外文翻译--快速自动机器人人平台

2.2.5 Vector fields A vector-field is essentially a 2-Dimentional field with vectors. A vector consists of magnitude and angle, which represent importance or speed and demanded heading angle respectively. The magnitude interpretation as a an importance is useful when vector fields are combined by addition of each vector. The more important vector is longer, and therefore the resulting heading angle will be more into the direction of the more important vector. Some vector field generators, such as basic potential field methods, are not concerned about the magnitude. In this case the magnitude is often normalized. 2.2.5.1 Potential fields The theory of potential fields as trajectories is derived from an electrical field of a sphere in physics. The ormulae for an attractive field is as follows: where T is a vector from the origin to the target position R is a vector from the origin to the robot tV is the resultant vector with normalized length, indicating the direction of the field at the robots current position. The resultant is pointing towards the target. The attractive potential field is therefore related to line of sight guidance. A repulsive field is generating vectors pointing away from T. The formulae is Fig 6: attractive potential field Figure 6 shows a attractive potential field with a target point at T(0,0) . In an application usually only the vector at the current position of the robot is calculated, for demonstration graphs such as Figure 6 the robot is assumed to be in every possible position in the field, and therefore generating the vectors at each point. 2.2.5.2 Limit cycle based vector fields Limit cycles are part of nonlinear control theory. However the properties of a graph representing a limit cycle, Figure 7, can be adopted for path generation. For further reading see D-H Kim (2000). The limit-cycle characteristics of the 2nd order nonlinear function can be represented as a vector field containing a unit circle. Vectors outside the circle will be directed tangentially onto the circle. It can be seen as an arc/circle trajectory generator that lines up the robot coming in from any direction automatically. The resulting vector-field can be used like a arc trajectory generator or for obstacle avoidance. The disadvantage of the limit cycle method is that once the robot crosses the unit circle, the vector pointing towards a singularity in the centre. Therefore, a practical implementation is not easy, since is likely to overshoot the circle border slightly when arriving at the circle. A modification of the field within the circle is a proposed solution to the problem. Fig 7: limit cycle 2.2.5.3 Vector field fusion All discussed vector field methods can be applied at the same time. The author developed a way of combining (fusing) vector fields, which is published in Robinson P. (2004). Constraints and requirements: -Two or more vector fields are given -These vector fields contain normalized vectors The method is best described in an example. A typical combination of vector-field shall be analyzed where a Robot R avoids and obstacle Robot O on the way to a target point T. See figure 8 below. A weighting function is required to fuse the vector fields together. Experiments have shown that the Gaussian normal distribution function is an acceptable method of combining these fields. (A cylinder or cone would create a sudden change in heading angle and excites instability.) The angle is the difference between the instant heading angle of the robot and the vector ro which points from robot to obstacle. Fig 8: avoidance scenario Thus is an indication of how much the robot is on collision course with the obstacle. The smaller the angle, the more it is on collision course and the importance to avoid the obstacle is high. The mission of the robot is to go to T. In order to take into account the obstacle on its way towards the target it must consider how close the obstacle is. The distance to the obstacle is defined as ro . A smaller distance to an obstacle means that is more important to avoid it. An avoidance vector field VOshall be defined which is normal tot he mission vector field rt .The normalized target vector is VT. Suppose two vectors VTand VOare added together fused -with a Gaussian weighting function m*G(d). Where: VMT is the resultant modified target vector Mis a additional constant weighting factor G() is the Gaussian distribution function. is the offset of the Gaussian hat is the distribution of the Gaussian hat We just learned that there are essentially two factors that define how important it is to avoid the obstacle. and ro . The author will base the principle of vector field fusion by relating the length of each vector to importance towards the mission at a particular point in the field. Thus and ro can be modelled as follows to influence the length of VO. -r1 is the maximum offset that can cause. is steepness of the slope ( relationship of and ) A larger will result in higher angles already to be considered as important. And the distance of the robot to the obstacle ro is modelled as the position parameter in the Gaussian function. Finally, the resultant vector field VMTindicates the new instant heading angle for the robot. Test results at different speeds with a robot football robot. The maximum speed is 100% corresponding to 3.0 m/sec. The coordinate system is in inches. Fig 9: avoidance path at 0.36 m/sec Fig 10: avoidance path at 0.51 m/sec Fig 11: avoidance path at 0.84 m/sec 2.2.6 Matching the trajectories to the dynamic model of mobile robots A current attempt of the author is to compare a path through a potential field with the robots dynamics model in order to determine if the robot can follow it. This can be done in frequency domain, by comparing the bandwidth of the robot plus controller model to the bandwidth of the input signal when trying to follow the path. This approach can be taken further. This could provide a basis of matching a vector-field by design to the robots bandwidth. 2.3 Modelling mobile robots This chapter is concerned with developing and understanding models of mobile robot kinematics and the control of each individual motor actuating the links within the kinematic model. Further reading is available in McKerrow P J (1991) chapter 8.1 which references to Muir P F and Neuman C P (1986). Muir and Neuman introduced a way of model ling wheeled mobile robots. It is related to model ling the kinematics of robot arms (manipulator kinematics). Differential driven Robot Differential driving is one of the simplest methods of model ling a mobile robot. This is probably why it is so common. The robot consists of 2 diagonally opposing wheels, see Fig. 12. If both wheels have the same velocity, the robot will go straight. If one wheel goes faster than the other the robot will follow a circular trajectory. If one wheel turns in the opposite direction of the other but with the same ma gnitude in speed, the robot will turn around its cent re, “on the spot”. The wheel Jacobian matrix is given and can be used as follows: Where v is the velocity forward of the centre of the robot and . is the angular velocity around the centre of the robot, see Fig 12. p& wheel Jacobian. p is the posture of the robot. The posture gives information about how the robot moves with respect to the floor. indicates the instant heading angle of the robot. Assuming no slip, the direction the vehicle is facing towards, is the same as the direction of the velocity vector (at and instant in time). An advantage of this fact, it simplifies calculations. A disadvantage however is that it can not move side wards. Fig 12: Differential driven Robot 3 DESIGN AND IMPLEMENTATION 3.1 Specification for fast autonomous mobile platform: faster than 1m/sec large enough for real world application, such as picking up goods space for a onboard laptop enough sensors for autonomous movements battery life for several hours inexpensive ( 1000) 3.2 Mechanical Design Every part of the mechanical design is build from basic materials, only the caster wheels are a ready made construction. One focus of the project was to build the mechanical construction rather than buy a ready made gearbox and frame. As a benefit the authors machining skills has improved. 3.2.1 Frame The robot body consists of a steel frame that is welded together forming a box. Initially the frame was screwed together until the design was fully developed. Then the screws and brackets have been replaced by welded joints. The top rectangle can be taken of in order to do repair work. A large orange plastic sheet is mounted on top as a base for the circuit boards and the notebook. The battery is placed on top of the bottom frame. The key point is here that the bottom frame is lower than the wheel axis. It is placed just 2 cm above ground to prevent the robot from toppling at high speed. 3.2.2 Steering The steering consists of 2 links, i.e. 2 wheels. Fig 13: Explosion picture of one steering link One steering link consists of a medium duty caster wheel that has been welded to a plate. The plate and the underlying caster-wheel have a 12 mm shaft welded on in order to enable steering of the wheel. The wheel is not offset its centre, unlike on a shopping trolley for example. Therefore it must be controlled by active steering to line it up with the direction of movement. Both steering shafts are driven by a motor-gearbox combination (gear-ratio 1:50) over a belt system (ratio 1:2). The motor is a 12 Volt DC Motor. A potentiometer on the top of one shaft is read by a micro con troller to determine the current steering angle. The overall system is a servo system, since it has positional feedback, see section 3.3.5 for a description of the control. The above design, is the finally implemented one, the initial design had a stepper motor with controller circuit. However, the stepper motor was not powerful enough to turn the steering on rough surfaces. The implemented system responds quick and accurate within a fraction of a second to any angle. There are 3 ball bearings per link: one in the axis of the wheel and two in line with the 12mm steering shaft. This two ball-bearings shift the weight of the robot onto the wheel. One steering link is designed to carry a weight of 120Kg. One could argue that axial-ball bearings would have been better, but the axial load of the radial ball-bearings chosen is much higher than the maximum weight that the robot will ever experience. The two ball-bearings are placed in a machined al u minium housing. All the machining for the slot and the place to fit the bearing was done with a lathe and a milling machine. 3.2.3 Gearbox Fig 14: Gearbox in AutoCAD The two gearboxes are constructed out of 4 solid al u minium bars each, which are bolted together. On the bottom bar two slots are milled out, increasing the accuracy of their alignment with the other bars. During construction the bars where clamped together, in order to align the shaft holes of both bars precisely. The surfaces of the bars have been milled straight at the beginning, to have accurate reference during construction. The gearbox has 2 ball bearings on the shaft that is connected to the wheel. The other two shafts are for transmission gears. Each shaft has sleeves to adapt to the different diameters of the gears. The gear ratio is: n.b. Wheel diameter = 125mm Wheel circumference 392.7mm A further ball bearing with housing is mounted onto the frame. Thus the frame is connected to the housing and the housing to the gearbox. The holes marked with stripes in figure 15 are for fixing frame an housing together. Fig 15: Housing with 3 holes for gearbox-mount 3.2.4 Accuracy For the construction of the gearbox, only machine tools such as a lathe and a milling machine can achieve the accuracy. A stand drill is already problematic. The machines should be calibrated with a dial indicator. A dial indicator is a dial gauge that can measure distance in fractions of millime tres. It is mounted onto the lathe or milling machine to align the tool with the work piece. 3.3 Electronic Hardware Design Every circuit in the robot has been designed from basic principles. The design consists of two modular Micro controllers, the power electronics and the ultrasonic sensors. 3.3.1 Power Supply circuit The robot runs of a 12Volt battery. In the cent re of the frame is place to strap on a car battery or motor-cycle battery. With a car battery, the robot runs approximately 3-4 hours in constant action. The power is split up into signal power and motor power from the battery on wards to minimize noise distribution. The motor power goes through an emergency stop button before being fed to the electronics board. All circuits can be switched of through a lever switch added next to the emergency stop. A bipolar capacitor with 4700uF is placed on the power electronics board. Each power regulator is surrounded by capacitors as well. The larger electrolytic capacitors are always accompanied by a bipolar 10nF or 100nF ceramic capacitor. The tracks on the power electronics board have a diameter of 6mm. The motor power cables have a diameter of 4.4mm. The cable is originally designed for speakers. The noise amplitude on the 12Volt rail is less than 100mV. 3.3.2 Micro controller Module The modular micro controllers was designed to be an improvement from the popular robot football circuit, which is used by many students at the university. Unfortunately the chip used in the old circuit (90S8515) is discontinued and the new generation, the Atmel Mega series usually comes as surface mount device). At a development stage, surface mount is a problem. Firstly, it is not easy to unsolder asurface mount chip and secondly, a surface mount chip can not be stuck into a breadboard to do a quick design check. The module was designed with the following specification in mind: -similar amount of ports as the 90S8515 -only a bare minimum on components on board -serial and programming connector (Robot football compatible) -Avoid extra features such as test LEDs, I2C connector etc. since they are application dependant -Power LED for quick confirmation -Crystal with build-in capacitors -Plug-in design with a Pin distance usable for bread-boards The specification is appreciated by the technicians and other students of the University. Several other students already applied this design to their final year project, which proves the flexibility of the design. The author is currently writing a guide on how to develop with an At mel Mega and the new g cc 3.X compiler. A draft version of the guide can be found in the Appendix. Fig 16: At mel Mega16 Micro controller board used for designing the motor controllers Technical Details of the Microcontroller Module -Atmel Mega16-AI in TQFP package (Atmel Package Code 44A) -16 MHz Crystal -Atmel ISP Programming connector (IDC10, right angled) -Robot Football 4-Pin Molex Serial Port connector -3x 10Pin Single-in-Line connectors for IO-Ports 3.3.3 Ultra Sonic Sensors design The final design of the sensor is more simple than the original. The flexibility has increased since modulation and signal decoding is part of the software. Faster sensing is made possible through the changes. However, it demands more computing time. Features of the new design include: -frequency can be set by software -signal can be coded -reliable range 1.3 m The transmitter consists of a software running in a timer at 76 to 84 kHz and toggling the transistor Q1. The toggling divides the frequency by two. Unfortunately none of the timer frequency settings match the resonance frequency of the transducers. Therefore, the timer frequency must be programmed to sweep from a few kilohertz under the resonance frequency to a few over the resonance frequency. Fig 17: Ultra sonic distance measurement electronics The receiver end consists of a operational amplifier for signal boosting, a transistor Q2 for level shifting (12V to 5V) and a low pass filter R7,C7. The Op Amp is configured with a only positive rail at 12V. The positive input is clamped to 6V. Feedback resistor RV1 is a 47KOhm potentiometer in the final version, thus creating a variable gain from 1 to 48. Practically gain values over about 30 amplify noise created by the transmitter over the power rail. Even the extensive use of capacitors could not remove this problem. The sensor can detect flat objects, such as walls and boxes up to 3 meters away. Reliable detection of humans can only be achieved within 1.3 meters. Fig 18: design of a ultra sonic distance sensor with 8-bit bus connector (original design) Low pass Filter The micro controller recognizes a logical high at 3.5V and above, Atmel (2003), on an digital IO pin. The filter must be matched to give this voltage at the maximum acceptable frequency. Experiments show that, the a design with the 3dB point at 42KHz (Transducer frequency) has not enough safety margin and the micro controller does not always recognise the signal as high when it should be. Therefore the 3dB point is set to 49KHz. The question is which R and C values to choose in order to have 3.5 Volt at the output at 49 kHz. Fig 19: low pass filter (used in ultra sonic circuit) Initial formulae (15) rearranged for R. (16) n.b. the output impedance of the transistor circuit has been neglected, since it is lower than the low-pass circuit. The input impedance of the micro controller is much higher than the one of the low-pass circuit, and the impedance can be neglected in the calculation again. Fig 20: Ultrasonic sensor electronics (final design) 快速自动机器人人平台 -2 2.2.5 向量场 一个向量场实质是由一个 2-维向量组成的区域。一个向量由大小和方向组成，向量对于速度和航向角而言相当重要。 大小被认为是向量场中很重要的问题，大小对于通过每个向量组合成为向量场是很有用的。越重要的向量越长，航向角贴近的是更加重要的向量。 一些向量场产生器，像是基础的势场产生法，是不考虑大小的。这种情况下大小经常被忽略。 2.2.5.1势场 势场的一些理论像是轨迹的概念是从物理领域中的电学部分中分 化而出的。 引力场公式如下： 这里 是一个冲起始到目标位置的向量 是一个从起始指向机器人的向量 是一个表征机器人当前位置的单位化的长度和预计的角度。结果是指向目标的。引力场是关联其中的可视的指引。斥力场产生背向目标的向量。等式是 表格 6 展示了一个引力场指向目标点（ 0.0）。在当前应用的机器人仅有当前位置的向量才加入计算 ，对于多为图表像表格 6这样，机器人可以在场中任何可能的地方，同时也可以在任何点长生向量。 表格 6：引力场 2.2.5.2 基于极限环的向量场 极限环是非线性控制理论的一部分。但是一个表格能够表现极限环的属性，像是表格 7，那么这个表格便可以适应路径生成。此问题更深入的解读请阅读 D-H Kim（ 2000）。极限环的非线性功能的第二位表现为一个向量场包含一个单位环。单位环外的向量将产生于单位环相切的方向。这可以看成是一个圆弧 /圆轨迹生成率可以引导机器人自动从任何方向进入该圆。最终生成的向量场可以用来产生圆弧轨迹或者是用于避障。 极限环的缺点在于一旦机器恩跨过了单位元，向量场将指向中心。所以，具体实现极限环控制并不容易，因为机器人在接近单位圆时可能会 稍稍的越过边界。 这种场在单位环内进行修改时一个解决此种问题的可行的措施。 对图表 7：极限环 2.2.5.3 矢量场的融合 所有的可提供向量场都可以在同一时间进行讨论。作者开发了一种可供合并向量场合并的方法，该方法在 Robinson P(2004)中论述。 约束和要求： -两个或者更多的向量场。 -这些向量场包含标准化的向量。 这种方法最好用一个例子来描述。一个典型的需要向量场合并的地方在于当一个机器人 R 需要避免和机器人 O在路上相遇去目标 T 时。看下面图表 8。 在融合向量场过程中，需要一个加权函 数。经验已经证明，高斯正态分布函数在合并两个场域是很合适的方式。（一个圆柱体或是一个椎体都可能产生一个突然的冲击以使航向角发生变化并产生激发不稳定现象。） 图表 8：回避方案 ro 向量是指向机器人回避方向。 那个 角是表征机器人和障碍物碰撞程度的量。这个角度越小，碰撞事件发生的情况就越小，同时避开障碍物的可能性越高。 入 考虑，那个机器人就必须计算障碍物和自己的距离。这个距离在式子中是以矢量 ro 定义的。和障碍物的距离越短就意味着避开障碍物的重要性越大。 一个回避向量场 应该被定义的和任务向量场 rt 场一样。标准化后的目标向量是 。 提供的两个向量 和 是用高斯加权方程 加在一起的 -融合。 这里： 是结果典型的目标向量 M是一个固定的加权因素 G()是高斯方程。 , 是对高斯方程的安全系数 ro 是高斯方程的分布 我们可以知道要回避一个障碍，本质上有两个因素。 , 和 ro。 作者按对于在场域内特定点完成这个任务的重要程度关联每个向量的长度来作为向量融合的 基础原则。 呢个 , ro可以作为限制蓝本来影响 的长度。 表示 所能带来的最大的安全度。 是沟槽的陡峭斜坡的斜度。 一个更大的 将会到这更高的角度。这已经是被认 为很重要的。机器人距离障碍 ro的路程在高斯方程中被认为是位置参数的蓝本。 最终，结果向量场 为机器人表征了新的瞬时航向角。 在不同速度的足球机器人上实验，最大速度为 3米每秒。坐标系统已英寸为单位。 表格 9:在 0.36米每秒速度下的避障路径 表格 10:0.51米每秒速度下的避障路径 表格 11:0.84米每秒速度下的避障路线 2.2.6设置轨迹舍弃匹配移动机器人的动态模型。 作者当前的尝试是将势力 场的路径和机器人的动态模型进行对比以决定是否机器人会按路径移动。这可以在频域进行，通过在需要按路径行动时对机器人频宽加上模型频宽和输入信号作比较来进行研究。这种方法可以进一步研究。这可以为根据机器人频宽定制向量场提供基础。 2.3模型化移动机器人 这一章研究的是开发和理解分析运动机器人的运动学模型和致力于控制运动模型上运动链的每个马达。此理论更深入的阅读请参阅 McKerrow P J (1991)章节 8.1此书参考 Muir P F和 Neuman C P (1986)。 Muir和 Neuman介绍了一个 模型化轮动移动机器人的方法。这和机器人手臂的模型化很有用（机械手运动学）。 差动驱动机器人 差动驱动是模型化一个移动机器人的一种简单方法。这也是为什么这种方法如此的普遍。这种机器人是由 2个对角线发转车轮组成，具体见表格 12.如果两个轮子都有同样的向量，机器人将会走直线。如果一个轮子比另一个轮子比另一个快，机器人将会转圈。如果一个轮子开向反方向同速度，机器人将会在原地打转，“在一点上”。 雅克比轮的矩阵如下： 这里 V是指向机器人中心的向量。 是绕机器人中心的角度向量，具体看图表 12.p通 过雅克比轮和 P进行联系。 P表示机器人姿态。机器人姿态可以表征机器人运动相对地板的运动程度。 指示机器人的瞬时航向角。 假设没有摩擦，轮子的方向会指向正前，瞬时和速度方向一直。这种现象的优点是计算简单。缺点是不能向侧移动。 图表 12:差动驱动机器人 3 设计与实现 3.1规范 高速自动化移动平台： 高于 1米每秒的移动速度。 足够大的体积，能够用于实际应用，像是提起货物。 为一个平台预留空间。 有足够多的传感器以完成自动移动。 能够几小时工作的电池。 机械设计 每一个机械设计的部件都是从基础毛坯加工而来，只有铸造车轮是已经制造的部件。这项工作的核心是构建一个机械结构而非购买一个已经制造完成的齿轮箱和结构。这样做的优点是作者可以提高机械制造技能。 3.2.1结构 机器人身体结构是由钢制结构焊接而成的箱体。实质上，结构在设计完全设计之前是拧在一起的。然后将螺栓接头用焊接点结构代替。顶端的矩形可以去掉以便于维修。在顶部固定一个大的橘红色塑料 支架用来作为环形板和笔记本的基础。电池放置在底部构架之上。重点在于底部构架在轮轴线之下。底部构架仅仅比地面高出 2厘米来防止机器人高速移动时被推翻。 3.2.2操舵机构 操舵机构有两条线，例如两个轮子。 表格 13：一个操舵线的爆炸图 一条操舵线包括一个中等尺寸的铸造轮用来在平台上滚动。平台和相关的铸造轮有一个 12mm的转轴为了保证操舵轮的转动。轮子不能抵消它的中心，不像超市购物车哪种。不过它必须要有可用的操舵控制仪将它牵引到运动方向。每个操舵轴都被一个马达齿轮箱结合一个带传动系 统驱动，马达齿轮箱齿轮传动比1:50，带传动比 1:2.马达采用 12 Volt DC马达。一个电位器安装在一个轴的上面可以被一个微型控制器读出数据来决定当前的操舵轮角度。整个系统是一个闭环控制系统，具体请看 3.3.5章节来对这种控制有一个理解。 上述的设计，是最终实现的部分，初始设计拥有一个步进电机和一个闭环控制系统。但是，步进电机不能提供足够的动力保证操舵轮在粗糙的表面工作。实际上的系统反应快，准确率在任何角度都能达到几分之一秒。 每个链接有 3个球轴承：一个在轮子的轴向，另两个在 12mm的操舵轮轴线上。后两个球轴承支承机器人传递到轴的重量。一条操舵链被设计可以负重 120千克的重力。可能有人会说一