外文翻譯--快速自動機器人人平臺

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) 快速自動機器人人平臺 -2 2.2.5 向量場 一個向量場實質是由一個 2-維向量組成的區(qū)域。一個向量由大小和方向組成，向量對于速度和航向角而言相當重要。 大小被認為是向量場中很重要的問題，大小對于通過每個向量組合成為向量場是很有用的。越重要的向量越長，航向角貼近的是更加重要的向量。 一些向量場產生器，像是基礎的勢場產生法，是不考慮大小的。這種情況下大小經(jīng)常被忽略。 2.2.5.1勢場 勢場的一些理論像是軌跡的概念是從物理領域中的電學部分中分 化而出的。 引力場公式如下： 這里 是一個沖起始到目標位置的向量 是一個從起始指向機器人的向量 是一個表征機器人當前位置的單位化的長度和預計的角度。結果是指向目標的。引力場是關聯(lián)其中的可視的指引。斥力場產生背向目標的向量。等式是 表格 6 展示了一個引力場指向目標點（ 0.0）。在當前應用的機器人僅有當前位置的向量才加入計算 ，對于多為圖表像表格 6這樣，機器人可以在場中任何可能的地方，同時也可以在任何點長生向量。 表格 6：引力場 2.2.5.2 基于極限環(huán)的向量場 極限環(huán)是非線性控制理論的一部分。但是一個表格能夠表現(xiàn)極限環(huán)的屬性，像是表格 7，那么這個表格便可以適應路徑生成。此問題更深入的解讀請閱讀 D-H Kim（ 2000）。極限環(huán)的非線性功能的第二位表現(xiàn)為一個向量場包含一個單位環(huán)。單位環(huán)外的向量將產生于單位環(huán)相切的方向。這可以看成是一個圓弧 /圓軌跡生成率可以引導機器人自動從任何方向進入該圓。最終生成的向量場可以用來產生圓弧軌跡或者是用于避障。 極限環(huán)的缺點在于一旦機器恩跨過了單位元，向量場將指向中心。所以，具體實現(xiàn)極限環(huán)控制并不容易，因為機器人在接近單位圓時可能會 稍稍的越過邊界。 這種場在單位環(huán)內進行修改時一個解決此種問題的可行的措施。 對圖表 7：極限環(huán) 2.2.5.3 矢量場的融合 所有的可提供向量場都可以在同一時間進行討論。作者開發(fā)了一種可供合并向量場合并的方法，該方法在 Robinson P(2004)中論述。 約束和要求： -兩個或者更多的向量場。 -這些向量場包含標準化的向量。 這種方法最好用一個例子來描述。一個典型的需要向量場合并的地方在于當一個機器人 R 需要避免和機器人 O在路上相遇去目標 T 時?？聪旅鎴D表 8。 在融合向量場過程中，需要一個加權函 數(shù)。經(jīng)驗已經(jīng)證明，高斯正態(tài)分布函數(shù)在合并兩個場域是很合適的方式。（一個圓柱體或是一個椎體都可能產生一個突然的沖擊以使航向角發(fā)生變化并產生激發(fā)不穩(wěn)定現(xiàn)象。） 圖表 8：回避方案 ro 向量是指向機器人回避方向。 那個 角是表征機器人和障礙物碰撞程度的量。這個角度越小，碰撞事件發(fā)生的情況就越小，同時避開障礙物的可能性越高。 入 考慮，那個機器人就必須計算障礙物和自己的距離。這個距離在式子中是以矢量 ro 定義的。和障礙物的距離越短就意味著避開障礙物的重要性越大。 一個回避向量場 應該被定義的和任務向量場 rt 場一樣。標準化后的目標向量是 。 提供的兩個向量 和 是用高斯加權方程 加在一起的 -融合。 這里： 是結果典型的目標向量 M是一個固定的加權因素 G()是高斯方程。 , 是對高斯方程的安全系數(shù) ro 是高斯方程的分布 我們可以知道要回避一個障礙，本質上有兩個因素。 , 和 ro。 作者按對于在場域內特定點完成這個任務的重要程度關聯(lián)每個向量的長度來作為向量融合的 基礎原則。 呢個 , ro可以作為限制藍本來影響 的長度。 表示 所能帶來的最大的安全度。 是溝槽的陡峭斜坡的斜度。 一個更大的 將會到這更高的角度。這已經(jīng)是被認 為很重要的。機器人距離障礙 ro的路程在高斯方程中被認為是位置參數(shù)的藍本。 最終，結果向量場 為機器人表征了新的瞬時航向角。 在不同速度的足球機器人上實驗，最大速度為 3米每秒。坐標系統(tǒng)已英寸為單位。 表格 9:在 0.36米每秒速度下的避障路徑 表格 10:0.51米每秒速度下的避障路徑 表格 11:0.84米每秒速度下的避障路線 2.2.6設置軌跡舍棄匹配移動機器人的動態(tài)模型。 作者當前的嘗試是將勢力 場的路徑和機器人的動態(tài)模型進行對比以決定是否機器人會按路徑移動。這可以在頻域進行，通過在需要按路徑行動時對機器人頻寬加上模型頻寬和輸入信號作比較來進行研究。這種方法可以進一步研究。這可以為根據(jù)機器人頻寬定制向量場提供基礎。 2.3模型化移動機器人 這一章研究的是開發(fā)和理解分析運動機器人的運動學模型和致力于控制運動模型上運動鏈的每個馬達。此理論更深入的閱讀請參閱 McKerrow P J (1991)章節(jié) 8.1此書參考 Muir P F和 Neuman C P (1986)。 Muir和 Neuman介紹了一個 模型化輪動移動機器人的方法。這和機器人手臂的模型化很有用（機械手運動學）。 差動驅動機器人 差動驅動是模型化一個移動機器人的一種簡單方法。這也是為什么這種方法如此的普遍。這種機器人是由 2個對角線發(fā)轉車輪組成，具體見表格 12.如果兩個輪子都有同樣的向量，機器人將會走直線。如果一個輪子比另一個輪子比另一個快，機器人將會轉圈。如果一個輪子開向反方向同速度，機器人將會在原地打轉，“在一點上”。 雅克比輪的矩陣如下： 這里 V是指向機器人中心的向量。 是繞機器人中心的角度向量，具體看圖表 12.p通 過雅克比輪和 P進行聯(lián)系。 P表示機器人姿態(tài)。機器人姿態(tài)可以表征機器人運動相對地板的運動程度。 指示機器人的瞬時航向角。 假設沒有摩擦，輪子的方向會指向正前，瞬時和速度方向一直。這種現(xiàn)象的優(yōu)點是計算簡單。缺點是不能向側移動。 圖表 12:差動驅動機器人 3 設計與實現(xiàn) 3.1規(guī)范 高速自動化移動平臺： 高于 1米每秒的移動速度。 足夠大的體積，能夠用于實際應用，像是提起貨物。 為一個平臺預留空間。 有足夠多的傳感器以完成自動移動。 能夠幾小時工作的電池。 機械設計 每一個機械設計的部件都是從基礎毛坯加工而來，只有鑄造車輪是已經(jīng)制造的部件。這項工作的核心是構建一個機械結構而非購買一個已經(jīng)制造完成的齒輪箱和結構。這樣做的優(yōu)點是作者可以提高機械制造技能。 3.2.1結構 機器人身體結構是由鋼制結構焊接而成的箱體。實質上，結構在設計完全設計之前是擰在一起的。然后將螺栓接頭用焊接點結構代替。頂端的矩形可以去掉以便于維修。在頂部固定一個大的橘紅色塑料 支架用來作為環(huán)形板和筆記本的基礎。電池放置在底部構架之上。重點在于底部構架在輪軸線之下。底部構架僅僅比地面高出 2厘米來防止機器人高速移動時被推翻。 3.2.2操舵機構 操舵機構有兩條線，例如兩個輪子。 表格 13：一個操舵線的爆炸圖 一條操舵線包括一個中等尺寸的鑄造輪用來在平臺上滾動。平臺和相關的鑄造輪有一個 12mm的轉軸為了保證操舵輪的轉動。輪子不能抵消它的中心，不像超市購物車哪種。不過它必須要有可用的操舵控制儀將它牽引到運動方向。每個操舵軸都被一個馬達齒輪箱結合一個帶傳動系 統(tǒng)驅動，馬達齒輪箱齒輪傳動比1:50，帶傳動比 1:2.馬達采用 12 Volt DC馬達。一個電位器安裝在一個軸的上面可以被一個微型控制器讀出數(shù)據(jù)來決定當前的操舵輪角度。整個系統(tǒng)是一個閉環(huán)控制系統(tǒng)，具體請看 3.3.5章節(jié)來對這種控制有一個理解。 上述的設計，是最終實現(xiàn)的部分，初始設計擁有一個步進電機和一個閉環(huán)控制系統(tǒng)。但是，步進電機不能提供足夠的動力保證操舵輪在粗糙的表面工作。實際上的系統(tǒng)反應快，準確率在任何角度都能達到幾分之一秒。 每個鏈接有 3個球軸承：一個在輪子的軸向，另兩個在 12mm的操舵輪軸線上。后兩個球軸承支承機器人傳遞到軸的重量。一條操舵鏈被設計可以負重 120千克的重力?？赡苡腥藭f一