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1、外文翻譯 ? An?adaptive?dynamic?controller?for?autonomous?mobile?robot??rajectory?tracking abstract ??????This?paper?proposes?an?adaptive?controller?to?guide?an?unicycle-like?mobile?robot during?trajectory?tracking.?Initially,?the?desired?values?of?the?linear?and?angular velocities?are?generated,

2、?considering?only?the?kinematic?model?of?the?robot.?Next,such?values?are?processed?to?compensate?for?the?robot?dynamics,?thus?generating?the commands?of?linear?and?angular?velocities?delivered?to?the?robot?actuators.?The parameters?characterizing?the?robot?dynamics?are?updated?on-line,?thus?providin

3、g smaller?errors?and?better?performance?in?applications?in?which?these?parameters?can vary,?such?as?load?transportation.?The?stability?of?the?whole?system?is?analyzed?using Lyapunov?theory,?and?the?control?errors?are?proved?to?be?ultimately?bounded.Simulation?and?experimental?results?are?also?presen

4、ted,?which?demonstrate?the?good performance?of?the?proposed?controller?for?trajectory?tracking?under?different?load conditions. ??????1.?Introduction ? Among?different?mobile?robot?structures,?unicycle-like?platforms?are?frequently adopted?to?accomplish?different?tasks,?due?to?their?good?mob

5、ility?and?simple configuration.?Nonlinear?control?for?this?type?of?robot?has?been?studied?for?several years?and?such?robot?structure?has?been?used?in?various?applications,such?as??surveillance?and?floor?cleaning.?Other?applications,?like?industrial?load?transportation using?automated?guided?vehicles

6、?(AGVs)?automatic?highway?maintenance?and construction,?and?autonomous?wheelchairs,?also?make?use?of?the?unicycle-like?structure.?Some?authors?have?addressed?the?problem?of?trajectory?tracking,?a?quite important?functionality?that?allows?a?mobile?robot?to?describe?a?desired?trajectory when?accomplis

7、hing?a?task. ??An?important?issue?in?the?nonlinear?control?of?AGVs?is?that?most?controllers designed?so?far?are?based?only?on?the?kinematics?of?the?mobile?robot. However,?when?high-speed?movements?and/or?heavy?load?transportation?are required,?it?becomes?essential?to?consider?the?robot?dynami

8、cs,?in?addition?to?its kinematics.?Thus,?some?controllers?that?compensate?for?the?robot?dynamics?have?been proposed. ?As?an?example,?Fierro?and?Lewis?(1995)?proposed?a?combined?kinematic/torque control?law?for?nonholonomic?mobile?robots?taking?into?account?the?modeled?vehicle dynamics.?The?control

9、?commands?they?used?were?torques,?which?are?hard?to?deal?with?when?regarding?most?commercial?robots.?Moreover,?only?simulation?results?were reported.?Fierro?and?Lewis?(1997)?also?proposed?a?robust-adaptive?controller?based?on neural?networks?to?deal?with?disturbances?and?non-modeled?dynamics,?althou

10、gh not?reporting?experimental?results.?Das?and?Kar?(2006)?showed?an?adaptive?fuzzy logic-based?controller?in?which?the?uncertainty?is?estimated?by?a?fuzzy?logic?system and?its?parameters?were?tuned?on-line.?The?dynamic?model?included?the?actuator dynamics,?and?the?commands?generated?by?the?controlle

11、r?were?voltages?for?the?robot motors. ?The?Neural?Networks?were?used?for?identification?and?control,?and?the?control signals?were?linear?and?angular?velocities,?but?the?realtime?implementation?of?their??solution?required?a?high?-performance?computer?architecture?based?on?a?multiprocessor system.

12、 On the other hand, De La Cruz and Carelli(2006) proposed a dynamic model using linear and velocities as inputs,and showed the design of a trajectory tracking controller based on their model. One advantage of their controller is that its parameters are directly related to the robot parameters.

13、 However, if the parameters are not correctly identified or if they change with time,for example, due to load variation, the performance of their controller will be severely affected.To reduce performance degradation, on-line parameter adaptation becomes quite important in applications in which the

14、robot dynamic parameters may vary, such as load transportation. It is also useful when the knowledge of the dynamic parameters is limited or does not exist at all.In this paper, an adaptive trajectory-tracking controller based on the robot dynamics is proposed, and its stability property is proved

15、using the Lyapunov theory. The design of the controller was divided in two parts, each part being a controller itself. The first one is a kinematic controller, which is based on the robot kinematics,and the second one is a dynamic controller, which is based on the robot dynamics.The dynamic contro

16、ller is capable of updating the estimated parameters, which are directly related to physical parameters of the robot. Both controllers working together form a complete trajectory-tracking controller for the mobile robot. The controller shave been designed based on the model of a unicycle-like mobile

17、 robot proposed by De La Cruz and Carelli A s-modification term is applied to the parameter- updating law to prevent possible parameter drift. The asymptotic stability of both the kinematic and the dynamic controllers is proven. Simulation results show that parameter drift does not arise even when

18、 the system works for a long period of time. Experimental results regarding such a controller are also presented and show that the proposed controller is capable of updating its parameters in order to reduce the tracking error. An experiment dealing with the case of load transportation is also prese

19、nted, and the results show that the proposed controller is capable of guiding the robot to follow a desired trajectory with a quite small error even when its dynamic parameters change. The main contributions of the paper are: (I) the use of a dynamic model whose in put commands are velocities, whic

20、h is usual in commercial mobile obots, while most of the works in the literature deals with torque commands; (2) the design of an adaptive controller with a s-modification term, which makes it robust, with the corresponding stability study for the whole adaptive control system; and (3) the presentat

21、ion of experimental results showing the good performance of the controller in a typical industrial application, namely load transportation. 2. Dynamic model In this section, the dynamic model of the unicycle-like mobile robot proposed by De La Cruz and Carelli (2006) is reviewed. Fig. 1dep

22、icts the mobile robot, its parameters and variables of interest. u and o are the linear and angular velocities developed by the robot, respectively, G is the center of mass of the robot, C is the position of the castor wheel, E is the location of a tool on board the robot, h is the point of interest

23、 with coordinates x and y in the XY plane, c is the robot orientation,and a is the distance between the point of interest and the central point of the virtual axis linking the traction wheels (point B). The complete mathematical model is written as. whеrе иg аnd о аrе thе dе??rеd vаluе? оf thе l?

24、nеаr аnd аngulаr vеlос?t?е?,respectively, and represent the input signals of the system.A vector of identified parameters and a vector of parametric uncertainties are associated with the above model of the mobile robot, which are, respectively. where dx and dy are functions of the slip velociti

25、es and the robot orientation, duand do are functions of physical parameters as mass, inertia, wheel and tire diameters,parameters of the motors and its servos, forces on the wheels, etc., and are consideredas disturbances. The equations describing the parameters h were firstly presented in, and are

26、reproduced here for convenience. They are It is important to point out that a nonholonomic mobile robot must be oriented according to the tangent of the trajectory path to track a trajectory with small error. Otherwise, the control errors would increase. This is true because the nonholonomic p

27、latform restricts the direction of the linear velocity developed by the robot. So, if the robot orientation is not tangent to the trajectory, the distance to the desired position at each instant will increase. The fact that the control errors converge to a bounded value shows that robot orientation

28、does not need to be explicitly controlled, and will be tangent to the trajectory path while the control errors remain small. 3. Experimental results To show the performance of the proposed controller several experiments andsimulations were executed. Some of the results are presented in t

29、his section. The .proposed controller was implemented on a Pioneer 3-DX mobile robot, which admits linear and angular velocities as input reference signals, and for which the distance b inFig. 2 is nonzero. In the first experiment, the controller was initialized with the dynamic parametersof a Pio

30、neer 2-DX mobile robot, weighing about 10 kg (which were obtained via identification). Both robots are shown in Fig.3,where the Pioneer 3-DX has a laser sensor weighing about 6 kg mounted on its platform, which makes its dynamics significantly different from that of the Pioneer2-DX. In the experime

31、nt, the robot starts at x=0.2m and y=0.0 m, and should follow aeircular trajectory of reference. The center of the reference circle is at x =0.0m and y=0.8 m. The reference trajectory starts at x=0.8m and y=0.8m and follows a circle having a radius of 0.8 m. After 50 s, the reference trajectory sudd

32、enly changes to a circle of radius 0.7 m. After that, the radius of the reference trajectory alternates between 0.7 and 0.8m each 60 s. presents the reference and the actual robot trajectories for a part of the experiment that includes a change in the trajectory radius, In this case, the parameter

33、updating was active.shows the distance errors for experiments using the proposed controller, wit hand without parameter updating, to follow the described reference trajectory. The distance error is defined as the instantaneous distance between the reference and the robot position. Notice the high in

34、itial error, which is due to the fact that the reference trajectory starts at a point that is far from the initial robot position. First, the proposed controller was tested with no parameter updating. It can be seen in Fig. 5 that, in this .case, the trajectory tracking error exhibits a steady-state

35、 value of about 0.17 m, which does not vary even after the change in the radius of the reference trajectory. This figure also presents the distance error for the case in which the dynamic parameters are updated. By activating the parameter-updating, and repeating the same experiment,the trajectory t

36、racking error achieves a much smaller value, in comparison with the case in which is no ig .3. the robpts uesd in the experiments. 4. Concusion An adaptive trajectory-tracking controller for a unicycle-like mobile robot was designed and fully tested in this work. Such a controller is divided in

37、 two parts, which are based on the kinematic and dynamic models of the robot. The model on side red takes the linear and angular velocities as input reference signals, which is usual when regarding commercial mobile robots. It was considered a parameter-updating law for the dynamic part of the contr

38、oller, improving the system performance. A s-modification term was included in the parameter up dating law to prevent possible parameter drift. Stability analysis based on Lyapunov theory was performed for both kinematic and dynamic controller. For the last one, stability was proved considering a

39、parameter-updating law with and without the s-modification term.Experimental results were presented, and showed the good performance of the proposed controller for trajectory tracking when applied to an experimental mobile robot. A long-term simulation result was also presented to demonstrate that

40、the updated parameters converge even if the system works for a long period of time. The results proved that the proposed controller is capable of tracking a desired trajectory with as mall distance error when the dynamic parameters are adapted. The importance of on-line parameter updating was illust

41、rated for the cases where the robot parameters are. not exactly known or might change from task to task. A possible application for the proposed controller is to industrial AGVs used for load transportation, because on-line parameter adaptation would maintain small tracking error even in the case of

42、important changes in the robot load. 一種用于自主移動機器人目標跟蹤的自適應(yīng)動態(tài)控制器 摘要 本文提出了一種自適應(yīng)控制器來指導(dǎo)單輪移動機器人進行軌跡跟蹤。在初始階段，只考慮機器人的運動學(xué)模型，即可得到所需的線速度和角速度。然后，對這些值進行處理以補償機器人的動力學(xué)，從而生成傳遞給機器人執(zhí)行器的線速度和角速度命令。表征機器人動力學(xué)的參數(shù)是在線更新的，因此在這些參數(shù)可以變化的應(yīng)用中，如負載運輸，提供了更小的誤差和更好的性能。利用李亞普諾夫理論分析了整個系統(tǒng)的穩(wěn)定性，證明了控制誤差是有界的。仿真和實驗結(jié)果表明，該控制器在不同負載條件下具有良好的跟蹤性能。

43、 1 .介紹 在不同的移動機器人結(jié)構(gòu)中，由于單環(huán)類平臺具有良好的機動性和簡單的配置，因此常被用于完成不同的任務(wù)。針對這類機器人的非線性控制研究已有多年，該機器人結(jié)構(gòu)已應(yīng)用于監(jiān)視、地板清洗等諸多領(lǐng)域。其他應(yīng)用，如使用自動導(dǎo)向車輛(AGVs)的工業(yè)負荷運輸，自動公路維護和建設(shè)，以及自動輪椅，也使用了獨輪車式的結(jié)構(gòu)。一些作者已經(jīng)解決了軌跡跟蹤的問題，這是一個非常重要的功能，允許移動機器人在完成任務(wù)時描述所需的軌跡。 agv非線性控制的一個重要問題是，目前設(shè)計的控制器大多只基于移動機器人的運動學(xué)。然而，當(dāng)需要高速運動和/或重載運輸時，除了考慮機器人的運動學(xué)外，還必須考慮機器人的動力學(xué)。因

44、此，提出了一些補償機器人動力學(xué)的控制器。 Fierro和Lewis(1995)以非完整移動機器人為例，提出了一種考慮建模車輛動力學(xué)的運動學(xué)/轉(zhuǎn)矩聯(lián)合控制律，其控制指令為力矩，對于大多數(shù)商用機器人來說，力矩是難以處理的。此外,只報道。仿真結(jié)果Fierro和劉易斯(1997)也提出了一個基于神經(jīng)網(wǎng)絡(luò)的魯棒自適應(yīng)控制器來處理干擾和non-modeled動態(tài),雖然不是報告實驗結(jié)果。Das和冰斗(2006)顯示一個自適應(yīng)模糊控制器基于邏輯的模糊邏輯系統(tǒng)估計的不確定性和參數(shù)調(diào)優(yōu)在線。動態(tài)模型包括執(zhí)行器動力學(xué)，控制器生成的命令為機器人電機的電壓。神經(jīng)網(wǎng)絡(luò)用于辨識和控制，控制信號為線速度和角速度，但其實時實

45、現(xiàn)要求基于多處理器系統(tǒng)的高性能計算機體系結(jié)構(gòu)。 另一方面，De La Cruz和Carelli(2006)提出了一個以線性和速度為輸入的動態(tài)模型，并展示了基于該模型的軌跡跟蹤控制器的設(shè)計。其控制器的一個優(yōu)點是其參數(shù)與機器人參數(shù)直接相關(guān)。 但是，如果參數(shù)識別不正確，或者隨著時間的推移而變化，例如由于負載的變化，會嚴重影響控制器的性能。為了減少性能下降，在線參數(shù)自適應(yīng)在機器人動態(tài)參數(shù)變化的應(yīng)用中變得非常重要，例如負載運輸。 當(dāng)動態(tài)參數(shù)的知識有限或根本不存在時，它也很有用。本文提出了一種基于機器人動力學(xué)的自適應(yīng)軌跡跟蹤控制器，并用李亞普諾夫理論證明了其穩(wěn)定性。 控制器的設(shè)計分為兩部分，每一部

46、分都是控制器本身。第一個是基于機器人運動學(xué)的運動控制器，第二個是基于機器人動力學(xué)的動態(tài)控制器。動態(tài)控制器能夠更新與機器人物理參數(shù)直接相關(guān)的估計參數(shù)。這兩個控制器共同工作，形成了一個完整的移動機器人軌跡跟蹤控制器?；贒e La Cruz和Carelli提出的單環(huán)類移動機器人模型設(shè)計了控制器，并將s修正項應(yīng)用于參數(shù)更新律中，以防止可能出現(xiàn)的參數(shù)漂移。證明了運動控制器和動態(tài)控制器的漸近穩(wěn)定性。仿真結(jié)果表明，即使系統(tǒng)工作時間較長，也不會產(chǎn)生參數(shù)漂移。實驗結(jié)果表明，該控制器具有較強的參數(shù)更新能力，能夠有效地降低跟蹤誤差。實驗結(jié)果表明，該控制器能夠在動態(tài)參數(shù)變化的情況下，以較小的誤差引導(dǎo)機器人沿預(yù)定軌跡

47、運動。 本文的主要貢獻是:(I)使用了一個動態(tài)模型，該模型的put命令中包含速度，這在商用移動機器人中很常見，而文獻中的大部分工作都是關(guān)于扭矩命令的;(2)設(shè)計了具有修改項的自適應(yīng)控制器，使其具有魯棒性，并對整個自適應(yīng)控制系統(tǒng)進行了相應(yīng)的穩(wěn)定性研究;(3)實驗結(jié)果表明，該控制器在典型的工業(yè)應(yīng)用，即負荷輸送中具有良好的性能。 2. 動態(tài)模型 本節(jié)對De La Cruz和Carelli(2006)提出的單環(huán)類移動機器人的動力學(xué)模型進行了綜述。圖1描述了移動機器人及其感興趣的參數(shù)和變量。u和o線速度和角速度都是由機器人,分別G是機器人的質(zhì)心,C是castor輪的位置,E是一個工具的位置上機器人

48、,h是感興趣的點與XY平面的x和y坐標,C是機器人取向和興趣點之間的距離和中心點的虛擬軸連接牽引輪(B點),寫成完整的數(shù)學(xué)模型。分別代表系統(tǒng)的輸入信號。上述移動機器人模型分別與確定的參數(shù)向量和參數(shù)不確定性向量相關(guān)聯(lián)，分別為其中dx和dy是滑移速度和機器人方向的函數(shù)，是質(zhì)量、慣量、車輪和輪胎直徑、電機及其伺服參數(shù)、車輪上的力等物理參數(shù)的函數(shù)，被認為是擾動。文中首先給出了參數(shù)h的描述方程，為了方便起見，在此重新給出。他們是需要指出的是，非完整移動機器人必須根據(jù)軌跡軌跡的切線進行定向，才能跟蹤誤差較小的軌跡。否則，控制誤差將會增加。這是真的，因為非完整平臺限制了機器人所發(fā)展的線速度方向。所以，如果機

49、器人的方向與軌跡不相切，那么每一瞬間到目標位置的距離就會增加。控制誤差收斂到有界值的事實表明，機器人的姿態(tài)不需要顯式控制，在控制誤差較小的情況下與軌跡軌跡相切。 3.實驗結(jié)果 為了驗證該控制器的性能，進行了實驗和仿真。本節(jié)將介紹一些結(jié)果。該控制器是在一個先進的3-DX移動機器人上實現(xiàn)的，該機器人以線速度和角速度作為輸入?yún)⒖夹盘?，距離b在圖中。2是零。 在第一個實驗中，控制器初始化為一個先鋒2-DX移動機器人的動態(tài)參數(shù)，重約10公斤(通過辨識得到)。兩個機器人如圖3所示，其中先鋒3-DX的平臺上安裝了一個重約6公斤的激光傳感器，這使得它的動力學(xué)特性與先鋒2- dx明顯不同。 在實驗中，機

50、器人從x=0.2m開始，y=0.0 m開始，應(yīng)遵循參考的圓周軌跡。參考圓的中心在x =0.0m和y=0.8 m處。參考軌跡從x=0.8m, y=0.8m開始，沿半徑為0.8m的圓運動。50秒后，參考軌跡突然變?yōu)榘霃綖?.7 m的圓。之后，參考軌跡半徑每60秒在0.7 ~ 0.8m之間變化。 給出了部分實驗機器人軌跡的參考和實際軌跡，其中包括軌跡半徑的變化，在這種情況下，參數(shù)更新是主動的。給出了該控制器在不進行參數(shù)更新的情況下，跟蹤所述參考軌跡的距離誤差。距離誤差定義為參考點到機器人位置的瞬時距離。注意初始誤差很大，這是由于參考軌跡從遠離初始機器人位置的點開始。首先，在不更新參數(shù)的情況下對該控

51、制器進行了測試。從圖5中可以看出，在這種情況下，軌跡跟蹤誤差的穩(wěn)態(tài)值約為0.17 m，即使在參考軌跡半徑改變后也沒有變化。該圖還顯示了動態(tài)參數(shù)更新時的距離誤差。通過激活參數(shù)更新，并重復(fù)相同的實驗，與ig .3不存在的情況相比，軌跡跟蹤誤差的值要小得多。這些機器人在實驗中使用。 4. 結(jié)論 設(shè)計了一種適用于單環(huán)類移動機器人的自適應(yīng)軌跡跟蹤控制器，并對其進行了全面測試?；跈C器人的運動學(xué)和動力學(xué)模型，將該控制器分為兩部分。側(cè)邊紅色的模型以線速度和角速度作為輸入?yún)⒖夹盘?，這在商用移動機器人中很常見。該方法被認為是控制器動態(tài)部分的參數(shù)更新律，提高了系統(tǒng)性能。 為了防止參數(shù)漂移，在參數(shù)更新

52、律中加入了s修正項。對運動控制器和動態(tài)控制器進行了基于李雅普諾夫理論的穩(wěn)定性分析。最后，證明了考慮參數(shù)更新律的穩(wěn)定性，其中包含和不包含s修正項。給出了實驗結(jié)果，并將該控制器應(yīng)用于實驗移動機器人的軌跡跟蹤中，取得了較好的效果。 仿真結(jié)果表明，即使系統(tǒng)工作時間較長，更新后的參數(shù)也會收斂。實驗結(jié)果表明，該控制器在動態(tài)參數(shù)調(diào)整的情況下，能夠以較小的距離誤差跟蹤目標軌跡。闡述了機器人參數(shù)在線更新的重要性。不完全知道或可能在不同的任務(wù)之間更改。該控制器的一個可能的應(yīng)用是用于工業(yè)agv的負荷運輸，因為即使在機器人負荷發(fā)生重要變化的情況下，在線參數(shù)自適應(yīng)也能保持較小的跟蹤誤差。 Raspberry?Pi?

53、3 2016?Raspberry?Pi?3?User?Guide By Ted Lebowski Copyright 2016 Ted Lebowski -All rights reserved. This document is geared towards providing exact and reliable information in regards to the topic and issue covered. The publication is sold with the idea that the publisher is not required to

54、 render accounting, officially permitted, or otherwise, qualified services. If advice is necessary, legal or professional, a practiced individual in the profession should be ordered. - From a Declaration of Principles which was accepted and approved equally by a Committee of the American Bar Associ

55、ation and a Committee of Publishers and Associations. In no way is it legal to reproduce, duplicate, or transmit any part of this document in either electronic means or in printed format. Recording of this publication is strictly prohibited and any storage of this document is not allowed unless wit

56、h written permission from the publisher. All rights reserved. The information provided herein is stated to be truthful and consistent, in that any liability,in terms of inattention or otherwise, by any usage or abuse of any policies, processes, or directions contained within is the solitary and utt

57、er responsibility of the recipient reader.Under no circumstances will any legal responsibility or blame be held against the publisher for any reparation, damages, or monetary loss due to the information herein,either directly or indirectly. Respective authors own all copyrights not held by the p

58、ublisher. The information herein is offered for informational purposes solely, and is universal as so.The presentation of the information is without contract or any type of guarantee assurance.The trademarks that are used are without any consent, and the publication of the trade markis without perm

59、ission or backing by the trademark owner. All trademarks and brands within this book are for clarifying purposes only and are the owned by the owners themselves, not affiliated with this document. ? Effective?use?of?Terminal?commands ??????Оnе?оf?thе?kеу?а?ресt??оf?u??ng?а?tеrm?nаl????bе?ng?аbl

60、е?tо?nаv?gаtе?уоur?f?lе system.?Firstly,?run?the?following?command:?ls?-la.?You?should?see?something?similar?to: ???The?Is?command?lists?the?contents?of?the?directory?that?you?are?currently?in?or?yourpresent?worki ng?directory.?The?-la?component?of?the?command?is?what's?known?as?a?flag'.Flags?mod

61、ify?the?com mand?that's?being?run.?In?order?to?navigate?to?other?directories?the change?directory?command,?cd?c an?be?used.?You?can?specify?the?directory?that?you?want??to?by?either?the?'absolute?or?the?'relative?p ath.?So?if?you?wanted?to?navigate?to?the?/pi directory,?you?could?either?do?cd?/

62、home/pi/?or?just??pi?if?you?are?currently?in?/home.?There?aresome ?special?cases?that?may?be?useful:?~?acts?as?an?alias?for?your?home?directory,?so~/Desktop?is?the?sa me?as?/home/pi/Desktop;?.?and?..?are?aliases?for?the?current?directory?and?the parent?directory?respectively,?e.g.?if?you?were?in

63、?/home/pi. Auto-detect command Rather than type every command, the terminal allows you to scroll through previous commands that you run by pressing the up or down keys on your keyboard. If you are writing the name of a file or directory as part of a command then the pressing tab :will a

64、ttempt to Auto complete the name of what you are typing. For example, if you have a file in a directory called Test File Name then pressing tab after typing 'T' will allow you to choose from all file and directory names beginning with an in the current directory,allowing you to choose Test Fil

65、e Name. Sudo privilege Some command that make permanent changes to the state of your system require you to have root privileges to run. The command temporarily gives your account (if you re not already logged in as root) the ability to run these commands, provided your user name is in a

66、 list of users . When you append sudo to the start of a command and press enter you will be asked for your password, if that is entered correctly then the command you want to run will be run using root privileges. Be careful, though some commands that require sudo to run can irreparably damage your system so be careful! Install Software or other utilities using apt-get Rather than using the Pi Store to download new software you can use the command apt-get, this is the 'packag