多自由度串联机器人关节摩擦分析与低速高精度运动控制
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摘要
多自由度串联机器人广泛应用于工业自动化、医疗、航天、海洋等领域。虽然历经数十年的发展,其相关技术已基本成熟,但从运动控制的角度看,极端情况下的运动控制仍然是个没有很好解决的问题,如低速高精度控制、高速高精度控制,从而导致机器人在很多特殊工况的应用受到较大限制。本文针对多自由度串联机器人低速高精度运动控制的问题开展研究,在机器人结构确定的情况下,主要从关节摩擦建模与补偿、提高速度信号品质、设计高精度运动控制策略这三个角度出发来提升低速运动的性能。
本文首先介绍相关研究背景,全面分析影响机器人低速运动性能的几方面因素,包括系统结构设计、测量元件分辨率、非线性环节的影响、控制系统的性能等,而结构设计与优化、低速下高品质速度信号获取方法、非线性摩擦建模与补偿,以及高级运动控制策略设计是目前几个主要研究方向。
设计基于动力学模型的运动控制器是提高低速运动控制精度及平稳性的有效途径。该方法的前提是已知机器人的动力学模型及参数值。因而,本文第二章在动力学建模的基础上,系统地研究了一种在闭环控制下进行的离线辨识方法来获取机器人的动力学参数。该方法针对传统傅里叶级数不满足速度、加速度边界条件的缺陷,提出一种改进傅里叶级数作为激励轨迹。为提升抗噪声能力,以最小化观测矩阵条件数作为优化准则,采用遗传算法来优化激励轨迹系数。进一步,采用最大似然法作为参数估计方法,以便考虑测量噪声的影响。
在诸多非线性环节中,关节摩擦是影响低速运动性能的核心因素,有必要作深入分析。在机器人系统中,广泛采用RV减速器与谐波减速器作为传动元件,本文的第三章对RV驱动与谐波驱动这两种典型关节的摩擦来源、摩擦测量方法、摩擦特征、建模及辨识方法进行了系统研究。对于RV驱动大惯量关节,分析了不同负载力矩下摩擦参数的变化规律,并基于传统指数模型,提出一种扩展摩擦模型以补充描述负载力矩的影响。对于谐波驱动关节,为描述摩擦随输入角位置变化而周期性波动的现象,采用快速傅里叶变换对摩擦数据作频域分析,提取主导频率成分。提出采用指数模型+正余弦函数的组合形式来描述关节摩擦特性。
机器人系统中,高品质的关节角速度信号对于补偿非线性摩擦的影响、设计基于全状态反馈的控制器等具有重要的意义。因而在研究补偿控制算法之前,需要设计一种有效的速度估计方法。针对低速下量化误差及测量噪声对速度估计精度产生较大影响的问题,本文探讨了非线性跟踪微分器在实时速度估计中的应用(第四章)。非线性跟踪微分器具有实现便捷、参数整定简单、不依赖于对象模型的优点,非常适合于机器人系统。
在第二、三章建模及参数辨识的基础上,设计基于模型的补偿控制算法可以明显改善低速运动性能。对于RV驱动关节,为克服固定补偿难以处理摩擦不确定性的弱点,控制器设计时利用了自适应控制在线学习的能力。首先,通过引入模糊逻辑系统逼近关节摩擦,并实现模糊模型的线性化以便设计自适应学习机制。在此基础上,提出一种模糊自适应鲁棒控制算法。对于谐波驱动关节,其摩擦具有随角位置周期性波动的特征,非线性强,难以变换为合理的线性形式,自适应控制并不适用。考虑到当不确定性在一定范围内变化时,鲁棒控制能够保证系统稳定且维持一定的性能指标,因而提出一种具有摩擦补偿的鲁棒控制器。
当关节数目较多(>3)时,由于模型复杂度、计算量、参数辨识难度的急剧增加,第五章提出的基于模型的控制策略将难以应用。对模型依赖度度低、实时性强、实现便捷的控制器更受工程人员的青睐。因而第六章在开展多关节联动低速控制问题的研究时,以设计对模型依赖程度低或独立于模型的控制算法为目标。首先在交流伺服系统三闭环结构的基础上,设计了具有摩擦前馈的模糊PID控制算法,该算法采用Mamdani型模糊逻辑系统在线调整控制器参数,采用指数摩擦模型作为前馈补偿项。对于不具备摩擦测试条件的情况,本文提出了一种带跟踪微分器的滑模PID控制算法,算法有机结合了PID控制稳态精度高,滑模变结构控制快速性好、鲁棒性强的特点。最后,分别选取了激光切割机器人的两种典型作业轨迹,小圆和腰型孔,进行了平台六轴联动实验或仿真。
Multi-DOF serial robots are widely used in fields such as industrial automation, medical, aerospace, marine. In spite of the seeming mature of industrial robot technology after decades of development, high precision motion control in extreme conditions is still a problem, e.g., moving at extreme low or high speed. So it is difficult for robots to meet the requirements of applications which need low-speed high-precision or high-speed high-precision movement. This dissertation is dedicated to study on the low-speed high-precision motion control of multi-DOF serial robots. After the robot structure determined, we try to improve the low-speed performance mainly through following ways:model and compensate the joint friction, estimate the joint velocity accurately, improve the control algorithm design.
Firstly, we introduced the background of the research and conducted a comprehensive analysis of factors affecting the low-speed motion performance, including structure design, sensor resolution, nonlinear phenomenon, controller design, etc. Structural design and optimization, joint velocity estimation, joint friction modeling and compensation, as well as motion control strategy are currently the major research directions.
Designing model-based control algorithm is an effective way to improve low-speed control precision. However, it needs to know the robot dynamic model and parameters. After the dynamic modeling, we studied on a systematic off-line dynamic parameter identification method conducted under closed-loop control in chapter Ⅱ. Since traditional Fourier series do not satisfy velocity and acceleration boundary conditions, we designed modified Fourier series as exciting trajectory. Then, to minimize the sensitivity to measurement noise, the coefficients of modified Fourier series were optimized according to the condition number criterion using genetic algorithm. In addition, considering the measurement noise effects, maximum likelihood estimation method was adopted to obtain accurate parameter estimates.
Among the nonlinear phenomenon, joint friction is the main factor which causes control performance deterioration at low speed. Since RV reducer and harmonic reducer are widely used in robots, we studied on the friction of RV-drive-based joint and harmonic-drive-based joint in chapter Ⅲ. We mainly discussed the friction sources, measurement method, the friction characteristics, modeling and identification. For RV-drive-based joints with large inertia, we analyzed the friction parameter variation with different load torque. Then, based on the exponential model, we proposed an extended friction model which can describe the load torque effect. For harmonic-drive-based joints, the friction changes periodically with the joint angle. Based on the frequency domain analysis of the friction data using FFT, the main frequency components were determined. Then a friction model, which is the combination of the exponential model and sine/cosine functions, was involved to model the friction.
In robot systems, high-quality joint velocity estimation is of great significance for friction compensation, full state feedback controller design, etc. Before controller design, it needs to design an efficient method for velocity estimation. At low speed, quantization error and measurement noise may cause large velocity estimation error. To deal with this problem, we discussed the use of nonlinear tracking differentiator to estimate joint velocity in chapter IV. The nonlinear tracking differentiator has advantages such as easy to use, simple parameter tuning procedure, independent of model, which make it well adapted to robot system.
Based on the modeling and parameter identification in chapter Ⅱ and Ⅲ, we designed model-based controllers. For RV-drive-based joint, since the friction uncertainty, fixed compensation can not work well. To deal with this problem, we adopted adaptive control to learn the uncertainty. First, fuzzy logic system was involved to approximate the friction phenomenon, and linear model was derived for design of adaptive learning algorithm. Then, we proposed a fuzzy adaptive robust controller. For harmonic-drive-based joints, due to the cyclical changes of friction, it is difficult to obtain linear form, and adaptive control is not applicable. Since robust control can guarantee stable and performance with bounded uncertainty, we proposed a robust controller with friction compensation.
For robots with multiple joints (>3), it is difficult to design model-based controller due to the model complexity, large calculation and difficulty of parameter identification. Controllers which have strong real-time, simple implementation and low dependence of the model are favored by researchers. We tried to design controllers with little dependence or independent of the model in chapter VI. Firstly, we designed a fuzzy PID controller with friction feedforward. In the controller, Mamdani fuzzy logic system was adopted to tune the controller parameters. Exponential model was used in the friction compensation. For applications with the friction model unknown, we proposed a sliding PID controller with tracking differentiator. As we known, the PID control has good steady-state accuracy. Sliding mode variable structure control has the features of fast response and strong robustness. The designed controller combines the advantages of both. Experimental and simulation studies were conducted. Two typical operating trajectories in robot laser cutting, i.e., small circle and waist-shaped hole, were tested.
本文首先介绍相关研究背景,全面分析影响机器人低速运动性能的几方面因素,包括系统结构设计、测量元件分辨率、非线性环节的影响、控制系统的性能等,而结构设计与优化、低速下高品质速度信号获取方法、非线性摩擦建模与补偿,以及高级运动控制策略设计是目前几个主要研究方向。
设计基于动力学模型的运动控制器是提高低速运动控制精度及平稳性的有效途径。该方法的前提是已知机器人的动力学模型及参数值。因而,本文第二章在动力学建模的基础上,系统地研究了一种在闭环控制下进行的离线辨识方法来获取机器人的动力学参数。该方法针对传统傅里叶级数不满足速度、加速度边界条件的缺陷,提出一种改进傅里叶级数作为激励轨迹。为提升抗噪声能力,以最小化观测矩阵条件数作为优化准则,采用遗传算法来优化激励轨迹系数。进一步,采用最大似然法作为参数估计方法,以便考虑测量噪声的影响。
在诸多非线性环节中,关节摩擦是影响低速运动性能的核心因素,有必要作深入分析。在机器人系统中,广泛采用RV减速器与谐波减速器作为传动元件,本文的第三章对RV驱动与谐波驱动这两种典型关节的摩擦来源、摩擦测量方法、摩擦特征、建模及辨识方法进行了系统研究。对于RV驱动大惯量关节,分析了不同负载力矩下摩擦参数的变化规律,并基于传统指数模型,提出一种扩展摩擦模型以补充描述负载力矩的影响。对于谐波驱动关节,为描述摩擦随输入角位置变化而周期性波动的现象,采用快速傅里叶变换对摩擦数据作频域分析,提取主导频率成分。提出采用指数模型+正余弦函数的组合形式来描述关节摩擦特性。
机器人系统中,高品质的关节角速度信号对于补偿非线性摩擦的影响、设计基于全状态反馈的控制器等具有重要的意义。因而在研究补偿控制算法之前,需要设计一种有效的速度估计方法。针对低速下量化误差及测量噪声对速度估计精度产生较大影响的问题,本文探讨了非线性跟踪微分器在实时速度估计中的应用(第四章)。非线性跟踪微分器具有实现便捷、参数整定简单、不依赖于对象模型的优点,非常适合于机器人系统。
在第二、三章建模及参数辨识的基础上,设计基于模型的补偿控制算法可以明显改善低速运动性能。对于RV驱动关节,为克服固定补偿难以处理摩擦不确定性的弱点,控制器设计时利用了自适应控制在线学习的能力。首先,通过引入模糊逻辑系统逼近关节摩擦,并实现模糊模型的线性化以便设计自适应学习机制。在此基础上,提出一种模糊自适应鲁棒控制算法。对于谐波驱动关节,其摩擦具有随角位置周期性波动的特征,非线性强,难以变换为合理的线性形式,自适应控制并不适用。考虑到当不确定性在一定范围内变化时,鲁棒控制能够保证系统稳定且维持一定的性能指标,因而提出一种具有摩擦补偿的鲁棒控制器。
当关节数目较多(>3)时,由于模型复杂度、计算量、参数辨识难度的急剧增加,第五章提出的基于模型的控制策略将难以应用。对模型依赖度度低、实时性强、实现便捷的控制器更受工程人员的青睐。因而第六章在开展多关节联动低速控制问题的研究时,以设计对模型依赖程度低或独立于模型的控制算法为目标。首先在交流伺服系统三闭环结构的基础上,设计了具有摩擦前馈的模糊PID控制算法,该算法采用Mamdani型模糊逻辑系统在线调整控制器参数,采用指数摩擦模型作为前馈补偿项。对于不具备摩擦测试条件的情况,本文提出了一种带跟踪微分器的滑模PID控制算法,算法有机结合了PID控制稳态精度高,滑模变结构控制快速性好、鲁棒性强的特点。最后,分别选取了激光切割机器人的两种典型作业轨迹,小圆和腰型孔,进行了平台六轴联动实验或仿真。
Multi-DOF serial robots are widely used in fields such as industrial automation, medical, aerospace, marine. In spite of the seeming mature of industrial robot technology after decades of development, high precision motion control in extreme conditions is still a problem, e.g., moving at extreme low or high speed. So it is difficult for robots to meet the requirements of applications which need low-speed high-precision or high-speed high-precision movement. This dissertation is dedicated to study on the low-speed high-precision motion control of multi-DOF serial robots. After the robot structure determined, we try to improve the low-speed performance mainly through following ways:model and compensate the joint friction, estimate the joint velocity accurately, improve the control algorithm design.
Firstly, we introduced the background of the research and conducted a comprehensive analysis of factors affecting the low-speed motion performance, including structure design, sensor resolution, nonlinear phenomenon, controller design, etc. Structural design and optimization, joint velocity estimation, joint friction modeling and compensation, as well as motion control strategy are currently the major research directions.
Designing model-based control algorithm is an effective way to improve low-speed control precision. However, it needs to know the robot dynamic model and parameters. After the dynamic modeling, we studied on a systematic off-line dynamic parameter identification method conducted under closed-loop control in chapter Ⅱ. Since traditional Fourier series do not satisfy velocity and acceleration boundary conditions, we designed modified Fourier series as exciting trajectory. Then, to minimize the sensitivity to measurement noise, the coefficients of modified Fourier series were optimized according to the condition number criterion using genetic algorithm. In addition, considering the measurement noise effects, maximum likelihood estimation method was adopted to obtain accurate parameter estimates.
Among the nonlinear phenomenon, joint friction is the main factor which causes control performance deterioration at low speed. Since RV reducer and harmonic reducer are widely used in robots, we studied on the friction of RV-drive-based joint and harmonic-drive-based joint in chapter Ⅲ. We mainly discussed the friction sources, measurement method, the friction characteristics, modeling and identification. For RV-drive-based joints with large inertia, we analyzed the friction parameter variation with different load torque. Then, based on the exponential model, we proposed an extended friction model which can describe the load torque effect. For harmonic-drive-based joints, the friction changes periodically with the joint angle. Based on the frequency domain analysis of the friction data using FFT, the main frequency components were determined. Then a friction model, which is the combination of the exponential model and sine/cosine functions, was involved to model the friction.
In robot systems, high-quality joint velocity estimation is of great significance for friction compensation, full state feedback controller design, etc. Before controller design, it needs to design an efficient method for velocity estimation. At low speed, quantization error and measurement noise may cause large velocity estimation error. To deal with this problem, we discussed the use of nonlinear tracking differentiator to estimate joint velocity in chapter IV. The nonlinear tracking differentiator has advantages such as easy to use, simple parameter tuning procedure, independent of model, which make it well adapted to robot system.
Based on the modeling and parameter identification in chapter Ⅱ and Ⅲ, we designed model-based controllers. For RV-drive-based joint, since the friction uncertainty, fixed compensation can not work well. To deal with this problem, we adopted adaptive control to learn the uncertainty. First, fuzzy logic system was involved to approximate the friction phenomenon, and linear model was derived for design of adaptive learning algorithm. Then, we proposed a fuzzy adaptive robust controller. For harmonic-drive-based joints, due to the cyclical changes of friction, it is difficult to obtain linear form, and adaptive control is not applicable. Since robust control can guarantee stable and performance with bounded uncertainty, we proposed a robust controller with friction compensation.
For robots with multiple joints (>3), it is difficult to design model-based controller due to the model complexity, large calculation and difficulty of parameter identification. Controllers which have strong real-time, simple implementation and low dependence of the model are favored by researchers. We tried to design controllers with little dependence or independent of the model in chapter VI. Firstly, we designed a fuzzy PID controller with friction feedforward. In the controller, Mamdani fuzzy logic system was adopted to tune the controller parameters. Exponential model was used in the friction compensation. For applications with the friction model unknown, we proposed a sliding PID controller with tracking differentiator. As we known, the PID control has good steady-state accuracy. Sliding mode variable structure control has the features of fast response and strong robustness. The designed controller combines the advantages of both. Experimental and simulation studies were conducted. Two typical operating trajectories in robot laser cutting, i.e., small circle and waist-shaped hole, were tested.
引文
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