自動(dòng)化專業(yè)畢業(yè)設(shè)計(jì)外文翻譯--輸入力矩受限的機(jī)器人魯棒自適應(yīng)控制

1、<p><b>　　外文文獻(xiàn)原文</b></p><p>　　Limited torque input Robust Adaptive Tracking Control of Robot</p><p><b>　　Abstract</b></p><p>　　Based on input constraints

2、, a novel robust-adaptive tracking control algorithm is proposed for robot manipulators since stability if the standard adaptive control system is problematic when some disturbance exists. The proposed controller stabili

3、zes the system with some disturbance and guarantees asymptotic stability in the case if non-disturbance. Robust-adaptive algorithm can be received as the extension of the conventional adaptive scheme. The estimated param

4、eters enter the controller non-lin</p><p>　　Keywords: Adaptive control; robot manipulator; parametric uncertainties; robust-adaptive;</p><p>　　So far, almost all of the controller design is base

5、d on joint drive to produce any torque on the basis of; and is subject to the physical conditions, the output of the drive torque is limited, so the controller may lead to the control failure or deterioration of the qual

6、ity control.Therefore the controller design must take into account the limited joint drive dynamic capability. For example, the operation of the industry to help the robot, some parameters are uncertain or unknown,

7、adaptive </p><p>　　MANIPULATOR DYNAMIC MODEL</p><p>　　AND CHARACTERISTIC MODEL</p><p>　　Consider a robotic manipulator with n degrees of freedom. The continuous Lagrange dynamic mod

8、el is given by</p><p>　　Where q∈R n and ∈R n are the vector of generalized joint coordinates and velocity coordinates, respectively. The inertia matrix M(q)-MT(q)> 0 ，and there exist two constant positiv

9、e scalars M min and M max such that ≤ ≤, is the vector of commanded generalized force, and and G(q) are the terms due to Carioles, Centripetal and gravity forces. In actual application, the uncertain parameters and un-m

10、odeled dynamics usually exist in the established dynamic model in (1).</p><p>　　When the sample time is small enough, at instant t=k􀀅q and can be approximated by</p><p><b>　　and .

11、</b></p><p>　　Respectively Using the above relationships the discrete-time representation of (1) becomes</p><p><b>　　(2a)</b></p><p>　　Premultiplying (2a) by resul

12、ts in </p><p><b>　　where</b></p><p><b>　　,</b></p><p>　　and I denotes the unitary diagonal matrix with an appropriate dimension.</p><p>　　If the

13、 designed is continuous in t ,q and , then the solution (q,) of (1) will be continuously differentiable. Let and be ij-th element of matrix ; We define </p><p>　　and then ΔF1(k) can be expressed as</p&g

14、t;<p>　　For the ij-th element Δf1,ij(k) of matrix ΔF1(k)</p><p>　　we can get</p><p><b>　　= </b></p><p><b>　　= </b></p><p>　　with 0≤≤1,an

15、d,≈1 for a small sample time Ts . From (3), it can be seen that ΔF1(k)→0 as Ts converges to zero in a compact set of .Similar properties can also be achieved for the coefficient matrixes f2(k), and β (k) .</p><

16、;p>　　In a compact set of, the following properties can be deduced from (3) and the expressions of the coefficient matrixes of (2b):</p><p>　　Property 1: If the sample time Ts is small enough,then all coef

17、ficient matrixes of (2b) are slowly time varying;</p><p>　　Property 2: f1(k)→2I,f2(k)→ ?I and f1(k)+f2(k)→I, as the sample time Ts converges to zero. Then we can define the discrete equation (2b) with Prope

18、rties 1 and 2 as the robotic manipulator characteristic model.</p><p>　　MULTI-VARIABLE GSA CONTROLLER </p><p>　　WITH NN COMPENSATION</p><p>　　Discrete equation (2b) can be expressed

19、 as follows:</p><p><b>　　(4)</b></p><p><b>　　Where</b></p><p><b>　　,</b></p><p><b>　　,</b></p><p>　　e(k) de

20、notes the vector of white noise with zero mean. In the case of ≡0, and can be reduced to</p><p>　　Then the elements of q(k +1) can be expressed as </p><p><b>　　(5)</b></p>&

21、lt;p>　　where i = 1,…,n, (k+1)) is the element i of q(k +1), is the element i of e(k) and is the column i of the matrix </p><p><b>　　. </b></p><p>　　When the coefficient matrixes

22、are unknown, it can be estimated by</p><p>　　=π (q(k),q(k?1),...,u(k?1),...) , (6a)</p><p>　　where is the estimated coefficient matrix of Θ(k) at the instant t=kTs , and denotes an

23、 estimation operator. Considering the coefficient matrixes of the characteristic model being slowly time-varying, we can obtain the selected estimation operator by the weighted least squares method (WLS)[13], namely <

24、/p><p><b>　　,</b></p><p>　　with λ(k+1)=μ0λ(k)+(1?μ0), 0<μ0 ≤1, and the column i of the matrix.</p><p>　　Given a desired smooth trajectory , the adaptive control contro

25、ller is designed as follows </p><p><b>　　(7)</b></p><p>　　with the feed forward control law designed as</p><p><b>　　(7a)</b></p><p>　　and the mu

26、lti-variable GSAC feedback law as</p><p><b>　　(7b)</b></p><p>　　where is the tracking error andε(k) >0 is a small scalar that avoids the estimated matrix being singular. The term

27、 of will be designed later; L1 and L2 are golden-section coefficients, that is,</p><p><b>　　, ,</b></p><p>　　which satisfy the relationship L1+L2=1 and </p><p>　　Sub

28、stituting (7) into (2), we can get</p><p><b>　　(8)</b></p><p>　　and .Defining the tracking filtered error s(k +1) as and using the relationships L1+L2=1 and , (8) can be expressed as

29、</p><p>　　= (9)</p><p><b>　　Which</b></p><p>　　Assuming , , and </p><p>　　,if is selected as</p><p>　　then Δ(k) = 0 , and then (9) ca

30、n be written as</p><p><b>　　(10)</b></p><p>　　Since in Property 2 as Ts → 0 in a compact set of, a small sample time Ts can be selected such that the inequality can be satisfied. Th

31、erefore, the tracking filtered error s(k) asymptotically converges to zero in this case. The convergence of s(k) to zero in turn guarantees the convergence of q(k) to zero. Because of the dynamics of the estimator and th

32、e time-varying coefficients of the characteristic model, it is almost impossible to satisfy the above assumptions. Therefore, we can design a su</p><p><b>　　(11)</b></p><p>　　where

33、is the estimate of Δ(k) .</p><p>　　Assuming Δ(k) is smooth enough and bounded, it then can be approximated by the linearly parameterized NN to any required degree of accuracy [6,14]. Then the element Δi(k) o

34、f Δ(k) can be expressed as</p><p><b>　　(12)</b></p><p>　　where i= 1,…n, is the column i of the optimal NN weight matrix,.Activation functions</p><p>　　represent the bas

35、is function vector, which can be selected as any one of Gaussian radial basis, B-spine basis, Wavelet basis, and etc. [14], and δi (k) denotes the element I of the NN reconstruction error vectork δ(k), namely</p>

36、<p><b>　　.</b></p><p>　　Using compensation control law , (9) can be written as</p><p><b>　　(13)</b></p><p>　　Where is the estimate of , and </p>

37、<p>　　An estimate is now obtained by minimizing the cost function</p><p><b>　　(14)</b></p><p>　　After substituting (13) into (14), the gradient of the cost function in (14) is

38、 derived as</p><p><b>　　(15)</b></p><p>　　According to the gradient descent method the NN weight adaptation law can be designed as</p><p><b>　　(16)</b></p

39、><p>　　with α > 0 . Then the compensation control law in (11) can be written as</p><p><b>　　(17)</b></p><p>　　In view of the case the term can be simplified as</p&

40、gt;<p>　　4. SIMULATION RESULTS</p><p>　　Consider a planar, two-link, articulated manipulator as in [3] (as presented in Fig. 1), whose dynamics can be written explicitly as</p><p><b&g

41、t;　　Where</b></p><p><b>　　With,</b></p><p><b>　　,,</b></p><p><b>　　and .</b></p><p>　　In the simulation, the sample time Ts =

42、2ms, the initial values and the parameters of the estimator and the controller are selected as P(0) =1×I,λ(0) = 0.96 , μ0 = 0.98 , the anti-singularity factors (k) can be designed as ε(k) =5×exp(?kTs).</p>

43、;<p>　　According to the Property 2, the initial estimate values of the characteristic model coefficient matrixes are chosen as </p><p>　　A basis set of activation function y(k) can be selected as in t

44、he Random Vector Function Link net [16], namely,</p><p><b>　　(19)</b></p><p>　　with V a randomly selected matrix and X(k) the NN input vector. can be chosen as the hyperbolic tangen

45、t function, and X(k) can be taken as</p><p><b>　　?? .</b></p><p>　　The adaptation gain for the NN weight tuning is taken as α = 0.005 , and the initial values of the weights are set

46、to zeros.</p><p>　　The desired trajectory is chosen as</p><p><b>　　(20)</b></p><p><b>　　外文翻譯</b></p><p>　　輸入力矩受限的機(jī)器人魯棒自適應(yīng)控制</p><p>

47、<b>　　摘要</b></p><p>　　在輸入力矩受限的情況下，提出一種全的簡(jiǎn)單魯棒自適應(yīng)控制算法。當(dāng)參數(shù)的估計(jì)范圍包含其真實(shí)值時(shí)，證明了閉環(huán)系統(tǒng)的漸進(jìn)穩(wěn)定跟蹤；當(dāng)有干擾存在，常規(guī)參數(shù)估計(jì)自適應(yīng)控制算法不能實(shí)現(xiàn)穩(wěn)定控制時(shí)，本算法仍然使系統(tǒng)穩(wěn)定。在本算法中，所估計(jì)的參數(shù)在跟蹤控制前饋?lái)?xiàng)中表現(xiàn)為非線性，這是區(qū)別于常規(guī)參數(shù)估計(jì)自適應(yīng)算法的一個(gè)最重要特征。因此本算法控制器的設(shè)計(jì)更有靈活性，另一

48、方面獲得更好的控制品質(zhì)和魯棒性，特別是對(duì)參數(shù)估計(jì)域軌跡誤差即參數(shù)估計(jì)崔無(wú)的強(qiáng)魯棒性，均為仿真算例所驗(yàn)證。</p><p>　　關(guān)鍵詞：自適應(yīng)控制；自適應(yīng)系統(tǒng)；機(jī)器人；魯棒自適應(yīng)控制；輸入力矩受限 </p><p><b>　　1 前言</b></p><p>　　迄今為止，幾乎所有控制器設(shè)計(jì)都建立在關(guān)節(jié)驅(qū)動(dòng)器能產(chǎn)生任意力矩的基礎(chǔ)上；而實(shí)際上受物

49、理?xiàng)l件限制，驅(qū)動(dòng)器的輸出力矩是有限的，這樣的控制器可能導(dǎo)致控制失敗或控制品質(zhì)的惡化。因此控制器的設(shè)計(jì)必須考慮到關(guān)節(jié)驅(qū)動(dòng)器的有限動(dòng)能力。</p><p>　　對(duì)于例如幫運(yùn)作業(yè)的機(jī)器人，有些參數(shù)是不確定或者不可知的，基于估計(jì)參數(shù)自適應(yīng)控制是處理此類問(wèn)題的主要控制策略之一，利用機(jī)器人動(dòng)力學(xué)方程的線性參數(shù)化性質(zhì)，通過(guò)一個(gè)積分運(yùn)算估計(jì)機(jī)器人參數(shù)。由于積分環(huán)節(jié)的作用，在持續(xù)干擾條件下，控制系統(tǒng)不容易穩(wěn)定，因此適當(dāng)限制或調(diào)整積

50、分環(huán)節(jié)的作用是實(shí)現(xiàn)自適應(yīng)系統(tǒng)穩(wěn)定的一個(gè)有效手段。能把估計(jì)參數(shù)限制子啊所規(guī)定的范圍內(nèi)，從而提高了自適應(yīng)控制系統(tǒng)的魯棒性。但這種算法有六個(gè)開(kāi)關(guān)組成，稍微復(fù)雜，而且當(dāng)真是參數(shù)不在所規(guī)定的范圍內(nèi)時(shí)，它不能給出系統(tǒng)控制品質(zhì)及其魯棒性等信息。</p><p>　　本文提出一種簡(jiǎn)單的魯棒自適應(yīng)控制算法，當(dāng)估計(jì)參數(shù)域包含參數(shù)真實(shí)值時(shí)，閉環(huán)系統(tǒng)實(shí)現(xiàn)漸進(jìn)穩(wěn)定跟蹤；當(dāng)存在干擾或估計(jì)參數(shù)域不含參數(shù)真實(shí)值即有誤差時(shí)系統(tǒng)是穩(wěn)定的。</

51、p><p>　　2.機(jī)械手的動(dòng)態(tài)模型和特征模型</p><p>　　考慮機(jī)械手與N自由度。連續(xù)拉格朗日動(dòng)態(tài)模型[ 1-3 ]是由</p><p><b>　　(1)</b></p><p>　　其中q ∈Rn和∈R n 分別為都N的矢量廣義的聯(lián)合坐標(biāo)和速度坐標(biāo)系。慣性矩陣M(q)-MT(q)> 0，存在兩個(gè)常數(shù)正面標(biāo)米

52、M的最小值和最大值，如≤≤，是載體的指揮廣義力，和G(q)是哥氏力矩和重力力矩。在實(shí)際應(yīng)用中，不確定參數(shù)和聯(lián)合國(guó)的動(dòng)力學(xué)模型，通常存在于既定的動(dòng)態(tài)模型</p><p>　　當(dāng)樣品的時(shí)間是夠小，在即時(shí)可分別逼近</p><p><b>　　和 .</b></p><p>　　使用上述的關(guān)系，離散時(shí)間的代表性（ 1 ）成為</p>&

53、lt;p><b>　　(2a)</b></p><p><b>　　把代入(2a)得 </b></p><p><b>　　(2b)</b></p><p><b>　　其中</b></p><p><b>　　,</b><

54、;/p><p>　　同樣，I 指單一的對(duì)角矩陣與一個(gè)適當(dāng)?shù)膶用?，如果設(shè)計(jì) (0.2)是連續(xù)的在T中，那么結(jié)果就是 (q, ) of (1).就要持續(xù)將 and 成為ij-th 要素矩陣 ; 我們可以界定</p><p>　　然后 ΔF1(k) 可以表達(dá)為</p><p>　　對(duì)于 ij-th 元素 的矩陣ΔF1(k)</p><p><

55、b>　　我們可以得到</b></p><p><b>　　= </b></p><p>　　= </p><p>　　當(dāng) 0≤≤1,and,≈1 對(duì)于一個(gè)小樣本的時(shí)間 Ts .從(3)得到, 它可以被看作為 ΔF1(k)→0 當(dāng)Ts 趨近于零在在一個(gè)緊湊的設(shè)置 中. 類似的性能也可以達(dá)到為系數(shù)

56、矩陣 f2(k), and β(k) .在一個(gè)緊湊的一套, 下列屬性可以推斷，從(3)和表達(dá)的系數(shù)矩陣(2b)條：</p><p>　　所有物1: 如果樣品時(shí)間 Ts 足夠小,那么所有系數(shù)矩陣(2b)條的時(shí)間正在慢慢變;</p><p>　　所有物2: f1(k)→2I,f2(k)→ ?I 和 f1(k)+f2(k)→I, 當(dāng)樣品時(shí)間Ts 趨近于零. 然后我們可以定于離散方程(2b)與性

57、能的第一和第二款作為機(jī)械手特征模型。</p><p>　　3多變量GSA的控制器與神經(jīng)網(wǎng)絡(luò)補(bǔ)償</p><p>　　離散方程(2b)條可表示為如下</p><p><b>　　(4)</b></p><p><b>　　當(dāng)</b></p><p><b>　　,&l

58、t;/b></p><p><b>　　,</b></p><p>　　e(k)是指載體的白噪聲與零的意思. 在 ≡0, and 的情況下可以減少到</p><p>　　然后元素 q(k +1) 可以表示為</p><p>　　(5) 當(dāng) i = 1,…,n, (k+1)) 是q(k +1)的元素i, ei(k)

59、 是o e(k)的元素i， 并且θi(k) 是矩陣中的圓柱</p><p><b>　　i . </b></p><p>　　當(dāng)系數(shù)矩陣都是未知，可以估計(jì)為=π (q(k),q(k?1),...,u(k?1),...) , (6a)</p><p>　　當(dāng) 是Θ(k)在當(dāng)時(shí)估計(jì)的系數(shù)矩陣 t=kTs , and

60、 意味著 操縱者的意愿。考慮到系數(shù)矩陣的特征模型的時(shí)間正在慢慢變，我們可以獲取選定的估計(jì)運(yùn)營(yíng)商的加權(quán)最小二乘法 (WLS)[13],</p><p><b>　　,</b></p><p>　　當(dāng) λ(k+1)=μ0λ(k)+(1?μ0), 0<μ0 ≤1, and matrix圓柱 i .鑒于預(yù)期的順利軌跡 , 自適應(yīng)控制控制器的設(shè)計(jì)如下 </p>

61、;<p>　　(7) 當(dāng)前饋控制律設(shè)計(jì)</p><p><b>　　(7a)</b></p><p>　　并且和多變量gsac反饋法</p><p><b>　　(7b)</b></p><p>　　當(dāng) 是跟蹤誤差，并且ε(k) >0 是是一個(gè)很小的標(biāo)量，避免估計(jì)矩陣 存在差異.

62、 在這個(gè)期間 將稍后設(shè)計(jì); L1 和L2 是黃金分割系數(shù), 這就是:</p><p><b>　　, ,</b></p><p>　　并將滿足L1+L2=1 和 </p><p>　　從而取代 (7) 進(jìn)入 (2), 我們可以得到</p><p>　　和 . 確定跟蹤過(guò)濾錯(cuò)誤 s(k +1) 并且運(yùn)用其中的關(guān)心L1

63、+L2=1 和 , (8) 將被表達(dá)為</p><p><b>　　=</b></p><p><b>　　當(dāng)</b></p><p><b>　　假設(shè), , 和</b></p><p><b>　　,if 被選定為</b></p><

64、;p>　　然后 Δ(k) = 0,再(9) 可以被寫作</p><p><b>　　(10)</b></p><p>　　當(dāng)在所有物2 as Ts → 0 在一個(gè)緊湊的設(shè)置, 在一個(gè)小樣本時(shí)間Ts 中可以選擇不平等可以得到滿足。故在跟蹤過(guò)濾錯(cuò)誤 s(k) 在這種情況下趨近與零.收斂性的 S(k)至零，從而保證了收斂的Q(k)至零。由于動(dòng)態(tài)的估計(jì)和隨時(shí)間變化

65、的系數(shù)特征模型、它幾乎是不可能的，以滿足上述假設(shè)。</p><p>　　因此，我們可以設(shè)計(jì)一個(gè)適當(dāng)?shù)难a(bǔ)償控制法，以避免可能的情況出現(xiàn)，控制性能惡化，或該閉環(huán)系統(tǒng)是不穩(wěn)定的，甚至因估計(jì)錯(cuò)誤。因此，設(shè)計(jì)為</p><p>　　(11) 當(dāng) 是 Δ(k)的估計(jì)值 .</p><p>　　假設(shè)Δ(k)能夠的順利進(jìn)行和范圍內(nèi)，這樣它就能被近似線性參數(shù)神經(jīng)網(wǎng)絡(luò)的任何所需的準(zhǔn)確度

66、。</p><p>　　然后元素Δi(k) of Δ(k) 可以表達(dá)為</p><p>　　(12) 當(dāng) i= 1,…n, is 是圓柱體i的最優(yōu)神經(jīng)網(wǎng)絡(luò)的權(quán)重矩陣，,.激活功能代表基函數(shù)向量，它可以選擇任何一高斯徑向基，B樣條的基礎(chǔ)和小波巴斯等等。</p><p>　　[14], 并且δi (k) 表示 元素 i 在神經(jīng)網(wǎng)絡(luò)誤重建差量 k δ(k)</

67、p><p><b>　　.</b></p><p>　　使用補(bǔ)償控制定理 , (9) 可以被寫成為</p><p><b>　　(13)</b></p><p>　　在 是 的判斷, 并且 </p><p>　　對(duì) 的估計(jì)已經(jīng) 通過(guò)最小化成本函數(shù)得到了</p>&

68、lt;p><b>　　(14)</b></p><p>　　把(13)代入(14)之后，梯度成本函數(shù)在(14)導(dǎo)出</p><p><b>　　(15)</b></p><p>　　根據(jù)該梯度下降法神經(jīng)網(wǎng)絡(luò)的重量適應(yīng)的定理可以設(shè)計(jì)為</p><p><b>　　(16)</b&

69、gt;</p><p>　　當(dāng) α > 0,那么補(bǔ)償控制定理在(11)可以被寫成為</p><p><b>　　(17)</b></p><p>　　鑒于這個(gè)例子 之時(shí) 可以簡(jiǎn)化為</p><p><b>　　4.仿真結(jié)果</b></p><p>　　考慮一個(gè)平面，兩

70、個(gè)環(huán)節(jié)，闡述了機(jī)械手的作為，在（3）(如圖一介紹), 其動(dòng)態(tài)可以書面明確為</p><p><b>　　當(dāng)</b></p><p><b>　　其中</b></p><p><b>　　,</b></p><p><b>　　,,</b></p>

71、;<p><b>　　and .</b></p><p>　　在模擬設(shè)計(jì)中，樣本時(shí)間 Ts = 2ms,初始值和參數(shù)估計(jì)和控制器的選定為P(0) =1×I,λ(0) = 0.96 , μ0 = 0.98 , </p><p>　　反奇異因素ε(k) 可以被描述為 ε(k) =5×exp(?kTs).</p><p

72、>　　根據(jù)所有物2, 初步估計(jì)值的特征模型的系數(shù)矩陣選擇</p><p>　　一個(gè)基礎(chǔ)的一系列激活函數(shù)y （ k ）項(xiàng)可以選擇，因?yàn)樵陔S機(jī)向量函數(shù)的聯(lián)系網(wǎng)， [ 16 ] ，即 </p><p><b>　　(19)</b></p><p>　　與V隨機(jī)選取矩陣和和X(k) t神經(jīng)網(wǎng)絡(luò)的輸入向量?？梢员贿x擇為雙曲正切函數(shù)X(k) 可作為&