研抛大型复杂曲面自主作业微小机器人研究
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摘要
大型精密模具制造的自动化是汽车等制造行业产品加快更新、升级,提高效率、降低成本的重要保障。大力发展和创造高技术含量的自主知识产权机电产品是我国经济健康发展和经济安全的客观要求。复杂曲面的精整加工是大型模具制造的重要环节,急需实现自动化和智能化。目前在这方面的研究多集中于开发大型的精整加工设备,不仅成本高、技术难度大,而且对不同规格的工件缺乏适应性。为解决这个问题,本课题组基于用小型设备加工大型工件的理念,提出了用微小机器人自主研抛大型复杂曲面新的学术思想。利用微小机器人在大型复杂曲面上的灵活移动,依据曲面的几何信息和工艺信息自主决策,进行研抛作业,实现了一种以小型设备加工大型复杂曲面的技术构想。
本文根据以上思想,研发了一种具有高度机动和可操纵性运动机构的四轮移动机器人。由于其两个主动轮的转向和速度由四个直流电机独立控制,使它具有比普通车辆的同轴差速运动机构更好的机动性,可以实现在曲面上任意两点间、以任意姿态、沿任意指定轨迹的运动。所集成的研抛工具系统可以随机器人的运动实现对工件的主动柔顺研抛作业。由微小研抛机器人、工控机和机器视觉系统构成的研抛加工系统成为适合精整加工各种规格大型复杂曲面的柔性研抛加工平台。本文根据需求,设计了一种实用的柔性研抛工具,并且根据其磨粒高度的统计学分布规律和弹性理论对其进行了材料去除和工艺规律的研究。
针对该机器人的工作特点,通过对其主动轮非完整约束的分析,为其建立了运动学模型。在此基础上,提出航标循迹导航方法。即利用研抛轨迹上的离散点作为航标点对机器人逐次进行导航,通过控制航标点在机器人坐标系中的方位角,实现机器人对任意研抛轨迹的跟踪。为消除机器人轨迹跟踪计算中的奇点现象,采用虚拟的机器人视觉角度考虑航标点的方位,即以机器人自身动态联体坐标系作为航标点方位参照的方法,取得良好效果。对运动学和轨迹跟踪的仿真和实验证明了所建立运动学模型的正确性和轨迹跟踪方法的实用性。
利用罗伯森-维滕堡法(R\W法)对微小研抛机器人进行了动力学分析。针对多刚体系统中存在的间接驱动,提出了在间接驱动的刚体间设置虚拟力元的方法,以解决这类多刚体系统的动力学建模问题。在对该机器人动力学研究中,针对作用于内接滑移铰刚体的力元的动力学问题,对多刚体系统的广义力计算方法进行了推导和拓展,使利用R\W法动力学普遍方程可以解决这类刚体系统的动力学建模问题。
微小研抛机器人的研抛加工试验结果表明,初始Ra值约为1.6μm的工件表面经过机器人研抛后,可以达到粗糙度水平为Ra0.2μm的效果。证实了利用微小研抛机器人可以实现对大型复杂曲面的研抛加工,并达到理想的表面质量的技术创新思路是可行的。
Finishing process is one of the most important processes related to the surface quality in the process in manufacturing mold. And polishing mold free-form surface automatically and intelligently is a hot focus in the field of manufacturing mold research for a long time. For polishing large free-form surface of mold, traditional research focused in researching and developing large-scale automation finishing equipment mainly. But based on the concept of employing small equipment in processing large work-piece, our project group proposed a new solution of utilizing small mobile robot to polish large mold free-form surface. In this way, not only the disadvantages of high cost and technical difficulty in developing large fixed equipment but also the disadvantage of worse adaptability to different work-piece size is overcome.
Based on this theory, a novel four-wheeled mobile small polishing robot is developed, in which two driving wheels and two following caster wheels are configured diagonally. Each driving wheel is driven by two DC motors, one for controlling wheel’s steering angle and one for driving wheel. The two following wheels are caster wheels without kinematics constraint along robot working plane, and they can respond to and follow the robot main body’s any motion. The following wheel’s support is a kind of suspension mechanism includes cylinder damper and spring that can adapts it self to the height of terrain and damp the high frequency vibration from polishing tool. Because the two driving wheels’steering angle can be controlled independently, the speed proportion and steering angle combination can be adjusted properly to drive the robot moving along linear track and arc track with center positioned in any point in the robot working plane. This is because that two driving wheels’controlled independently provide the robot mobile ability degree ofδm=3. For normal differential coaxial two wheel mobile mechanism that is withδm=2, the instantaneous center of robot (ICR) always locates in the axis line of wheels, but for the mobile mechanism withδm=3, the ICR can be set in any place of the plane in any time, the latter has better mobile ability.
The integrated polishing tool’s compliance control in the robot is implemented by a set of pneumatic driving system, therefore polishing tool’s working pressure is kept constantly by pneumatic driving system. A kind of special polishing flexible tool was designed, and its ability in removal material when polishing is analyzed based on the abrasive grain height’s statistical distribution and elastic and plastic deformation theory. The polishing experiments showed that this tool has good effect in polishing metal work-piece. The small mobile polishing robot system is composed of three parts: small mobile polishing robot, industrial control computer and monocular machine vision systems. The machine vision systems that includes a mechanical CCD camera vision is the most out feedback section for robot position and pose, which can feedback the robot’s instantaneous pose and pose to the control system at any moment.
In accordance with the driving wheels’nonholonomic constraints, small mobile polishing robot is analyzed to obtain its kinematics model. On this basis, the robot trajectory tracking method and algorithm have been studied, and a navigation algorithm for guiding robot to track arbitrary curvilinear trajectory in uneven terrain has been put forward. Because the robot’s working terrain is free-form surface with three-dimensional characteristics, its polishing path must be curve along the fluctuant terrain. Thus the navigation algorithm must have the ability of controlling robot to track complex curves. The method proposed in this paper is that the planned track curve should be replaced by a series of discrete sequential control points distributed along the curve. Those points are called as beacon points. In this way, tracking polishing trajectory is realized by each point’s navigation to the robot in turn. This also can be thought as a kind interpolation. The robot is navigated by each beacon point by means of decreasing the deviation angle of robot’s motion direction to the beacon point. When robot’s moving, its position coordinates and pose angle is detected and sent to control system by machine vision system, then the robot’s pose angle is compared with the current beacon point’s position to obtain the robot’s motion deviation angle to the beacon point. A function of robot’s angular velocity is designed, in which the deviation angle value is set as independent variable, and the angular velocity calculated from this function always let the robot turn to decrease the deviation angle. When robot is driven by this angular velocity and given speed, it will be driven to approach the guiding beacon point. Input the angular velocity and speed to the inverse kinematics model, four controlling parameters can be obtained, i.e. two driving wheels’steering angles and speeds.
In order to avoid the phenomenon singular points in tracking trajectory computation, which can defeat the tracking computing and oscillate the robot, a virtual robot first-person view control method is proposed in this paper by imitating animal view frame and decision logic in their activity. by this way, in robot’s motion control computation, the coordinates value of robot and beacons in the inertia frame (the fixed reference coordinate system) are always converted as their homologous values in the frame attached to the robot body(robot mobile reference coordinate system). This just like considering the working environment and deciding the tracking motion in the robot self view. But in this robot polishing system, because the CCD camera is arranged over the robot and whole working space, which can be thought as a local work space GPS, therefore the so-called robot first person vision is not in the physical meaning. It’s only a virtual algorithm. Simulation and experiment showed there isn’t singular point in robot’s any motion direction when tracking trajectory by this method.
In this paper, Roberson-Wittenburg algorithm (R\W for short) is used in studying the multi-rigid-body system dynamics of the small polishing robot. By the hypothesis of wheel’s absence of sliding, both the two driving wheels and following wheels of the robot are subject to nonholonomic constrain. By analyzing the robot kinematics behavior based on this constrains, its four wheels kinematics models can be drawn and their kinematics state in robot’s any certain motion state can be worked out. Thus the kinematics models of velocities, acceleration of robot’s every body can be obtained, which are the basis in analyzing the dynamics of robot multi-rigid-body system. In studying dynamics of the robot, in accordance with conventional methods, to transform the robot multi-body system construct as tree construct, the joints between the four wheels and the ground are cut off, and add joints between the robot main body and ground, which include two prismatic joints along x and y direction respectively, and a rotating joint about z direction. During this kinematics study, to address the existence of indirect driving relation between the driving wheels and the robot main body, an algorithm of setting up virtual force elements between driving wheels and main body, in which the indirect driving relation is replaced by the direct driving relation. The force element is no-constrain force acting on rigid body in the system.
Among the added virtual force elements, there are two force elements that act on the bodies linked by prismatic joints (BLPJ for short). In general, the study about force element in multi-rigid-body system is focus in the force element acting on body adjoining rotation joint mainly. But multi-body system involving force acting on body adjoining prismatic joint is seldom mentioned. In the actual rigid body system, the body next to the prismatic joints also may be acted by those non-constrain force such as spring force, damping force and the electromagnetic force. In this paper, to address the dynamics study of multi-body system existing force element acting on BLPJ, the formula of equivalent force about force element in the R\W basic dynamics equation is derived, and dynamics model of the small polishing robot is set up.
Small polishing robot’s simulation model is set up in ADAMS software to simulate its kinematics ability. In this simulation, the steering angles of two driving wheels are controlled by two different sinusoids, and wheels’speed are controlled by designated value also, thus to drive the robot’s geometrical center to move along an S-shaped curve. The simulation result trace curves of geometrical center and four wheels are compared with the corresponding trace curves from calculated result by robot kinematics model, and the compare shows that two group curves are coincident very well. Therefore this shows that the kinematics model of the small polishing robot is right.
A prototype of the small polishing robot was made, on which a serious of experiments about kinematics, motion control and polishing operation were implemented. In the planar motion experiment, robot driving wheels’steering angles and speed is calculated in accordance with the specified robot motion speed and arc center in the robot working plane by the kinematics model to drive the robot move along this designated arc trajectory, and the result trace is coincident. It shows that the kinematics model is right. In the designed interpolation motion experiment of semi-circular arc and sinusoid trajectories, the robot fulfilled tracking the target curves navigated by the beacon points distributed along the target curves. This proves that the tracking trajectory control algorithm is practical. In using this robot control algorithm, the angular velocity of robot movement is calculated by a linear function of the angle deviation. The analysis in this paper proves that the chosen value of the constant coefficient of the linear function impacts the angular velocity control and robot’s tracking process remarkably. The robot experiment proved this analysis.
In the robot trajectory tracking experiment on free-form surface, the trajectories are used that are same to trajectories used in planar experiment. Although the interpolation errors in these experiment are bigger than that in planar experiment, the robot fulfilled trajectory tracking successfully also. This shows that although the surface fluctuation can disturb robot’s rectifying deviation angle effect lightly, but robot can implemented trajectories tracking rightly and steadily in its polishing condition. Experimental results show that each experiment has reached the expected requirements.
The experiments prove that the robot kinematics mechanism has so good mobile performance and manageability that can meet the performance requirements of polishing large-scale mold surface. Both the experiments of kinematics and polishing operation on the both planar and free-form surface prove that the kinematics model used is right, and that the used navigation algorithm is practical in guiding the robot to track trajectory stability on complex surface when polishing. The polishing experiments and analysis of experiments data shows that the three polishing process factors: tool rotation speed, feed speed and tool’s polishing pressure have different effect significant degree to polishing quality. Among them, the tool rotation speed and feed speed have bigger significant degree, but tool’s polishing pressure has smaller. The analysis of experiments data shows that, in the current hardware condition, when the tool rotational speed n = 1000 rpm, feed speed v = 120 mm/min, polishing pressure F = 15N and tool’s abrasive grain is 240#, the best surface quality of roughness Ra0.2μm can be obtained.
本文根据以上思想,研发了一种具有高度机动和可操纵性运动机构的四轮移动机器人。由于其两个主动轮的转向和速度由四个直流电机独立控制,使它具有比普通车辆的同轴差速运动机构更好的机动性,可以实现在曲面上任意两点间、以任意姿态、沿任意指定轨迹的运动。所集成的研抛工具系统可以随机器人的运动实现对工件的主动柔顺研抛作业。由微小研抛机器人、工控机和机器视觉系统构成的研抛加工系统成为适合精整加工各种规格大型复杂曲面的柔性研抛加工平台。本文根据需求,设计了一种实用的柔性研抛工具,并且根据其磨粒高度的统计学分布规律和弹性理论对其进行了材料去除和工艺规律的研究。
针对该机器人的工作特点,通过对其主动轮非完整约束的分析,为其建立了运动学模型。在此基础上,提出航标循迹导航方法。即利用研抛轨迹上的离散点作为航标点对机器人逐次进行导航,通过控制航标点在机器人坐标系中的方位角,实现机器人对任意研抛轨迹的跟踪。为消除机器人轨迹跟踪计算中的奇点现象,采用虚拟的机器人视觉角度考虑航标点的方位,即以机器人自身动态联体坐标系作为航标点方位参照的方法,取得良好效果。对运动学和轨迹跟踪的仿真和实验证明了所建立运动学模型的正确性和轨迹跟踪方法的实用性。
利用罗伯森-维滕堡法(R\W法)对微小研抛机器人进行了动力学分析。针对多刚体系统中存在的间接驱动,提出了在间接驱动的刚体间设置虚拟力元的方法,以解决这类多刚体系统的动力学建模问题。在对该机器人动力学研究中,针对作用于内接滑移铰刚体的力元的动力学问题,对多刚体系统的广义力计算方法进行了推导和拓展,使利用R\W法动力学普遍方程可以解决这类刚体系统的动力学建模问题。
微小研抛机器人的研抛加工试验结果表明,初始Ra值约为1.6μm的工件表面经过机器人研抛后,可以达到粗糙度水平为Ra0.2μm的效果。证实了利用微小研抛机器人可以实现对大型复杂曲面的研抛加工,并达到理想的表面质量的技术创新思路是可行的。
Finishing process is one of the most important processes related to the surface quality in the process in manufacturing mold. And polishing mold free-form surface automatically and intelligently is a hot focus in the field of manufacturing mold research for a long time. For polishing large free-form surface of mold, traditional research focused in researching and developing large-scale automation finishing equipment mainly. But based on the concept of employing small equipment in processing large work-piece, our project group proposed a new solution of utilizing small mobile robot to polish large mold free-form surface. In this way, not only the disadvantages of high cost and technical difficulty in developing large fixed equipment but also the disadvantage of worse adaptability to different work-piece size is overcome.
Based on this theory, a novel four-wheeled mobile small polishing robot is developed, in which two driving wheels and two following caster wheels are configured diagonally. Each driving wheel is driven by two DC motors, one for controlling wheel’s steering angle and one for driving wheel. The two following wheels are caster wheels without kinematics constraint along robot working plane, and they can respond to and follow the robot main body’s any motion. The following wheel’s support is a kind of suspension mechanism includes cylinder damper and spring that can adapts it self to the height of terrain and damp the high frequency vibration from polishing tool. Because the two driving wheels’steering angle can be controlled independently, the speed proportion and steering angle combination can be adjusted properly to drive the robot moving along linear track and arc track with center positioned in any point in the robot working plane. This is because that two driving wheels’controlled independently provide the robot mobile ability degree ofδm=3. For normal differential coaxial two wheel mobile mechanism that is withδm=2, the instantaneous center of robot (ICR) always locates in the axis line of wheels, but for the mobile mechanism withδm=3, the ICR can be set in any place of the plane in any time, the latter has better mobile ability.
The integrated polishing tool’s compliance control in the robot is implemented by a set of pneumatic driving system, therefore polishing tool’s working pressure is kept constantly by pneumatic driving system. A kind of special polishing flexible tool was designed, and its ability in removal material when polishing is analyzed based on the abrasive grain height’s statistical distribution and elastic and plastic deformation theory. The polishing experiments showed that this tool has good effect in polishing metal work-piece. The small mobile polishing robot system is composed of three parts: small mobile polishing robot, industrial control computer and monocular machine vision systems. The machine vision systems that includes a mechanical CCD camera vision is the most out feedback section for robot position and pose, which can feedback the robot’s instantaneous pose and pose to the control system at any moment.
In accordance with the driving wheels’nonholonomic constraints, small mobile polishing robot is analyzed to obtain its kinematics model. On this basis, the robot trajectory tracking method and algorithm have been studied, and a navigation algorithm for guiding robot to track arbitrary curvilinear trajectory in uneven terrain has been put forward. Because the robot’s working terrain is free-form surface with three-dimensional characteristics, its polishing path must be curve along the fluctuant terrain. Thus the navigation algorithm must have the ability of controlling robot to track complex curves. The method proposed in this paper is that the planned track curve should be replaced by a series of discrete sequential control points distributed along the curve. Those points are called as beacon points. In this way, tracking polishing trajectory is realized by each point’s navigation to the robot in turn. This also can be thought as a kind interpolation. The robot is navigated by each beacon point by means of decreasing the deviation angle of robot’s motion direction to the beacon point. When robot’s moving, its position coordinates and pose angle is detected and sent to control system by machine vision system, then the robot’s pose angle is compared with the current beacon point’s position to obtain the robot’s motion deviation angle to the beacon point. A function of robot’s angular velocity is designed, in which the deviation angle value is set as independent variable, and the angular velocity calculated from this function always let the robot turn to decrease the deviation angle. When robot is driven by this angular velocity and given speed, it will be driven to approach the guiding beacon point. Input the angular velocity and speed to the inverse kinematics model, four controlling parameters can be obtained, i.e. two driving wheels’steering angles and speeds.
In order to avoid the phenomenon singular points in tracking trajectory computation, which can defeat the tracking computing and oscillate the robot, a virtual robot first-person view control method is proposed in this paper by imitating animal view frame and decision logic in their activity. by this way, in robot’s motion control computation, the coordinates value of robot and beacons in the inertia frame (the fixed reference coordinate system) are always converted as their homologous values in the frame attached to the robot body(robot mobile reference coordinate system). This just like considering the working environment and deciding the tracking motion in the robot self view. But in this robot polishing system, because the CCD camera is arranged over the robot and whole working space, which can be thought as a local work space GPS, therefore the so-called robot first person vision is not in the physical meaning. It’s only a virtual algorithm. Simulation and experiment showed there isn’t singular point in robot’s any motion direction when tracking trajectory by this method.
In this paper, Roberson-Wittenburg algorithm (R\W for short) is used in studying the multi-rigid-body system dynamics of the small polishing robot. By the hypothesis of wheel’s absence of sliding, both the two driving wheels and following wheels of the robot are subject to nonholonomic constrain. By analyzing the robot kinematics behavior based on this constrains, its four wheels kinematics models can be drawn and their kinematics state in robot’s any certain motion state can be worked out. Thus the kinematics models of velocities, acceleration of robot’s every body can be obtained, which are the basis in analyzing the dynamics of robot multi-rigid-body system. In studying dynamics of the robot, in accordance with conventional methods, to transform the robot multi-body system construct as tree construct, the joints between the four wheels and the ground are cut off, and add joints between the robot main body and ground, which include two prismatic joints along x and y direction respectively, and a rotating joint about z direction. During this kinematics study, to address the existence of indirect driving relation between the driving wheels and the robot main body, an algorithm of setting up virtual force elements between driving wheels and main body, in which the indirect driving relation is replaced by the direct driving relation. The force element is no-constrain force acting on rigid body in the system.
Among the added virtual force elements, there are two force elements that act on the bodies linked by prismatic joints (BLPJ for short). In general, the study about force element in multi-rigid-body system is focus in the force element acting on body adjoining rotation joint mainly. But multi-body system involving force acting on body adjoining prismatic joint is seldom mentioned. In the actual rigid body system, the body next to the prismatic joints also may be acted by those non-constrain force such as spring force, damping force and the electromagnetic force. In this paper, to address the dynamics study of multi-body system existing force element acting on BLPJ, the formula of equivalent force about force element in the R\W basic dynamics equation is derived, and dynamics model of the small polishing robot is set up.
Small polishing robot’s simulation model is set up in ADAMS software to simulate its kinematics ability. In this simulation, the steering angles of two driving wheels are controlled by two different sinusoids, and wheels’speed are controlled by designated value also, thus to drive the robot’s geometrical center to move along an S-shaped curve. The simulation result trace curves of geometrical center and four wheels are compared with the corresponding trace curves from calculated result by robot kinematics model, and the compare shows that two group curves are coincident very well. Therefore this shows that the kinematics model of the small polishing robot is right.
A prototype of the small polishing robot was made, on which a serious of experiments about kinematics, motion control and polishing operation were implemented. In the planar motion experiment, robot driving wheels’steering angles and speed is calculated in accordance with the specified robot motion speed and arc center in the robot working plane by the kinematics model to drive the robot move along this designated arc trajectory, and the result trace is coincident. It shows that the kinematics model is right. In the designed interpolation motion experiment of semi-circular arc and sinusoid trajectories, the robot fulfilled tracking the target curves navigated by the beacon points distributed along the target curves. This proves that the tracking trajectory control algorithm is practical. In using this robot control algorithm, the angular velocity of robot movement is calculated by a linear function of the angle deviation. The analysis in this paper proves that the chosen value of the constant coefficient of the linear function impacts the angular velocity control and robot’s tracking process remarkably. The robot experiment proved this analysis.
In the robot trajectory tracking experiment on free-form surface, the trajectories are used that are same to trajectories used in planar experiment. Although the interpolation errors in these experiment are bigger than that in planar experiment, the robot fulfilled trajectory tracking successfully also. This shows that although the surface fluctuation can disturb robot’s rectifying deviation angle effect lightly, but robot can implemented trajectories tracking rightly and steadily in its polishing condition. Experimental results show that each experiment has reached the expected requirements.
The experiments prove that the robot kinematics mechanism has so good mobile performance and manageability that can meet the performance requirements of polishing large-scale mold surface. Both the experiments of kinematics and polishing operation on the both planar and free-form surface prove that the kinematics model used is right, and that the used navigation algorithm is practical in guiding the robot to track trajectory stability on complex surface when polishing. The polishing experiments and analysis of experiments data shows that the three polishing process factors: tool rotation speed, feed speed and tool’s polishing pressure have different effect significant degree to polishing quality. Among them, the tool rotation speed and feed speed have bigger significant degree, but tool’s polishing pressure has smaller. The analysis of experiments data shows that, in the current hardware condition, when the tool rotational speed n = 1000 rpm, feed speed v = 120 mm/min, polishing pressure F = 15N and tool’s abrasive grain is 240#, the best surface quality of roughness Ra0.2μm can be obtained.
引文
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