新型球面3-RRR并联机器人的构建及其性能研究
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摘要
球面3-RRR机器人具有十分广阔的应用前景,是目前机器人研究领域重要的研究方向之一。本文以球面3-RRR机器人为研究对象,从新型结构的构建、工作空间优化、运动路径规划、运动分析、控制方法等若干方面,进行了深入的研究。
针对并联机器人一类复杂机械结构,提出了一套系统性的考虑干涉影响的最大化工作空间设计方法(LIDeM)。将该方法分别应用于球面和平面3-RRR机器人,实现了各自的工作空间的最大化,并设计出一种新型3-RRR并联球面机器人机构(Triaster);对该机器人建立了数学模型,得到了终端与各杆件的运动位置关系。分析了在不同杆件系数取值下的工作空间大小,以及对应的干涉区域大小；针对Triaster,建立了运动学方程,分析了系统的奇异位形,并推导出并求解了正反运动学问题的解析公式。最后,针对一个具体的算例,通过电机和终端的转角速度和加速度之变化曲线,说明了运动学正反问题的求解过程；通过对运动学逆问题的研究,发现了保证终端输出轨迹不变的前提下电机加速度调整的规律,解决了在某一时间区间内电机加速度过高情况下的应对策略；找到了运动学正问题中三输入电机转速匹配的规律,并针对具体算例,计算并绘制了终端的运动速度、加速度与轨迹曲线；归纳推导了拉格朗日动力学方程,求得了Triaster各个运动构件相对于不同旋转轴的转动惯量、质心及质量,并以此为参数推导了每一时刻各部件的动能和势能的解析表达式,在给定终端轨迹的情况下,成功求解了输入电机的转矩变化曲线；给出了橡皮筋算法的伪代码,说明了其计算最短路径的过程,得到了终端运动空间和三电机转角空间的点云图。针对4组算例,在给定路径起点和终点坐标的前提下,计算并绘制了最短路径；获得了Triaster系统的状态空间方程,阐明了系统误差和电机输入转矩间的关系,分析了摩擦力这一系统不确定性变量的特点,讨论了其作为不确定有界函数在系统方程中的作用,及其扰动所带来的影响。随后分析了系统误差的李雅普诺夫稳定性,针对本系统的摩擦特性,设计出了一种鲁棒控制器,得出系统控制框图。最后,用一算例说明了该鲁棒控制器对机器人轨迹误差的控制；设计并建立了Triaster试验平台,针对两组输入电机的转角位移曲线,试验测试了系统的输出终端的运动轨迹,并通过与理论计算的终端轨迹的对比,说明本文所构建的球面3-RRR并联机器人能够很好地实现预定运动的输出。
本文的研究成果可为3-RRR球面机器人的进一步研究和应用提供理论借鉴。
In human daily life, there are many applications where a whirling motion is needed. To meet such needs, the dissertation was concentrated on some robot can achieve that function, which is called3-RRR Spherical Parallel Manipulator (SPM). The main content of the dissertation can be summarized into6parts, including structure design, kinematics, dynamics, path planning, robust control and prototype experiments.
At first, the Least Interference Design Methodology (LIDeM) was established to optimize the workspace of the robot with least mechanical interference. Based on this theory, a novel structure of3-RRR SPM, namely Triaster, was designed and built up. With its kinematics formulas, the singularity loci and interference distribution were attatined via3D spherical plots. Its inverse kinematic equation was derived, based on which Time-Interval-Proportional Extension (TIPE) strategy was raised up to insure the trajectory of Triaster's end effector unchanged when the accelerations of input motors are adjusted to meet the system requirements. The forward kinematic problem of the robot was also solved in the dissertation. Under all the reachable configurations of Triaster, the author found the angular displacements of three input motors should be matched in a range. The phenomenum was explained by some plots of angular displacements, velocities and accelerations of input motors, and some trajectory plots of its end effector. The rubberband algorithm was applied to solve the path planning of Triaster, and was proved to be feasible by4sets of testing datum. The shortest path projections were gained, which are from Riemann spherical space into Euclidian orthogonal space. For avoiding the drawbacks of Newtown method, which are too many intermediate variables and equations produced during the process, and which leads to manually unsolvable, and thus the Hamilton-Lagrangian dynamics method was adopted. The inertia, centroid and mass of each moving component of Triaster were calculated. With these parameters, the kinetic and potential energy of the robot at any moment was attained through the formulas. The relations between input torques and end effector motions were given by their plots. Each input motor power plot which is as a function of time was also given in the dissertation. There are many uncertainties in the robotic system, like friction in each joint. Focused on this uncertainty, the robust control method for the trajectory stability of Triaster was studied. The status space formula of the system was constructed and based on which the Lyapunov stability was analyzed. Accordingly, a specific robust controller was designed. With uncertain friction and robust controller impacted, the trajectory plot of Triaster's end effector was presented. In the end, for proving all these theorical things, an experiment prototyple of Triaster was built up. It connected Triaster robot body, circuit board for motor controlling, language programming software on PC and image caputure module all together. The control programs were written and burned into the circuit board to drive the motors to some expected positions. The images results of the trajectories were captured by the module. The entire image datum were analyzed and compared with the theoretical results, based on which some suggestions was given for future research.
The achievements obtained in this desertation will be helpful for the application and further research for3-RRR Spherical Parallel Manipulator.
针对并联机器人一类复杂机械结构,提出了一套系统性的考虑干涉影响的最大化工作空间设计方法(LIDeM)。将该方法分别应用于球面和平面3-RRR机器人,实现了各自的工作空间的最大化,并设计出一种新型3-RRR并联球面机器人机构(Triaster);对该机器人建立了数学模型,得到了终端与各杆件的运动位置关系。分析了在不同杆件系数取值下的工作空间大小,以及对应的干涉区域大小；针对Triaster,建立了运动学方程,分析了系统的奇异位形,并推导出并求解了正反运动学问题的解析公式。最后,针对一个具体的算例,通过电机和终端的转角速度和加速度之变化曲线,说明了运动学正反问题的求解过程；通过对运动学逆问题的研究,发现了保证终端输出轨迹不变的前提下电机加速度调整的规律,解决了在某一时间区间内电机加速度过高情况下的应对策略；找到了运动学正问题中三输入电机转速匹配的规律,并针对具体算例,计算并绘制了终端的运动速度、加速度与轨迹曲线；归纳推导了拉格朗日动力学方程,求得了Triaster各个运动构件相对于不同旋转轴的转动惯量、质心及质量,并以此为参数推导了每一时刻各部件的动能和势能的解析表达式,在给定终端轨迹的情况下,成功求解了输入电机的转矩变化曲线；给出了橡皮筋算法的伪代码,说明了其计算最短路径的过程,得到了终端运动空间和三电机转角空间的点云图。针对4组算例,在给定路径起点和终点坐标的前提下,计算并绘制了最短路径；获得了Triaster系统的状态空间方程,阐明了系统误差和电机输入转矩间的关系,分析了摩擦力这一系统不确定性变量的特点,讨论了其作为不确定有界函数在系统方程中的作用,及其扰动所带来的影响。随后分析了系统误差的李雅普诺夫稳定性,针对本系统的摩擦特性,设计出了一种鲁棒控制器,得出系统控制框图。最后,用一算例说明了该鲁棒控制器对机器人轨迹误差的控制；设计并建立了Triaster试验平台,针对两组输入电机的转角位移曲线,试验测试了系统的输出终端的运动轨迹,并通过与理论计算的终端轨迹的对比,说明本文所构建的球面3-RRR并联机器人能够很好地实现预定运动的输出。
本文的研究成果可为3-RRR球面机器人的进一步研究和应用提供理论借鉴。
In human daily life, there are many applications where a whirling motion is needed. To meet such needs, the dissertation was concentrated on some robot can achieve that function, which is called3-RRR Spherical Parallel Manipulator (SPM). The main content of the dissertation can be summarized into6parts, including structure design, kinematics, dynamics, path planning, robust control and prototype experiments.
At first, the Least Interference Design Methodology (LIDeM) was established to optimize the workspace of the robot with least mechanical interference. Based on this theory, a novel structure of3-RRR SPM, namely Triaster, was designed and built up. With its kinematics formulas, the singularity loci and interference distribution were attatined via3D spherical plots. Its inverse kinematic equation was derived, based on which Time-Interval-Proportional Extension (TIPE) strategy was raised up to insure the trajectory of Triaster's end effector unchanged when the accelerations of input motors are adjusted to meet the system requirements. The forward kinematic problem of the robot was also solved in the dissertation. Under all the reachable configurations of Triaster, the author found the angular displacements of three input motors should be matched in a range. The phenomenum was explained by some plots of angular displacements, velocities and accelerations of input motors, and some trajectory plots of its end effector. The rubberband algorithm was applied to solve the path planning of Triaster, and was proved to be feasible by4sets of testing datum. The shortest path projections were gained, which are from Riemann spherical space into Euclidian orthogonal space. For avoiding the drawbacks of Newtown method, which are too many intermediate variables and equations produced during the process, and which leads to manually unsolvable, and thus the Hamilton-Lagrangian dynamics method was adopted. The inertia, centroid and mass of each moving component of Triaster were calculated. With these parameters, the kinetic and potential energy of the robot at any moment was attained through the formulas. The relations between input torques and end effector motions were given by their plots. Each input motor power plot which is as a function of time was also given in the dissertation. There are many uncertainties in the robotic system, like friction in each joint. Focused on this uncertainty, the robust control method for the trajectory stability of Triaster was studied. The status space formula of the system was constructed and based on which the Lyapunov stability was analyzed. Accordingly, a specific robust controller was designed. With uncertain friction and robust controller impacted, the trajectory plot of Triaster's end effector was presented. In the end, for proving all these theorical things, an experiment prototyple of Triaster was built up. It connected Triaster robot body, circuit board for motor controlling, language programming software on PC and image caputure module all together. The control programs were written and burned into the circuit board to drive the motors to some expected positions. The images results of the trajectories were captured by the module. The entire image datum were analyzed and compared with the theoretical results, based on which some suggestions was given for future research.
The achievements obtained in this desertation will be helpful for the application and further research for3-RRR Spherical Parallel Manipulator.
引文
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