Key theoretical and technical problems existing in serial robots, especially industrial robots, are pointed out. Then the significances, difficulties and contents are presented according to status quo of research and application of industrial robots.
In chapterⅡ, coordinate systems of links are set up, and D-H parameters are obtained. Then equations of kinematics and inverse kinematics are derived. Because the one-to-many relationship of variable in task space and joint space, stability and real-time performance of inverse kinematics are focused on. The geometry of serial robots with six degree of freedom is extended from the style which satisfies Pieper's rules to general structure, and a real-time inverse kinematics algorithm based on matrix decompostion is proposed for general 6R robots, which have six rotate joints and general geometry. By combining with the closure method, Newton - Raphson iterative algorithm, a set of algorithm is obtained, and the inverse kinematics problem of serial robots with six rotate joints and various geometries can be solved efficiently. At last, C++ programming language is adopted to realize the set of algortithms, so it can be used for real-time control systems of 6R robots.
In chapterⅢ, the construction of trajectories in task space and joint space are established. Equations that describe line, arc and spline curve in three-dimensional space are derivated, which are the basic elements of any complex trajectory. In order to achieve flexibility of motion, cubic spline is adopted to contruct smooth trajectory of posiotn in task space, and spherical quaternion interpolation method is exploited to generate smooth trajectory of orientation in task space. Because the output torque of driving and transmitting components of every joint is limited and smooth movement is required, a smooth trajectory planning method that considers kinematic constraints is proposed. B-spline is utilized to generate joint trajectory, so joint velocity, acceleration and jerk are continuous, and, the velocity, acceleration and jerk at the starting and stopping points can be configured. In order to enhance the working efficiency of robot, time optimal trajectory planning method is researched. By setting the total executing time of trajectory as goal of optimization, and transforming the kinematic constraints to constraints on control points of B-spline, the optimal time nodes are seeked with sequential quadratic programming algorithm, then time-optimal and jerk-continous trajectory is generated. Similar procedures are used to generate smoothness-optimal trajectory by setting the cumulative jerk as the goal of optimization. The trajectory planning and optimization algorithm construct the foundation for robots to execute tasks efficiently and smoothly.
In chapterⅣ, the arc welding robot named "Qianjiang I" and its key technologies are introduced, including system architecture, mechanical structrue, hardware and software of embedded teaching box, main controller and main software, motion controller and motion control software, digital transfer module of manual arc welding machine. Lagrange method is exploited to obtain the dynamic equations of serial robot with six degrees of freedom. Then structural parameters of "Qianjiang I" are substituted into the equations, and its characteristics of inertia, Coriolis force and centrifugal force, and gravitational moment are analyzed. The results provide a theoretical basis for optimal design of mechanical structure and reasonable selection of drivers and actuators, and also provide dynamic model for research and design of joint controller and trajectory tracking controller.
In chapterⅤ, firstly, the control model of single joint driven by motor is analyzed. PID controller for AC servo motor is created in Matlab, by setting the transient characteristics and steady-state properties of step response as the optimizing target, optimal parameters of PI controller in velocity loop and PID controller in postion loop are seeked using the sequential quadratic programming method. And optimal parameters according to the largest inertial and the smallest inertial are obtained separately. Then, taking into account the dynamic, coupling and nonlinear characteristics when joints are runing simultaneously, fuzzy adaptive PID controller and PID controller with compensation of gravitational moment are designed. The performance of fuzzy adaptive PID controller in improving trajectory tracking accuracy is analyzed. The feasibility and effectiveness of PID controller with complete compensation of gravitational moment is discussed.
In chapterⅥ, iterative learning techniques are researched. Because tasks that industrial robots execute are often repeated, so, dynamic characteristics can be learned and adapted while the robot executes a certain task repeatedly, the dynamic characteristics include coupling inertia, coupling torque, friction and noise, etc. An adaptive iterative learning controller for trajectory tracking is proposed, which learns from trajectory tracking error and error derivative, and generates an incremental value that appends to the output of PD controller, so the trajectory tracking accuracy is improved. Then, an input-type iterative learning strategy is discussed, which does not change the model and parameters of controller, but modifies the input reference trajectory to achieve improved tracking accuracy of desired trajectory. At last, experiments are carried out on "Qianjiang I", and results verify the effectiveness of input-type iterative learning strategy.
In chapterⅦ, the main work, results and innovations of the thesis are summarized. Further research and domestic industrialization of serial robot are prospected, which provides a reference for the following research and design.
然而,机器人技术是集机构学、电子技术、计算机技术、传感技术、控制论、人工智能和仿生学等多学科于一体的高新技术。由于基础制造技术、多学科交叉融合以及产业化推动等诸多因素的影响,我国虽在1972年即开始研制工业机器人,但至今没有形成品牌,国内的工业机器人装备也主要依赖进口。因此,无论是在理论和技术上跟踪国际先进水平,还是在应用上服务国内制造业,进一步研究机器人的关键共性理论和技术,找到制约机器人国产化的核心问题和解决方案,都具有非常重要的意义。
本文以自主研制的钱江Ⅰ号焊接机器人作为载体,通过理论研究和实验验证相结合的方式,系统深入地研究了六自由度串联机器人的实时逆运动学、轨迹规划与优化、动力学耦合特性和高精度轨迹跟踪控制问题,旨在找到工业机器人国产化的受限因素,并为串联机器人的开发应用提供一套有效的理论和技术解决方案。
本文的研究共分为七章,各章内容概括如下:
第一章,调研分析国内外串联机器人的发展历程及应用现状,以工业机器人为重点指出串联机器人的核心理论和技术问题,结合国内工业机器人研究和产业现状,阐明本课题的研究意义、研究难点和研究内容。
第二章,建立机器人连杆坐标系并获得D-H参数,推导机器人正运动学和逆运动学计算公式。由于任务空间的位姿变量和关节空间的关节变量具有一对多关系,因此重点解决逆运动学算法的实时性和稳定性问题。将机器人的几何结构从满足Pieper准则拓展到一般几何结构,提出一种基于矩阵分解的一般6R机器人实时逆运动学算法,结合封闭解法、牛顿-拉夫森迭代算法,得到一套可以解决各类几何结构六自由度串联机器人逆运动学问题的高效算法。采用C++实现整套算法,使其可以用于6R机器人实时控制系统。
第三章,建立机器人任务空间和关节空间轨迹构造方法。推导三维空间直线、圆弧、样条曲线构造方程。为实现机器人作业的柔顺性,采用三次样条曲线构造任务空间平滑位置轨迹,采用四元数球面立体插值方法构造任务空间平滑姿态轨迹。由于机器人各关节驱动和传动部件具有输出力矩限制和运动平滑性要求,因此,提出一种考虑运动学约束的平滑轨迹规划方法,采用B样条曲线构造关节轨迹,使关节速度、加速度、加加速度均连续,且轨迹的起始和终止位置的速度、加速度和加加速度可以任意配置。为提高机器人的作业效率,研究时间最优轨迹规划,以轨迹执行时间作为优化目标,将运动学约束转化为B样条曲线控制顶点约束,采用序列二次规划算法搜索最优时间节点,进而规划出时间最优且加加速度连续的轨迹。将加加速度累积效果作为优化目标,采用类似的轨迹构造方法和寻优方法,规划出最优平滑轨迹。该套轨迹规划与优化算法为机器人快速平稳地执行作业任务奠定了基础。
第四章,讨论自主研制的钱江Ⅰ号焊接机器人及其关键技术,包括系统架构、机器人本体、嵌入式示教盒软硬件、主控制器及主控软件、运动控制器及运动控制软件、手动焊机数字化转接模块。采用拉格朗日功能平衡法推导六自由度串联机器人的动力学方程,代入钱江Ⅰ号焊接机器人的结构参数,分析其惯量特性、哥氏力和离心力特性、重力矩特性,为机械结构的优化设计和驱动传动部件的合理选型提供理论依据,为关节控制器和轨迹跟踪控制器的研究设计提供动力学模型。
第五章,首先分析电机驱动的机器人单关节控制模型。在Matlab中建立交流伺服电机PID控制模型,以单关节阶跃响应的瞬态性能和稳态性能作为优化指标,采用序列二次规划方法分别在单关节最大惯量和最小惯量处对速度闭环PI控制参数和位置闭环PID控制参数进行寻优。然后,考虑机器人六关节联动时的动态、耦合和非线性特性,分别采用模糊自适应PID控制策略和有重力补偿的PID控制策略提高轨迹跟踪精度,研究模糊自适应PID控制器对于提高轨迹跟踪精度的效果,研究完全重力补偿PID控制器应用于串联机器人的可行性和有效性。
第六章,针对工业机器人执行的作业任务具有重复性的特点,引入迭代学习控制技术,用于适应工业机器人重复执行作业任务时重复出现的动态特性,包括惯量耦合、力矩耦合、摩擦力、噪声干扰等。提出一种自适应迭代学习轨迹跟踪控制器,根据轨迹跟踪的误差和误差导数得到学习量,用于修正PD控制器的输出,从而提高轨迹跟踪精度。提出一种输入型迭代学习控制策略,在不改变控制器模型和参数的条件下,通过修正输入参考轨迹达到提高期望轨迹跟踪精度的目的。在钱江Ⅰ号焊接机器人系统上进行控制实验,结果验证了输入迭代学习策略的有效性。
第七章,总结归纳了本文的主要研究工作、研究结论和创新点,针对串联机器人的国产化和前沿研究作出展望,为后续研发工作提供参考。
In 1954, the first electronic programmable robot was born in the U.S. Since then, robot is no long a science fiction of Czech novelist, but the life-long goal struggled by many scientists and engineers. After 50 years of development, foreign technology and application of robots gradually matured, and a number of well-known companies such as Yaskawa, Panasonic, KUKA, ABB and iRobot were brought up. Today, robot has become an essential unit of automatic production lines and flexible manufacturing systems. At the end of 2004, totoal number of the world's industrial robots was more than one million, and the annual growth rate in 2005 was 30 percent, which created a new record, and the growth rate in Asia was up to 43%. In 2007, the world's newly installed industrial robots were more than one million sets. Research and application of robot is far from stopped, but developing day by day with the trend of intelligent, modular and systematic. Its applications are expanding from traditional field of manufacturing to new fileds of architecture, agriculture, disaster prevention, medical care, the universe, the ocean, and even the fields closely related to human activities such as entertainment, home service.
However, robotics is a high-tech technology which integrating the electronics technology, computer technology, sensor technology, control theory, artificial intelligence and bionics, etc. For the reasons of basic manufacturing technology, multi-disciplinary integration, promotion of industrialization and many other factors, although the research and development of robot began in 1972 in our country, but so far there is no successful domestic branch of robot, so the robots demanded still rely on imports. Therefore, whether for tracking the international advanced theory and technology, or for suppling services of robot application for domestic manufacturing, further research of key and common theories and technologies in robotics, and discovery of problems and solutions of domestic robot industrialization, are of great importance.
In this paper, an arc welding robot named Qianjiang I is designed, theoretical research and experimental verification are carried out systematicly and deeply on serial robot, especially serial robot with six degrees of freedom. The research focuses on real-time inverse kinematics, trajectory planning, trajectory optimizing, dynamics coupling characteristics and high-precision tracking control, and aims to finding the constraints on domestic robot industrialization, as well as obtaining an effective solution of theory and technology for the development and application of serial robots.
The thesis is divided into seven chapters, each chapter is summarized as follows:
In the first chapter, development and application of serial robots at home and abroad are investigated and analyesed. Key theoretical and technical problems existing in serial robots, especially industrial robots, are pointed out. Then the significances, difficulties and contents are presented according to status quo of research and application of industrial robots.
In chapterⅡ, coordinate systems of links are set up, and D-H parameters are obtained. Then equations of kinematics and inverse kinematics are derived. Because the one-to-many relationship of variable in task space and joint space, stability and real-time performance of inverse kinematics are focused on. The geometry of serial robots with six degree of freedom is extended from the style which satisfies Pieper's rules to general structure, and a real-time inverse kinematics algorithm based on matrix decompostion is proposed for general 6R robots, which have six rotate joints and general geometry. By combining with the closure method, Newton - Raphson iterative algorithm, a set of algorithm is obtained, and the inverse kinematics problem of serial robots with six rotate joints and various geometries can be solved efficiently. At last, C++ programming language is adopted to realize the set of algortithms, so it can be used for real-time control systems of 6R robots.
In chapterⅢ, the construction of trajectories in task space and joint space are established. Equations that describe line, arc and spline curve in three-dimensional space are derivated, which are the basic elements of any complex trajectory. In order to achieve flexibility of motion, cubic spline is adopted to contruct smooth trajectory of posiotn in task space, and spherical quaternion interpolation method is exploited to generate smooth trajectory of orientation in task space. Because the output torque of driving and transmitting components of every joint is limited and smooth movement is required, a smooth trajectory planning method that considers kinematic constraints is proposed. B-spline is utilized to generate joint trajectory, so joint velocity, acceleration and jerk are continuous, and, the velocity, acceleration and jerk at the starting and stopping points can be configured. In order to enhance the working efficiency of robot, time optimal trajectory planning method is researched. By setting the total executing time of trajectory as goal of optimization, and transforming the kinematic constraints to constraints on control points of B-spline, the optimal time nodes are seeked with sequential quadratic programming algorithm, then time-optimal and jerk-continous trajectory is generated. Similar procedures are used to generate smoothness-optimal trajectory by setting the cumulative jerk as the goal of optimization. The trajectory planning and optimization algorithm construct the foundation for robots to execute tasks efficiently and smoothly.
In chapterⅣ, the arc welding robot named "Qianjiang I" and its key technologies are introduced, including system architecture, mechanical structrue, hardware and software of embedded teaching box, main controller and main software, motion controller and motion control software, digital transfer module of manual arc welding machine. Lagrange method is exploited to obtain the dynamic equations of serial robot with six degrees of freedom. Then structural parameters of "Qianjiang I" are substituted into the equations, and its characteristics of inertia, Coriolis force and centrifugal force, and gravitational moment are analyzed. The results provide a theoretical basis for optimal design of mechanical structure and reasonable selection of drivers and actuators, and also provide dynamic model for research and design of joint controller and trajectory tracking controller.
In chapterⅤ, firstly, the control model of single joint driven by motor is analyzed. PID controller for AC servo motor is created in Matlab, by setting the transient characteristics and steady-state properties of step response as the optimizing target, optimal parameters of PI controller in velocity loop and PID controller in postion loop are seeked using the sequential quadratic programming method. And optimal parameters according to the largest inertial and the smallest inertial are obtained separately. Then, taking into account the dynamic, coupling and nonlinear characteristics when joints are runing simultaneously, fuzzy adaptive PID controller and PID controller with compensation of gravitational moment are designed. The performance of fuzzy adaptive PID controller in improving trajectory tracking accuracy is analyzed. The feasibility and effectiveness of PID controller with complete compensation of gravitational moment is discussed.
In chapterⅥ, iterative learning techniques are researched. Because tasks that industrial robots execute are often repeated, so, dynamic characteristics can be learned and adapted while the robot executes a certain task repeatedly, the dynamic characteristics include coupling inertia, coupling torque, friction and noise, etc. An adaptive iterative learning controller for trajectory tracking is proposed, which learns from trajectory tracking error and error derivative, and generates an incremental value that appends to the output of PD controller, so the trajectory tracking accuracy is improved. Then, an input-type iterative learning strategy is discussed, which does not change the model and parameters of controller, but modifies the input reference trajectory to achieve improved tracking accuracy of desired trajectory. At last, experiments are carried out on "Qianjiang I", and results verify the effectiveness of input-type iterative learning strategy.
In chapterⅦ, the main work, results and innovations of the thesis are summarized. Further research and domestic industrialization of serial robot are prospected, which provides a reference for the following research and design.
引文
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