平面二自由度并联机器人的控制策略及其性能研究
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摘要
由于拥有多条运动链,并联机器人的机械结构要比传统的串联机器人复杂得多,这使得并联机器人的运动学和动力学关系都非常复杂,而多条运动链对末端执行器运动的协调操作,更是给并联机器人的运动控制提出了挑战。本论文以一个平面二自由度并联机器人为研究对象,从力矩传递性能、摩擦力补偿和控制器设计三个方面,对并联机器人运动控制进行了理论研究和实验研究,主要内容可归纳如下:
(1)基于运动学反解,以速度雅克比矩阵条件数为指标,全面地研究了平面二自由度并联机器人的力矩传递性能与运动位形之间的关系,得到了最优的运动位形。
(2)针对平面二自由度并联机器人中的非线性摩擦力,将一个包含指数函数的非线性模型用于该并联机器人的摩擦力建模,提出了一种非线性摩擦力补偿方法,通过实际的轨迹跟踪实验将所提出的摩擦力补偿方法与现有的摩擦力补偿方法进行了对比研究。
(3)将非线性PD(nonlinear PD,NPD)控制分别与机器人中典型的增广PD控制器与计算力矩控制器相结合,提出了两种NPD型动力学控制器—增广NPD控制器和计算力矩NPD控制器,将这两种新的控制器用于平面二自由度并联机器人的控制,理论上证明了闭环系统的渐近稳定性。在并联机器人的实际轨迹跟踪实验中,将所提出的两种控制器与典型的两种控制器进行了对比研究。
(4)设计了一种工作空间的非线性自适应控制器,用于平面二自由度并联机器人的轨迹跟踪控制。采用梯度下降算法推导了参数自适应律,基于增广PD控制器结构设计了自适应控制律,运用Lyapunov方法证明了所提出的非线性自适应控制器的稳定性,并且利用Barbalat引理进一步证明了末端执行器的位置误差和速度误差将同时收敛到零。最后将所设计的控制器用于实际平面二自由度并联机器人的轨迹跟踪控制,对实验结果进行了深入分析。
(5)针对并联机器人多运动链之间的协调运动这一难题,基于同步控制思想,提出了两种同步控制器用于平面二自由度并联机器人的控制。首先提出了主动关节同步(Active Joint-Synchronization,AJ-S)控制器,在主动关节空间中推导了并联机器人的动力学模型,运用同步控制思想,基于此模型设计出了AJ-S控制律,并且理论证明了并联机器人系统的渐近稳定性,最后把所提出的AJ-S控制器用于实际平面二自由度并联机器人的轨迹跟踪控制。在设计AJ-S控制器时,需要考虑各支链间约束力的影响,而计算约束力时用到的加速度信号难以准确获得。因此,进一步提出了轮廓误差同步(Contour Error-Synchronization,CE-S)控制器,首先引入轮廓误差来定义并联机器人的同步行为;然后,基于工作空间的动力学模型设计CE-S控制器,该控制器中不包含约束力补偿项;最后,对并联机器人系统的渐近稳定性进行了理论证明,并且将其轨迹跟踪的实验结果与AJ-S控制器的结果进行了对比。
For the multiple kinematic chains, the mechanism structure of parallel manipulator is much more complex than serial manipulator. The kinematics and dynamics of parallel manipulator are very complex. The coordinated manipulation of the end-effector with multiple kinematic chains makes the motion control of parallel manipulator challenging. In this dissertation, based on a planar 2-DOF parallel manipulator, theory and experiment of the motion control for the parallel manipulator were studied from three aspects, including torque transmission, friction compensation and controller design. The main work is as follows:
(1) Based on the inverse kinematic, relations between the torque transmission and the kinematic configuration of the planar 2-DOF parallel manipulator were studied with the condition number of velocity Jacobian matrix, and the optimal kinematic configuration was solved.
(2) Considering the nonlinear friction in the planar 2-DOF parallel manipulator, a nonlinear model with exponential functions was used to construct the friction of the parallel manipulator, and a nonlinear friction compensation method was proposed. The friction compensation performances were compared between the proposed friction compensation method and the existing friction compensation methods.
(3) By combining the nonlinear PD (NPD) control with the typical augmented PD and computed torque controller of the robot manipulator respectively, two new dynamic controllers of augmented NPD and computed torque NPD were proposed. The two new controllers were used to control the planar 2-DOF parallel manipulator, and the asymptotic stability was proved in theory. In the actual trajectory tracking experiment of the parallel manipulator, the proposed controllers were compared with the two typical controllers.
(4) A nonlinear adaptive controller in the task space was designed for trajectory tracking of the planar 2-DOF parallel manipulator. The parameter adaptation law was derived with the gradient descent algorithm, and the control law was designed based on the augmented PD controller. The stability of the parallel manipulator system was proved by the Lyapunov stability theorem, and the convergence of the tracking error and the error rate were proved by the Barbalat lemma. The designed controller was implemented in trajectory tracking experiments of an actual planar 2-DOF parallel manipulator, and the experiment results were analyzed in detail.
(5) Considering the coordinated motion of the multiple kinematic chains in parallel manipulator, two synchronization controllers were proposed for the planar 2-DOF parallel manipulator with the synchronization control idea. Firstly, the active joint-synchronization (AJ-S) controller was proposed. The dynamic model of the parallel manipulator was formulated in the active joint space, and the AJ-S control law was designed based on this dynamic model, then the asymptotic stability of the parallel manipulator was proved in theory. The AJ-S controller was implemented in the trajectory tracking experiments of an actual planar 2-DOF parallel manipulator. When designing the AJ-S controller, the constraint force between the kinematic chains must be considered, and the acceleration using for the calculation of the constraint force was difficult to be measured. Thus, the contour error-synchronization (CE-S) controller was proposed, the compensation item of the constraint force was not contained in this controller. At first, contour error was introduced to define the synchronization behavior of the parallel manipulator; then the CE-S controller was designed based on the dynamic model in the task space; finally, the asymptotic stability was proved in theory, and the experiment results of trajectory tracking were compared between the AJ-S controller and the CE-S controller.
(1)基于运动学反解,以速度雅克比矩阵条件数为指标,全面地研究了平面二自由度并联机器人的力矩传递性能与运动位形之间的关系,得到了最优的运动位形。
(2)针对平面二自由度并联机器人中的非线性摩擦力,将一个包含指数函数的非线性模型用于该并联机器人的摩擦力建模,提出了一种非线性摩擦力补偿方法,通过实际的轨迹跟踪实验将所提出的摩擦力补偿方法与现有的摩擦力补偿方法进行了对比研究。
(3)将非线性PD(nonlinear PD,NPD)控制分别与机器人中典型的增广PD控制器与计算力矩控制器相结合,提出了两种NPD型动力学控制器—增广NPD控制器和计算力矩NPD控制器,将这两种新的控制器用于平面二自由度并联机器人的控制,理论上证明了闭环系统的渐近稳定性。在并联机器人的实际轨迹跟踪实验中,将所提出的两种控制器与典型的两种控制器进行了对比研究。
(4)设计了一种工作空间的非线性自适应控制器,用于平面二自由度并联机器人的轨迹跟踪控制。采用梯度下降算法推导了参数自适应律,基于增广PD控制器结构设计了自适应控制律,运用Lyapunov方法证明了所提出的非线性自适应控制器的稳定性,并且利用Barbalat引理进一步证明了末端执行器的位置误差和速度误差将同时收敛到零。最后将所设计的控制器用于实际平面二自由度并联机器人的轨迹跟踪控制,对实验结果进行了深入分析。
(5)针对并联机器人多运动链之间的协调运动这一难题,基于同步控制思想,提出了两种同步控制器用于平面二自由度并联机器人的控制。首先提出了主动关节同步(Active Joint-Synchronization,AJ-S)控制器,在主动关节空间中推导了并联机器人的动力学模型,运用同步控制思想,基于此模型设计出了AJ-S控制律,并且理论证明了并联机器人系统的渐近稳定性,最后把所提出的AJ-S控制器用于实际平面二自由度并联机器人的轨迹跟踪控制。在设计AJ-S控制器时,需要考虑各支链间约束力的影响,而计算约束力时用到的加速度信号难以准确获得。因此,进一步提出了轮廓误差同步(Contour Error-Synchronization,CE-S)控制器,首先引入轮廓误差来定义并联机器人的同步行为;然后,基于工作空间的动力学模型设计CE-S控制器,该控制器中不包含约束力补偿项;最后,对并联机器人系统的渐近稳定性进行了理论证明,并且将其轨迹跟踪的实验结果与AJ-S控制器的结果进行了对比。
For the multiple kinematic chains, the mechanism structure of parallel manipulator is much more complex than serial manipulator. The kinematics and dynamics of parallel manipulator are very complex. The coordinated manipulation of the end-effector with multiple kinematic chains makes the motion control of parallel manipulator challenging. In this dissertation, based on a planar 2-DOF parallel manipulator, theory and experiment of the motion control for the parallel manipulator were studied from three aspects, including torque transmission, friction compensation and controller design. The main work is as follows:
(1) Based on the inverse kinematic, relations between the torque transmission and the kinematic configuration of the planar 2-DOF parallel manipulator were studied with the condition number of velocity Jacobian matrix, and the optimal kinematic configuration was solved.
(2) Considering the nonlinear friction in the planar 2-DOF parallel manipulator, a nonlinear model with exponential functions was used to construct the friction of the parallel manipulator, and a nonlinear friction compensation method was proposed. The friction compensation performances were compared between the proposed friction compensation method and the existing friction compensation methods.
(3) By combining the nonlinear PD (NPD) control with the typical augmented PD and computed torque controller of the robot manipulator respectively, two new dynamic controllers of augmented NPD and computed torque NPD were proposed. The two new controllers were used to control the planar 2-DOF parallel manipulator, and the asymptotic stability was proved in theory. In the actual trajectory tracking experiment of the parallel manipulator, the proposed controllers were compared with the two typical controllers.
(4) A nonlinear adaptive controller in the task space was designed for trajectory tracking of the planar 2-DOF parallel manipulator. The parameter adaptation law was derived with the gradient descent algorithm, and the control law was designed based on the augmented PD controller. The stability of the parallel manipulator system was proved by the Lyapunov stability theorem, and the convergence of the tracking error and the error rate were proved by the Barbalat lemma. The designed controller was implemented in trajectory tracking experiments of an actual planar 2-DOF parallel manipulator, and the experiment results were analyzed in detail.
(5) Considering the coordinated motion of the multiple kinematic chains in parallel manipulator, two synchronization controllers were proposed for the planar 2-DOF parallel manipulator with the synchronization control idea. Firstly, the active joint-synchronization (AJ-S) controller was proposed. The dynamic model of the parallel manipulator was formulated in the active joint space, and the AJ-S control law was designed based on this dynamic model, then the asymptotic stability of the parallel manipulator was proved in theory. The AJ-S controller was implemented in the trajectory tracking experiments of an actual planar 2-DOF parallel manipulator. When designing the AJ-S controller, the constraint force between the kinematic chains must be considered, and the acceleration using for the calculation of the constraint force was difficult to be measured. Thus, the contour error-synchronization (CE-S) controller was proposed, the compensation item of the constraint force was not contained in this controller. At first, contour error was introduced to define the synchronization behavior of the parallel manipulator; then the CE-S controller was designed based on the dynamic model in the task space; finally, the asymptotic stability was proved in theory, and the experiment results of trajectory tracking were compared between the AJ-S controller and the CE-S controller.
引文
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