平面并联机器人设计、分析与控制
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摘要
本文研究平面并联机器人尺度优化设计，并以3-RRR为例进行优化设计。同时研究了动力学建模方法，在此基础上，分析了机构在奇异位形的动态特性，提出了振动抑制策略，通过仿真和实验进行分析和验证。
并联机器人的尺度参数可以决定其性能。针对其尺度参数设计，本文提出一种方法步骤进行优化设计，以满足有效工作空间的无奇异高速运动的要求。首先分析推导了3-RRR/4-RRR机构的逆运动学和正运动学，在此基础上，得到机构的雅可比矩阵。然后在机构的参数设计空间，绘制机构的奇异曲线分布图。最后结合奇异曲线分布图，以全局条件数为目标函数，力传递能力为约束条件，对机构进行优化设计。依据上述步骤，优化设计制造了一台3-RRR机构，同时，也设计制作了一台4-RRR机构。
基于螺旋理论，提出一种平面并联机构（冗余/非冗余）动力学的通用建模方法。利用螺旋理论分析平面并联机构的运动螺旋和力螺旋，在此基础上，基于虚功原理推导了平面并联机构的通用刚体动力学公式。根据公式，分析并建立3-RRR/4-RRR机构的刚体动力学模型。在Adams中对3-RRR机构进行分析，并与matlab分析的结果进行比较，结果相符。对4-RRR机构的驱动力进行力优化和能耗优化，同时和3-RRR机构的驱动力进行比较，结果表明4-RRR机构的驱动力峰值有所下降。
奇异位形是并联机构的一个固有现象。在前人的研究基础上，利用螺旋理论，分析指出一种新的奇异位形，并称之为约束奇异。它是由于机构局部刚度不足而引起的，同时指出它本质上是力奇异。通过分析推导，得到机构在奇异位形无振动的条件。
在高速运动中，机构易发生弹性变形，从而易激发机构的振动。本文假定机构弹性变形为线弹性变形，基于等效刚体法，建立机构的坐标系。在惯性坐标系中，先建立了机构单元的动能和势能公式，然后推导了机构支链的动能和势能公式，最后建立了系统的动能和势能公式。考虑机构的主动铰变形的情况，建立了惯性坐标系下的3-RRR机构的弹性动力学公式。因此，此公式可以用于分析机构的残余振动，也可用于分析机构的自激振动。利用弹性动力学公式分析并阐释了机构在奇异位形的残余振动的机理。在研究中，发现了机构在奇异位形发生的非线性振动现象-自激振动。从理论上分析阐释了自激振动的发生机理，并建立了自激振动的公式。
针对机构在奇异位形的振动，研究振动的抑制策略。分别设计单模态输入整形器和多模态输入整形器抑制残余振动的产生。对于高速运动的机构，动力学的控制显得尤为必要。本文设计了基于滑模原理的鲁棒控制器，建立3-RRR机构的控制方程，分析了其稳定性，仿真结果表明效果较好。
最后以dSPACE1103为控制器、交流伺服电机为驱动搭建了3-RRR并联机器人。以XL-80激光测量系统和ControlDesk设计实验方案进行实验研究。首先用XL-80对机构在奇异位形的残余振动和自激振动进行实验，结果验证了前述的分析。然后，用ControlDesk对自激振动时的电机转角进行测量，结果表明和前述分析的规律一致。最后，对残余振动的抑制进行实验，结果表明输入整形控制有效地抑制了残余振动，且多模态输入整形器的抑振效果最好。
This thesis proposed a method of the parameters optimal design of the planar parallelrobot, which is applied to3-RRR mechanism. Simultaneously a dynamic modeling, which isused to analyzing the dynamic characteristics of3-RRR mechanism at the singularities, ispresented. A strategy to suspress vibration of the mechanism is put forward and examedexperimently.
The performation of parallel robot is decided by it kinematic parameters. A methody foroptimal design is proposed to meet the needs of no singularities and high-speed motion in theused work space. Firstly, the inverse and forward kinematic of3-RRR/4-RRR mechanism isderived and Jacobia matrics of the mechanism is attained. Then, the distributioncharacteristics of singular locis in the design space is plotted. Finally, a procedure of optimumdesign of mechanism is addressed, whose objiect function is global condition index subjectedto force transmission capacity. On the method, a3-RRR mechanism is designed andmanufactured. Followly4-RRR parallel mechanism is made.
An approach to rigid body dynamic analysis of planar parallel mechanism (redulant andnon-redulant) is presented by means of screw theory. Based on the theory of screws and onthe principle of virtual work, a formulation for parallel mechanism is derived. Formulas for3-RRR/4-RRR mechanisms are obtained. The resulting from matlab matchs the analysis resultfrom Adams. Driving forces of4-RRR mechanism is optimized and is compared with thedriving forces of3-RRR mechanism. The result of comparison shows than peak value of4-RRR’s driving forces are smaller.
Singularities are the nature phenomenon of parallel manipulator. A new singularitynamed constrained singularity, which is caused by deficient rigidity and is force singularity innature, is proposed using screw theory. The condition for no oscillation is derived atsingularity configuration.
Elastic deformation of the mechanism, which easily leads to oscillation, is arised in thehigh-speed movemotion. Given the linear elastic deformation, a frame is set up using anequivalent rigid link system model. The kinetic and strain energy equation for element e of themechanism are derived firstly and then kinetic and strain energy equation for chains of themechanism are obtained. An elastic equation of motion for3-RRR manipulator, which couldis used to analyze the residu vibration and self-excited oscillation, is constructed in inertialframe by taking into consideration the variation of the driver joint.
The reason for residu vibration is explained at singularity configuration. A nonlinear self-excited vibration is found at the neighborhood of the singularity configuration of themanipulator. The reason for causing the self-excited vibration is explained and a formulationabout self-excited vibration is builded.
A scheme for suspressing the oscillation is presented. One modal input shaper andmulti-modal input shaper are constructed respectively to reducing the vibration. Forhigh-speed motion, the dynamical control is needed. Therefore, a slide modal controller,whose control eqution is set up and stability is checked, is designed for motion control. Thesimulation shows that the result is good.
A3-RRR parallel robot is made with dSPACE1103as controller and AC servo motors onthe basis of3-RRR mechanism. A set of experiments are designed based on XL-80lasersystem and ControlDesk software. A set of experiments about risidu vibration and self-excitedvibration at the singularities are made. The results check the prior analysis about residualvibration and self-excited vibration. And then the rotation angles of servo motors aremeasured with ControlDesk. The resulting angles are in accordance with the priviousexplaination. The experiments of suspressing the residual vibration are done, which show thatinput shaping controller redues the residual oscillation effectively and multi-modal inputshaper suspresses the oscillation in effect.
并联机器人的尺度参数可以决定其性能。针对其尺度参数设计，本文提出一种方法步骤进行优化设计，以满足有效工作空间的无奇异高速运动的要求。首先分析推导了3-RRR/4-RRR机构的逆运动学和正运动学，在此基础上，得到机构的雅可比矩阵。然后在机构的参数设计空间，绘制机构的奇异曲线分布图。最后结合奇异曲线分布图，以全局条件数为目标函数，力传递能力为约束条件，对机构进行优化设计。依据上述步骤，优化设计制造了一台3-RRR机构，同时，也设计制作了一台4-RRR机构。
基于螺旋理论，提出一种平面并联机构（冗余/非冗余）动力学的通用建模方法。利用螺旋理论分析平面并联机构的运动螺旋和力螺旋，在此基础上，基于虚功原理推导了平面并联机构的通用刚体动力学公式。根据公式，分析并建立3-RRR/4-RRR机构的刚体动力学模型。在Adams中对3-RRR机构进行分析，并与matlab分析的结果进行比较，结果相符。对4-RRR机构的驱动力进行力优化和能耗优化，同时和3-RRR机构的驱动力进行比较，结果表明4-RRR机构的驱动力峰值有所下降。
奇异位形是并联机构的一个固有现象。在前人的研究基础上，利用螺旋理论，分析指出一种新的奇异位形，并称之为约束奇异。它是由于机构局部刚度不足而引起的，同时指出它本质上是力奇异。通过分析推导，得到机构在奇异位形无振动的条件。
在高速运动中，机构易发生弹性变形，从而易激发机构的振动。本文假定机构弹性变形为线弹性变形，基于等效刚体法，建立机构的坐标系。在惯性坐标系中，先建立了机构单元的动能和势能公式，然后推导了机构支链的动能和势能公式，最后建立了系统的动能和势能公式。考虑机构的主动铰变形的情况，建立了惯性坐标系下的3-RRR机构的弹性动力学公式。因此，此公式可以用于分析机构的残余振动，也可用于分析机构的自激振动。利用弹性动力学公式分析并阐释了机构在奇异位形的残余振动的机理。在研究中，发现了机构在奇异位形发生的非线性振动现象-自激振动。从理论上分析阐释了自激振动的发生机理，并建立了自激振动的公式。
针对机构在奇异位形的振动，研究振动的抑制策略。分别设计单模态输入整形器和多模态输入整形器抑制残余振动的产生。对于高速运动的机构，动力学的控制显得尤为必要。本文设计了基于滑模原理的鲁棒控制器，建立3-RRR机构的控制方程，分析了其稳定性，仿真结果表明效果较好。
最后以dSPACE1103为控制器、交流伺服电机为驱动搭建了3-RRR并联机器人。以XL-80激光测量系统和ControlDesk设计实验方案进行实验研究。首先用XL-80对机构在奇异位形的残余振动和自激振动进行实验，结果验证了前述的分析。然后，用ControlDesk对自激振动时的电机转角进行测量，结果表明和前述分析的规律一致。最后，对残余振动的抑制进行实验，结果表明输入整形控制有效地抑制了残余振动，且多模态输入整形器的抑振效果最好。
This thesis proposed a method of the parameters optimal design of the planar parallelrobot, which is applied to3-RRR mechanism. Simultaneously a dynamic modeling, which isused to analyzing the dynamic characteristics of3-RRR mechanism at the singularities, ispresented. A strategy to suspress vibration of the mechanism is put forward and examedexperimently.
The performation of parallel robot is decided by it kinematic parameters. A methody foroptimal design is proposed to meet the needs of no singularities and high-speed motion in theused work space. Firstly, the inverse and forward kinematic of3-RRR/4-RRR mechanism isderived and Jacobia matrics of the mechanism is attained. Then, the distributioncharacteristics of singular locis in the design space is plotted. Finally, a procedure of optimumdesign of mechanism is addressed, whose objiect function is global condition index subjectedto force transmission capacity. On the method, a3-RRR mechanism is designed andmanufactured. Followly4-RRR parallel mechanism is made.
An approach to rigid body dynamic analysis of planar parallel mechanism (redulant andnon-redulant) is presented by means of screw theory. Based on the theory of screws and onthe principle of virtual work, a formulation for parallel mechanism is derived. Formulas for3-RRR/4-RRR mechanisms are obtained. The resulting from matlab matchs the analysis resultfrom Adams. Driving forces of4-RRR mechanism is optimized and is compared with thedriving forces of3-RRR mechanism. The result of comparison shows than peak value of4-RRR’s driving forces are smaller.
Singularities are the nature phenomenon of parallel manipulator. A new singularitynamed constrained singularity, which is caused by deficient rigidity and is force singularity innature, is proposed using screw theory. The condition for no oscillation is derived atsingularity configuration.
Elastic deformation of the mechanism, which easily leads to oscillation, is arised in thehigh-speed movemotion. Given the linear elastic deformation, a frame is set up using anequivalent rigid link system model. The kinetic and strain energy equation for element e of themechanism are derived firstly and then kinetic and strain energy equation for chains of themechanism are obtained. An elastic equation of motion for3-RRR manipulator, which couldis used to analyze the residu vibration and self-excited oscillation, is constructed in inertialframe by taking into consideration the variation of the driver joint.
The reason for residu vibration is explained at singularity configuration. A nonlinear self-excited vibration is found at the neighborhood of the singularity configuration of themanipulator. The reason for causing the self-excited vibration is explained and a formulationabout self-excited vibration is builded.
A scheme for suspressing the oscillation is presented. One modal input shaper andmulti-modal input shaper are constructed respectively to reducing the vibration. Forhigh-speed motion, the dynamical control is needed. Therefore, a slide modal controller,whose control eqution is set up and stability is checked, is designed for motion control. Thesimulation shows that the result is good.
A3-RRR parallel robot is made with dSPACE1103as controller and AC servo motors onthe basis of3-RRR mechanism. A set of experiments are designed based on XL-80lasersystem and ControlDesk software. A set of experiments about risidu vibration and self-excitedvibration at the singularities are made. The results check the prior analysis about residualvibration and self-excited vibration. And then the rotation angles of servo motors aremeasured with ControlDesk. The resulting angles are in accordance with the priviousexplaination. The experiments of suspressing the residual vibration are done, which show thatinput shaping controller redues the residual oscillation effectively and multi-modal inputshaper suspresses the oscillation in effect.
引文
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