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2007年IEEE的程序
機器人與仿生學國際會議
2007年12月15日-18，三亞，中國
割草機器人多傳感器融合與導航技術的研究
從明和房波
大連理工大學機械工程學院
大連，116024，中國
congm@dlut.edu.cn
引言——本文提出了一種多傳感器系統從超聲波傳感器和導航相結合的測量機器人割草機。利用傳感系統使機器人割草機來映射未知的環(huán)境。對于自動割草機器人能在未知的環(huán)境中進行定位和導航執(zhí)行割草任務是很重要的。由于環(huán)境的復雜性，簡單的一種傳感器是不足夠割草機器人來完成這些任務。我們開發(fā)了一個配有DSPTMS320F2812作為CPU割草機器人。感測系統集成由超聲波傳感器，紅外傳感器，碰撞傳感器，編碼器，一個溫度傳感器和電子羅盤組成。超聲波測距技術變換是基于小波變換的精度高來表示的，以提高超聲波傳感器測量精度。仿真研究表明，所提出的多傳感器信息融合的方法是非常有效的對于導航割草機器人。實驗結果表明，該傳感系統基于相關的規(guī)定障礙檢測和定位顯示出巨大的潛力，為在動態(tài)工作條件下的割草機器人提供一個強大的高性價比的解決方案。
關鍵詞——多傳感器融合，超聲波傳感器，割草機機器人，定位，導航。
1.緒論
草坪修剪被許多人認為是一個最枯燥，累人的日常任務。首先迫切需要執(zhí)行的任務是能適應環(huán)境的機器人。一些預測表明，割草機器人將是一個最有前途的個人機器人應用，并有重大的市場在世界上。因此，智能化的概念割草機器人（IRM）在1997年度會議的OPEI（ 戶外電力會議設備研究所）上第一次提出[ 1 ]。該機器人主要面對一般家庭幫助忙碌的人們和乏力的老人們節(jié)省支付雇傭勞動力的報酬，同時消除人們來自噪聲中，花粉和割草刀片的危害。割草機器人是服務于家庭護理的室外移動機器人，是那種真正的智能機電一體化的環(huán)境清理設備[ 2 ] [ 3 ]。最重要的是割草機器人為代表的一些地區(qū)覆蓋的環(huán)保機器人不僅用于室內地面清潔，如[ 4 ]也在危險的環(huán)境中，例如去地雷，清理輻射點，勘探資源等。與室內移動機器人不同，割草機器人得到很大的挑戰(zhàn)。
在整個工作區(qū)域內，割草機器人使用傳感器來感知環(huán)境以及識別他們的實時狀態(tài)下的環(huán)境障礙，地圖構建，定位和導航。由于環(huán)境的復雜性，一種簡單的傳感器是不足以讓割草機器人來完成這些任務的。因此有必要結合來自不同的傳感器上觀察到的傳感器數據減少機器人在任何工作環(huán)境工作的不確定性。為來自各種傳感器的信息能合并，傳感器魯棒性和實時性的融合是必需的[ 5 ]。在傳感器出現誤差或失敗的情況下，多融合傳感器融合也可以減少不確定信息，并提高其可靠性。
低成本的傳感系統，說明其低功耗，高性能。超聲波傳感器檢測范圍是0.3m~ 5m，他們提供良好的范圍信息。然而，環(huán)境引起的鏡面漫反射是超聲波傳感器的不確定因素，讓他們不具吸引力。紅外傳感器的檢測范圍是0.02m~ 1m，他們可以檢測在超聲波傳感器的盲區(qū)的障礙。
為了滿足割草機器人低成本和高精度的測距技術的需求，在研究超聲波測距技術基于高精度的小波分析變換（WT）的數據報道，提高超聲波傳感器的測量精度。測量數據從傳感系統集成，實現規(guī)劃最佳的，可靠地，完全覆蓋整個工作計劃的地區(qū)，使割草機器人避免未知的障礙。
最后，通過仿真研究和實驗結果表明該傳感系統的導航效果，障礙物檢測和割草機器人定位。
2.信息資源管理系統的硬件
IRM采用DSP TMS320F2812作為其CPU，包括四個單元：車輛系統，切割系統，傳感系統和控制系統。傳感系統是用來收集外部動態(tài)信息的工作環(huán)境
避障，地圖構建，導航與定位。它也可以用來檢測車輛系統的運動參數和切削機構的工作狀況。該控制器將獲得的信息與數據庫進行比較，然后發(fā)出修正后精確的命令讓機器人完成任務。信息資源管理的硬件，如圖1所示。
IMR硬件概要圖1
機器人必須身體強壯，計算速度快，行動準確和安全。它應該有能力
，而在全部或大部分的割草期間無需人的干預。IRM由于模塊化設計，各單元的管理是相對獨立的。模塊化設計使維護更容易。IRM任何損壞單元都可以直接取代而不影響其它單元的功能。
3.傳感系統
A：超聲波傳感器單元
超聲波傳感器可以提供良好的范圍是基于飛行時間（TOF）信息原理，主要是由于其簡單性和成本相對較低，他們已廣泛應用于移動機器人的障礙物回避，地圖構建等。這種類型的外部傳感器能很好測量的障礙物的距離。靈敏度函數的主瓣內包含一個20度角，如圖2所示的【6】。大量的試驗結果表明，傳感器的精度范圍為±2cm。
圖2為超聲波傳感器的典型的強度分布
對于IRM，我們建立了一個傳感器陣列由12超聲波傳感器間隔30度的間隔。超聲波信號可以覆蓋所有的空間，可以要求哪些機器人檢測整個空間的環(huán)境信號。用基于TOF的測量的超聲換能器的經典技術，計算出的距離最近的反射器利用聲音在空氣中的速度從發(fā)射脈沖到回波到達時間。距離D為反映對象的計算
D =（C×T）/ 2 （1）
其中C是聲音的速度，T是飛行時間。該TOF法產生一系列的值時，回波幅度首次超過臨界值后發(fā)送，忽略第二回波從進一步的反射。
超聲波傳感器單元包括一個觸發(fā)脈沖生成單元，一個多通道選擇單元和回聲接收單元。傳感器接口電路設計發(fā)送和接收超聲波脈沖，捕獲的總是第一個返回的回聲。一個對象相關的數據的范圍要考慮到即使是位于在錐軸離軸。
超聲波頻率通常在40和180千赫之間，而在該系統中超聲波傳感器的頻率使用的是40千赫。光束角度是20度。40千赫PWM脈沖是由通用DSP的定時器單元產生的。驅動發(fā)射機有效而不帶來大的振動，40千赫的超聲波一次突發(fā)的時間是8周期。當超聲波脈沖發(fā)射時，傳感器將經歷“振鈴”。振鈴引起的由所發(fā)送的脈沖可以使接收器檢測到一個錯誤回聲。這個不能夠捕獲解決DSP中斷問題，直到延遲間隔已過。這意味著在延遲的時間間隔那測距儀不能檢測物體距離該傳感器是少于一半的聲音傳播的距離。這是該超聲波傳感器的盲區(qū)，如圖3所示。
圖3超聲波發(fā)射和接收示意圖
B.：.紅外傳感器裝置和其他傳感器
針對超聲波傳感器的盲區(qū)，增加了紅外傳感器。紅外傳感器可以檢測在20cm內的障礙，這彌補了超聲波傳感器由于失明問題所造成的區(qū)域的問題。
這個單元有16個紅外傳感器。每個紅外搜索器范圍有6度，是靈敏度函數主要的圓錐曲線的視圖。該傳感器具有一個高精度測量范圍，有效測量范圍是一個目標到一米左右。一些測試表明，該傳感器的測距精度在±1cm左右。
為了節(jié)省DSP的資源，16個紅外傳感器采用DSP TMS320F2812的數據接口代替IO接口。這種結構也可以同時讀取傳感器的狀態(tài)，以確保該系統的時間性能。傳感器接口電路用于發(fā)送和接收紅外脈沖并總是捕獲第一個回波來處理其振幅。
割草機器人在室外環(huán)境中工作時，其溫度變化迅速。溫度的變化會影響聲音的速度。因此，溫度傳感器用于保證超聲波傳感器的精度。碰撞傳感器是一組敏感的樣本，采用它是為了防止意外的碰撞造成的損害。由于潮濕的環(huán)境會危害IRM電路，濕度傳感器被引入用于檢測濕度環(huán)境。雖然這些傳感器不完全是
一個自主割草機器人機必要的，但他們可以提供有益的功能，讓工作更具有效性和安全性。
4.導航技術
A. 映射
正如圖4所示，基準方向的X定義和機器人的坐標為，。關于內置電子羅盤對于機器人的幫助，角，這是從第一個傳感器得來的角度，可容易衡量。實際上，如果只在角（標題的機器人角）的測量，從其他傳感器的角度可以發(fā)現
角是我們的世界坐標中心。該超聲波傳感器組的最大環(huán)數為n，半徑為R（在我們的系統中，n = 12和R = 0.25m）。該環(huán)的原點到中心之間的距離是r，并且該向中心的基準角度是Ω。根據參考位置機器人的中心是（，）。這個距離是從原點到通過兩個傳感器數據檢測的二維平面稱之為。
現在讓我們用DMI測量值來分別表示從超聲波和紅外傳感器得到的數據，用于精確距離。這些值之間會有一個誤差
在這項工作中，我們自然假設是一個均勻隨機變量在（W，W）范圍內。在這里，W表示最大距離測量誤差。這里的問題是，給定的，，r ，，，，，和，，，，，估計占用的坐標細胞和（或等價的）以最有效的方法。涉及檢測對象的方程可以寫為
圖4所示機器人在X-Y段的位置
由于對象涉及機器人的方程被寫為
如果我們定義的位置為：=，，，，，然后我們有
將插入到中，
在這里我們有N個這樣的方程。我們把它們矩陣形式
如果我們引入新的矩陣
，然后（10），
可以寫為
在這里，如果我們進行最小二乘法估計，我們得到
因此，我們用最小二乘法估計找到最好的位置。
B. 仿真研究
基于傳感器導航系統已經進行了測試在顯示該傳感器融合方法的有效性的兩種環(huán)境分別如圖5和圖6所示。割草機是一個結構化的實驗室初步測試如圖5所示。開始在（0.3m，0.5m，0°），一個虛擬的機器人在虛擬廣場走廊一次。墻在人工環(huán)境中是由真正的地圖表示的。
全車是獨立的。它有一個最大的運行速度是0.4米/秒。實驗室面積調查出在10cm精度優(yōu)于1cm為佳。提取映射，提出了一開始的目標。機器人位置和方向是由電子羅盤成立[ 8 ]。
圖5數據采集與導航在結構化環(huán)境中的結果
圖5中的結果顯示的映射質量和該傳感器融合方法的有效性。在測試中，我們發(fā)現，在估計的位置的平均誤差（ε）在環(huán)境中的障礙是在[ 0.2 ，0.2]米范圍內。
在模擬中，我們看到，在（11）中，實際上應該得到的是不滿足
。在可以為位置更好的估計的情況下可以表示為
在這種情況下，估計角不會改變但估計距離是縮放到它的最佳估計。
因此，對于位置，距離估計是和以前一樣，而最小二乘估計的作品只對角
。仿真結果表明，這種方法產生更精確的結果。
圖6仿真結果的墻下行為
墻后，被選定為初值問題域是因為它建立一個相當簡單的問題評價[ 9 ]。它這也奠定了更為復雜的基礎的問題領域，如迷宮的穿越，映射和用于草坪修剪和吸塵全覆蓋路徑規(guī)劃。墻上的仿真結果—圖6所示的行為后和實驗結果在圖6表明，該IRM有能力在非結構化的環(huán)境中執(zhí)行它的割草任務。
在圖5中傳感器的程序導航仿真如下。
5 . 超聲波測距技術基于小波變換
遺憾的是，由于環(huán)境的復雜性和噪聲的影響，實際接收到的多回波具有隨時間變化的特性，并且是一個典型的非平穩(wěn)信號。此外，在超聲波脈沖回聲混合噪聲是非高斯白噪聲，但噪聲，和與目標回波相關。TOF法不能在這樣的條件下直接使用。引用廣義相關方法估計時間延遲的[ 10 ]，我們把提出了廣義自相關方法基于小波變換的時延估計[ 11 ]出現在圖7。
圖7基于小波變換的廣義自相關延遲估計
其中（t）是母小波和（t）是女兒小波。該系數α是規(guī)模（或縮放
因素）和（τ）是時間位移。小波變換的信號x（t）是y（t）。實際上這是一個過濾過程使用大量的帶通濾波器的超聲回波等于的Q值，這相當于的白化濾波器對廣義相關方法的時間延遲的估計，為了消除輸入噪聲的影響做以下處理?？梢哉业?，作為
由于傅里葉變換關系自相關函數之間和他的力譜：
我們獲得的廣義自相關函數是：
最后，檢測到的峰值來完成TOF的估計和計算實際的超聲波速度。
圖8嘈雜的超聲回波
圖9基于小波去噪的回聲
圖10自相關函數
圖11峰值檢測
嘈雜的超聲回波信號如圖8所示，和利用小波變換去噪后的超聲回波顯示
圖9。很明顯，該噪聲混入的超聲波回波經WT操作后得到有效地消除作。自動去除噪聲的超聲波回波的相關運算如圖10所示。圖11顯示了包絡線，通過希爾伯特變換。正如我們可以看到，如果每一個峰的橫坐標點確定，TOF估計可計算?？紤]的超聲回波衰減和高精度的要求在實踐中的需求，只有前4回波被用來估計TOF。在TOF估計的值是，，，，，，這是對稱于X軸。使用這種方法，估計超聲波速度可以計算出來。
到目前為止，障礙檢測和定位系統成功實現。運用該方法，障礙物檢測和定位系統已成功實施。
基于廣義自相關法小波變換，提出了實現實時超聲波速度測量，該方法可以消除溫度，濕度和風力的影響，超聲波速度測量可以在機器人工作的動態(tài)條件下完成。在這種傳感系統的基礎上，廣義自相關方法顯示出巨大潛力提供用于割草機器人一個強大的解決方案在動態(tài)的工作條件下。
6. 實驗結果
我們利用超聲波傳感器測量機器人和平面之間的距離。測量結果和實際距離如表一所示：
表一
超聲波傳感器的實驗數據（單位：厘米）
從表一中，我們可以看到，超聲波傳感器測量誤差在3%。
然后，基于廣義自相關法小波變換，提出了實現實時超聲波速度測量。
通過上述方法，我們再次測量機器人和平面對象距離的。測量結果與實際距離顯示在表二中。
表二
超聲波傳感器的基于小波變換的數據（單位：厘米）
基于小波變換的實驗結果表明，使用上述的測量誤差技術是小于1% 為5m范圍區(qū)域內，這種傳感系統的障礙物檢測和定位擁有巨大的潛力，能作為—個強大的解決方案用提高于割草機器人性價比在動態(tài)工作條件下。
7. 結論
在本文中，我們提出了一個多傳感器系統結合超聲波傳感器測量用于割草機器人導航。該傳感系統具有低成本，低功耗，高性能，使割草機器人機能映射未知環(huán)境。其有效性是通過仿真研究和實驗結果得到的。
使用不同種類的傳感器集成在傳感系統可以克服超聲波傳感器的盲區(qū)和多傳感器融合的鏡面反射的缺陷。
一種高精度超聲波測距技術的方法基于小波變換已被引入到改善更多的超聲波傳感器的測量精度準確的感官信息。該系統應用于割草機器人，證明了實驗的可靠性和實時性。
今后的工作將著眼于應用所提出的跟蹤技術的多傳感器融合方案應用于在非結構化環(huán)境中的機器人割草機控制全覆蓋路徑規(guī)劃[ 12 ]。
參考文獻
Ming Cong and Bo Fang School of Mechanical Engineering Dalian University of Technology Dalian 116024 China congm This work is supported by national natural science fund 50675027to Ming Cong Abstract This paper presents a multisensor system for combining measurements from ultrasonic sensors and navigation for robot mowers The proposed sensing system enables robot mowers to mapping unknown environments It is important for an autonomous robot mower to explore its surroundings in performing the task of localization and navigation for mowing Because of the complexity of the environment one simple kind of sensors is not sufficient for robot mower to accomplish these tasks We develop a robot mower equipped with DSP TMS320F2812 as its CPU The sensing system integrates with ultrasonic sensors infrared sensors collision sensors encoders a temperature sensor and an electronic compass A method of high accuracy ultrasonic ranging technology based on wavelet transform is reported to improve the measurement precision of ultrasonic sensors Simulation studies show that the proposed multisensor fusion method is very effective for the navigation of robot mowers Experimental results indicate that this sensing system based on generalized auto correlation method for obstacle detection and localization shows great potential for providing a high performance to price ratio and robust solution for robot mowers in dynamic working condition Index Terms multisensor fusion ultrasonic sensors robot mower mapping navigation I INTRODUCTION Lawn mowing is considered by many to be one of the most boring and tiring routine tasks The environmental robots are needed urgently to perform the task Some predictions indicate that the robot mowers will be one of the most promising personal robot applications and have substantial market in the world Therefore the concept of Intelligent Robot Mower IRM had been proposed for the first time in 1997 s annual conference of the OPEI Outdoor Power Equipment Institute 1 The robots mainly face to the general families to help the busy people and the hypodynamic old folks save the payments for hiring labours also remove people from noise pollen and danger of mowing blade The robot mowers serve for home care as the outdoor mobile robots actually kind of intelligent mechatronics devices for environment clean up 2 3 The important thing is that the robot mowers are representative of some area covering environmental robots used not only for indoor floor cleaning as in 4 but also in hazardous environments such as removing landmines cleaning up radiant points and prospecting for resources etc The robot mowers get great challenges differing from indoor mobile robots The robot mowers use sensors to understand environments as well as their real time states for obstacle avoidance map building location and navigation in the whole work area Because of the complexity of the environment one simple kind of sensors is not sufficient for robot mower to accomplish these tasks It is necessary to combine the observed sensor data coming from different sensors to reduce the uncertainties of the robot in any working environment To merge the information from the various sensors robust and real time sensor fusion is required 5 In cases of sensor error or failure multisensor fusion can also reduce uncertainty in the information and increase its reliability A sensing system of low cost low power consumption high performance is described The detecting range of ultrasonic sensors is 0 3m 5m they provide good range information However uncertainties in ultrasonic sensors caused by the specular reflection from environments make them less attractive The detecting range of infrared sensors is 0 02m 1m they can detect the obstacles within the ultrasonic sensor s blind zone In order to satisfy the needs of robot mowers for the low cost and high accuracy ranging technology the research on the high accuracy ultrasonic ranging technology based on wavelet transform WT is reported to improve the measurement precision of ultrasonic sensors Measurement data gathered from the sensing system are integrated to avoid the robot mower from unknown obstacles and plan an optimum reliable and realizable plan completely coverage of entire working area Finally simulation studies and experimental results show the effectiveness of the sensing system for the navigation obstacle detection and localization of robot mowers II SYSTEM HARDWARE OF IRM The IRM uses DSP TMS320F2812 as its CPU including four units vehicle system cutting system sensing system and control system The sensing system is used to collect the external dynamic information of the working environment for obstacle avoidance map building navigation and localization It is also used to detect vehicle system s movement parameters and cutting mechanism s working status The controller compares the acquired information with the database and then sends out revisory and accurate command to the robot to perform its tasks The hardware of the IRM is shown in Fig 1 Multisensor Fusion and Navigation for Robot Mower 978 1 4244 1758 2 08 25 00 2008 IEEE 417 Proceedings of the 2007 IEEE International Conference on Robotics and Biomimetics December 15 18 2007 Sanya China Fig 1 Hardware overview of IMR The robot must be physically strong computationally fast behaviourally accurate and safety It should have the ability to perform on its own and required no human intervention during the whole or most part of the mowing period The IRM is modularized designed and each unit of the IRM is relatively independent Modularized design makes the maintenance much easier Any broken unit of the IRM can be replaced directly without influencing the functions of other units III SENSING SYSTEM A Ultrasonic Sensor Unit Because ultrasonic sensors can provide good range information based on the time of the flight TOF principle mainly due to their simplicity and relatively low cost they have been widely used in mobile robots for obstacle avoidance map building and so on This type of external sensor is very good in obstacles distance measurement The main lobe of the sensitivity function is contained within an angle of 20 degrees as shown in Fig 2 6 A number of tests showed that the range accuracy of the sensors is in the order of 2cm Fig 2 Typical intensity distribution of an ultrasonic sensor On IRM we set up a sensor array which consists of 12 ultrasonic sensors spaced 30 degrees apart The ultrasonic signals can cover all the space around and satisfy the space requirement about which robot can detect the environmental signals Classical techniques used in ultrasonic transducers are based on TOF measurement which calculates the distance of the nearest reflector using the speed of sound in air and the emitted pulse and echo arrival times The distance d to a reflected object is calculated by 2dct 1 where c is the speed of sound and t is the time of flight The TOF method produces a range value when the echo amplitude first exceeds the threshold level after transmitting ignoring a second echo from a further reflector The ultrasonic sensor unit includes a trigger pulse generation unit a multi channel selection unit and an echo receiving unit A sensor interface circuitry designed to send and receive ultrasonic sound pulses catches always the first returning echo The range data related to an object is considered to be on the conic axes even if it is located off the axes The ultrasonic wave typically has a frequency between 40 and 180 kHz and the frequency of the ultrasonic sensors used in the system is 40 kHz The beam angle is 20 degrees The 40 kHz PWM pulse is generated by the general purpose timer unit of DSP To drive the transmitter effectively and not to bring much vibration an 8 cycle burst of ultrasound at 40 kHz is sent out once a time When the ultrasonic pulse is emitted the sensor will experience ringing Ringing caused by the transmitted pulse can cause the receiver to detect a false echo This problem is solved by not enabling the capture interrupt of DSP until a delay interval has passed This means that the ranger can not detect an object whose distance from the sensor is less than half the distance that sound travels during the delay interval This is the blind zone of the ultrasonic sensor as shown in Fig 3 Trigger pulse Emitted signal Received signal TOF Blind zone Echo Fig 3 The sketch map of ultrasonic transmission and reception B Infrared Sensor Unit and Other Sensors To overcome the ultrasonic sensor s blind zone infrared sensors are added The infrared sensors can detect obstacles within 20cm which patch up the problem caused by the blind zone problem of ultrasonic sensors This unit has 16 infrared sensors Each infrared range finder has a conic view of 6 degrees which is the main lobe of the sensitivity function This sensor has a useful measuring range of a target up to about one meter with high accuracy A number of tests showed that the range accuracy of the sensors is in the order of lcm In order to save the DSP s resource 16 infrared sensors are connected with DSP TMS320F2812 s data interface 418 instead of the IO interface This kind of architecture can also read the sensors status at the same time ensuring the real time capability of the system A sensor interface circuitry designed to send and receive infrared pulses catches always the first retuning echo to process its amplitude Robot mower works in an outdoor environment where the temperature changes rapidly The changing of temperature will affect the speed of sound Therefore a temperature sensor is used to guarantee the precision of the ultrasonic sensor Collision sensor is a group of sensitive swatches which used to prevent the damage caused by unexpected collision Because moist environment do harm to the circuit of the IRM humidity sensors are introduced to detect the humidity of the environment Although these sensors are not absolutely necessary for an autonomous robot mower they can provide helpful functions to make the work availability and safety IV SENSOR BASED NAVIGATION A Mapping As seen in Fig 4 a reference direction x is defined and the robot coordinates are shown as R x R y By the help of an electronic compass built in on the robot 7 the angle i which is the ith sensor s angle from the 1st sensor can be easily measured Actually if only the angle S heading angle of the robot is measured other sensor angles can be found as iSi 2 where i is the angle to the our world coordinate center The number of maximum sensor group on the ultrasonic ring is n and the radius is r in our system n 12 and r 0 25m The distance between the origin and the center of the ring is R and reference angle to the center is The reference position of the robot s center is R x R y The distance from the origin to object which is detected by the ith sensor data on the two dimensional plane is called i R Now let i dm denote measured value which is combined data from the ultrasonic and infrared sensors for the exact distance i R There will be an error i between these values as iii dm d 3 In this work we naturally assume that i is a uniform random variable in the range of W W Here W denotes the maximum distance measurement error Here the problem is given R x R y r 12 n g34 and 12 n dm dm dmg34 to estimate the coordinates of the occupied cells i x and i y or equivalently i R in most efficient way The equations involving the detected object can be written as 222 cos sin iR i i R i i Rxrd yrd 4 22 2 2 cos sin iii RR rd rdx y 22 2 2 cos ii R R R rd rd 5 y x x y R R g455 d d O Fig 4 The robot position on x y section The equations involving the robot due to the object can be written as 222 cos sin iiii i Rxrd yrd 6 222 2 2 cos sin ii i ii ii i Rxy rd rdx y If we define the positions as 11 TT in Ppp p xy g34 then we have 22 2 2 cos sin ii ii ii R R rd rd y P 7 After the inserting the 2 i R in 2 R cos cos sin iiii rd R y P 8 Here again we have n such equations And we write them in matrix form i mAP 9 And if we introduce new matrix as cos sin iiii LP and 0 0 then 10 can be written as 111 1 2 cos cos R nRn nn rdm R L p L rdm R L p g170g186g170 g186g170g186 g171g187g171 g187g171g187 g171g187g171 g187g171g187 g171g187g171 g187g171g187 g171g187g171 g187g171g187 g171g187g171 g187g171g187 g171g187g171 g187g171g187 g172g188g172 g188g172g188 Here if we perform the least squares estimate for i P we obtain 1 TT lsq i PAAAm 11 Thus we find the best squares estimate of the positions B Simulation Studies Sensor based navigation has been tested with simulation to shown the usefulness of this sensor fusion method in the two environments respectively as shown in Fig 5 and Fig 6 The mower has been primarily tested in a structured laboratory as shown in Fig 5 Start at 0 3m 0 5m 0degree a virtual 419 robot was driven around a virtual square corridor one time The walls in the artificial environment are denoted by the real map The entire vehicle is self contained It has a maximum travel speed on 0 4 m s The laboratory area was surveyed out to a 10cm grid with accuracy better than about 1cm To extract the mapping a start and goal points were presented The robot position and orientation were established by the electronic compass 8 Fig 5 Data collection and navigation result in structured environment The result in Fig 5 demonstrates the mapping quality and the usefulness of this sensor fusion method In the tests we find that the average error in estimating the position of the obstacles in the environment was in the range of 0 2 0 2 m In the simulations we see that lsq i P in 11 obtained does not satisfy ilsqi RP which actually should In the case a better estimate for the positions can be given as i ei lsqi lsq i R PP P 12 In this case estimate for the angle i does not change but the estimate for distance i R is scaled to it best estimate Therefore for the position the distance estimate i R remains the same as before while the least squares estimate works only for the angle i Simulations show that this way produces more accurate results Fig 6 The simulation result of wall following behavior Wall following was selected for the initial problem domain because it is a fairly simple problem to set up and evaluate 9 It also lays the groundwork for more complex problem domains such as maze traversal mapping and complete coverage path planning which is used on lawn mowing and vacuuming The simulation result of wall following behavior shown in Fig 6 and the experimental result in Fig 6 demonstrate that the IRM have the capability to perform its mowing task in unstructured environment The program of sensor based navigation simulation in Fig 5 is given below Sub Main Dim PI Fcr Fct X target Y target X Y As Single Dim X grid Y grid i j C As Integer Dim Frx Fry d dist targ rot Fx Fy As Single Dim Fcx Fcy Rx Ry As Single PI 3 1415927 Fcr 1 Fct 1 X target GetMarkX 0 Y target GetMarkY 0 SetCellSize 0 0 1 Set cell size 10 cm x 10 cm SetTimeStep 0 1 Set simulation time step of 0 1 seconds Do Start main loop X GetMobotX 0 Present mobot coordinates in meters Y GetMobotY 0 X grid CoordToGrid 0 X indexes of cells where the Y grid CoordToGrid 0 Y mobot center is MeasureRange 0 1 3 Perform a range scan and update the Certainty Grid max cell value 3 Frx 0 Fry 0 Each ocuppied cell inside the windows of 33 x 33 cells applies a repulsive force to the mobot For i X grid 16 To X grid 16 For j Y grid 16 To Y grid 16 C GetCell 0 i j If C 0 Then d Sqr X grid i 2 Y grid j 2 If d 0 Then Frx Frx Fcr C d 2 X grid i d Fry Fry Fcr C d 2 Y grid j d End If End If Next Next dist targ Sqr X X target 2 Y Y target 2 Fcx Fct X target X dist targ Fcy Fct Y target Y dist targ Rx Frx Fcx Ry Fry Fcy rot RotationalDiff 0 X Rx Y Ry shortest rotational difference between current direction of travel and direction of vector R SetSteering 0 0 5 3 rot mobot turns into the direction of R at constant speed and steering rate proportional to the rotational difference StepForward Loop Until dist targ 0 1 Loop until mobot reaches the target End Sub 420 V ULTRASONIC RANGING TECHNOLOGY BASED ON WT Unfortunately the practical received multi echoes has time varying property and is a typical non stationary signal because the influence of the environmental complexity and the noise Furthermore the noise mixed in the ultrasonic pulse echo is Non Gaussian white noise but colored noise and correlated with the target echo The TOF method can not be used directly in such conditions Referencing the generalized correlation method for estimation of time delay 10 we put forward the generalized auto correlation method for estimation of time of flight based on wavelet transform 11 and present in Fig 7 Fig 7 Delay estimation of generalized auto correlation based on WT Where t is the mother wavelet and a t is the daughter wavelet The coefficient is the scale or scaling factor and is the time displacement The wavelet transform of the signal x t is yt Actually this is a filtering process of the ultrasonic echo using a multitude of bandpass filters of equal Q which is equivalent to the whitening filter of the generalized correlation method for estimation of time delay in order to eliminate the input noise which can influence the following processing yy R can be found as yy xx a a R Eyt yt R t t t As there has the relationship of Fourier transform between auto correlation function yy R and his power spectrume 2 yy yy xx xx GFRG aaG a We obtain the generalized auto correlation function as Last the peak values of yy R are detected to accomplish the estimation of TOF and calculate the real ultrasonic velocity Fig 8 Noisy ultrasonic echo Fig 9 Denoised echo using WT Fig 10 Auto correlation function yy R Fig 11 Peak detection The noisy ultrasonic echo is shown in Fig 8 and the denoised ultrasonic echo by wavelet transform is shown in Fig 9 It is obvious that the noise mixed in the ultrasonic echo is effectively eliminated after WT operation The auto correlation operation yy R of the denoised ultrasonic echo is shown in Fig 10 Fig 11 shows the envelope of yy R through Hilbert transform As we can see if the abscissa of every peak point is determined the estimation of TOF g109 ND can be calculated Considered the attenuation of the ultrasonic echo and the demand of the high precision in practice only the former four echoes are used to estimate the TOF The values of the TOF estimation are g110g110 g109 g108 g109 g109 3 2 2 3DDDDDD which are symmetrical to the x axis Using this method the estimation of the ultrasonic velocity can be calculated So far an obstacle detection and localization system has been implemented successfully By means of above method an obstacle detection and localization system has been implemented successfully The generalized auto correlation method based on wavelet transform is put forward to realize the real time ultrasonic velocity measurement and this method can 11 22 gj j yy yy g yy RG Ged g179g179 421 eliminate the influence of temperature humidity and wind on ultrasonic velocity measurements when the robots are working in dynamic condition And this sensing system based on generalized auto correlation method shows great potential for providing a robust solution for robot mowers in dynamic working condition VI EXPERIMENTAL RESULTS We measure the distance between the robot and plane objects using the ultrasonic sensors The measured results and the actual distances are shown in TABLE I TABLE I THE EXPERIMENTAL DATA OF THE ULTRASONIC SENSORS unit cm Actual distance Measured value1 Measured value2 Average error 30 30 62 30 61 2 50 40 40 70 41 69 1 73 50 50 64 50 67 1 31 60 60 73 60 73 1 22 70 70 81 70 84 1 19 80 81 09 81 04 1 33 90 91 10 91 13 1 24 100 98 82 99 15 1 02 150 148 24 148 37 1 13 200 201 85 201 85 0 93 250 252 71 252 74 1 09 300 302 52 302 58 0 85 350 347 63 347 61 0 68 400 405 75 405 77 1 44 450 456 22 456 26 1 39 500 508 87 508 90 1 77 From TABLE I we can see that the measurement error of the ultrasonic senso