一個(gè)精確的駕駛差異曲線移動(dòng)機(jī)器人運(yùn)動(dòng)規(guī)劃外文文獻(xiàn)翻譯、中英文翻譯

1、一個(gè)精確的駕駛差異曲線移動(dòng)機(jī)器人運(yùn)動(dòng)規(guī)劃摘要一個(gè)有固定單一曲率半徑旋轉(zhuǎn)軌跡建議，旨在將移動(dòng)機(jī)器人駕駛差最優(yōu)軌跡計(jì)劃捕捉移動(dòng)物體。一般來說，當(dāng)差分驅(qū)動(dòng)一路走來，其旋轉(zhuǎn)半徑移動(dòng)機(jī)器人的動(dòng)作不是常數(shù)，與旅行距離增加移動(dòng)機(jī)器人跟蹤誤差。此外，跟蹤誤差大大增加，當(dāng)移動(dòng)機(jī)器人如下與旋轉(zhuǎn)半徑小軌跡?；谝陨蟽牲c(diǎn)，一個(gè)單一的曲率軌跡，它不斷旋轉(zhuǎn)半徑大，建議作為最優(yōu)軌跡，以盡量減少移動(dòng)機(jī)器人駕駛差分跟蹤誤差。本文首先回顧了單一曲率軌跡的特點(diǎn)。接下來，一個(gè)算法捕捉運(yùn)動(dòng)物體的建議恰恰是使用單一曲率軌跡。由于預(yù)先確定的初始狀態(tài)（即位置和移動(dòng)機(jī)器人的方向和最后的狀態(tài)），移動(dòng)機(jī)器人是由此捕捉移動(dòng)物體的。通過模擬和使用兩自

2、由度的車輪實(shí)際試驗(yàn)為基礎(chǔ)的移動(dòng)機(jī)器人，該算法的有效性得到了驗(yàn)證。1.導(dǎo)言移動(dòng)機(jī)器人的研究被大體分為三種類別：路徑規(guī)劃，位置估計(jì)，和驅(qū)動(dòng)控制。移動(dòng)機(jī)器人軌跡規(guī)劃,旨在提供從初始位置的最佳路徑目標(biāo)位置。優(yōu)化的移動(dòng)機(jī)器人路徑規(guī)劃提供了一個(gè)路徑，它跟蹤誤差最小，最短的行車時(shí)間和距離。移動(dòng)機(jī)器人的跟蹤誤差會(huì)導(dǎo)致沖突的障礙由于偏離計(jì)劃的道路，也使機(jī)器人對(duì)未能成功的完成任務(wù)。跟蹤誤差減少要通過反饋控制。然而，這需要過度的控制努力是由于高增益控制。跟蹤誤差也造成了旅行時(shí)間的增加，以及旅行的距離，由于需要滿足駕駛的額外調(diào)整狀態(tài)。因此，軌跡規(guī)劃，以減少跟蹤誤差是非常重要，需要謹(jǐn)慎處理。跟蹤誤差的主要原因之一是差分

3、驅(qū)動(dòng)移動(dòng)機(jī)器人在不同的路徑的旋轉(zhuǎn)半徑不連續(xù)的。在直線和曲線路線，或在一個(gè)轉(zhuǎn)折點(diǎn)連接點(diǎn)的旋轉(zhuǎn)半徑的變化。在這幾點(diǎn)，差分驅(qū)動(dòng)移動(dòng)機(jī)器人由于方向的快速變化，很容易的脫離目標(biāo)軌道。因此，為了減少跟蹤誤差，在移動(dòng)機(jī)器人軌跡必須要有計(jì)劃，盡可能使旋轉(zhuǎn)半徑維持為一個(gè)常數(shù)。跟蹤誤差由于小旋轉(zhuǎn)半徑增加干擾了移動(dòng)機(jī)器人的準(zhǔn)確駕駛。路徑在移動(dòng)機(jī)器人可分為彎曲和直線段，總體看來。雖然跟蹤誤差不在直線部分產(chǎn)生的，產(chǎn)生重大的錯(cuò)誤，在彎曲的部分，由于離心力和向心力，它使機(jī)器人在地面滑動(dòng)。此外，跟蹤誤差增加旋轉(zhuǎn)時(shí)，半徑小。事實(shí)上，直線段可以被看作是一個(gè)彎曲的部分，其旋轉(zhuǎn)半徑無窮大。由于跟蹤誤差變大的彎曲段，一個(gè)同在彎曲的道路

4、，旋轉(zhuǎn)半徑減少跟蹤誤差增長(zhǎng)的可能性。請(qǐng)注意，一個(gè)相對(duì)較小的錯(cuò)誤在直線路徑發(fā)生。因此，重要的是要同時(shí)保持大并不斷旋轉(zhuǎn)半徑，以減少差分驅(qū)動(dòng)移動(dòng)機(jī)器人的跟蹤誤差。本文提出了一種單曲率軌跡，它不斷旋轉(zhuǎn)變大半徑。鑒于規(guī)模和旋轉(zhuǎn)半徑，單一曲率軌跡和雙曲率連續(xù)軌跡視圖比較顯示，隨著旋轉(zhuǎn)半徑減少跟蹤誤差增加。通過跟蹤沿每個(gè)軌道實(shí)驗(yàn)，證明了單曲率軌跡跟蹤誤差最小。精確軌跡規(guī)劃，一個(gè)算法的移動(dòng)機(jī)器人捕捉運(yùn)動(dòng)物體的建議。隨著預(yù)指定的初始位置和移動(dòng)機(jī)器人的方向和最后的狀態(tài)，并假設(shè)運(yùn)動(dòng)物體的速度是預(yù)先估計(jì)，最佳捕捉移動(dòng)機(jī)器人路徑作為這項(xiàng)研究的結(jié)果產(chǎn)生。在第2節(jié)用運(yùn)動(dòng)學(xué)分析移動(dòng)機(jī)器人的駕駛特點(diǎn)，同時(shí)分析了移動(dòng)機(jī)器人正在彎

5、曲的議案。單曲率軌跡和雙曲率軌跡說明，在第3節(jié)。第4節(jié)，講彎曲的軌跡形成的算法，根據(jù)單一曲率軌跡與理論公式.第五節(jié)引入顯示關(guān)于跟蹤誤差的比較單一曲率和雙曲率軌跡，在現(xiàn)實(shí)的捕捉實(shí)驗(yàn) 。第6節(jié)結(jié)束這份文件，為今后的工作議程。2移動(dòng)的移動(dòng)機(jī)器人駕駛差的特要形成駕駛移動(dòng)機(jī)器人，運(yùn)動(dòng)學(xué)分析，首先需要不同的軌跡進(jìn)行。根據(jù)運(yùn)動(dòng)學(xué)分析，移動(dòng)機(jī)器人駕駛差分驅(qū)動(dòng)機(jī)制的特點(diǎn)進(jìn)行建模，它提供了軌跡規(guī)劃的理論基礎(chǔ)。2.1 運(yùn)動(dòng)學(xué)分析的移動(dòng)機(jī)器人如圖所示。 1A是一個(gè)差分驅(qū)動(dòng)機(jī)制的移動(dòng)機(jī)器人有兩個(gè)在同一軸線車輪，每個(gè)車輪是由一個(gè)獨(dú)立的電機(jī)控制。讓我們定義Vl為左車輪速度，Vr為右車輪速度，l表示兩個(gè)輪子之間的距離。機(jī)器人

6、的馬達(dá)決定兩輪的速度，vL 和 vR表示線速度和角速度，移動(dòng)機(jī)器人vL和VR可以表示為：一個(gè)有差分驅(qū)動(dòng)機(jī)制的移動(dòng)機(jī)器人運(yùn)動(dòng)學(xué)模型，可以說，如圖1b中所示.兩個(gè)X _Y笛卡爾坐標(biāo)，對(duì)移動(dòng)機(jī)器人的狀態(tài)用(t)和(t)表示，而方向用(t)表示.同時(shí)，用 和代表線性速度，代表角速度。在移動(dòng)機(jī)器人速度矢量定義為：現(xiàn)在，移動(dòng)機(jī)器人運(yùn)動(dòng)學(xué)模型可以同樣地可以表示為2.2 驅(qū)動(dòng)移動(dòng)機(jī)器人的原則 通過運(yùn)動(dòng)學(xué)分析,可以確認(rèn)，移動(dòng)機(jī)器人的運(yùn)動(dòng)狀態(tài)與差分驅(qū)動(dòng)機(jī)制改變的兩個(gè)輪子的速度。當(dāng)多個(gè)輪子的機(jī)器人繞瞬間旋轉(zhuǎn)中心旋轉(zhuǎn)時(shí)，這個(gè)旋轉(zhuǎn)中心被稱為ICC（瞬時(shí)曲率中心）。如圖2b所示。ICC是位于橫截面的擴(kuò)展點(diǎn)的車輪中心的路線

7、。對(duì)于一個(gè)差分驅(qū)動(dòng)機(jī)制的移動(dòng)機(jī)器人，ICC可以設(shè)在方向盤上的任何軸點(diǎn)，因?yàn)檫@兩個(gè)輪子軸在同一行。在這種情況下，ICC將取決于兩個(gè)輪子之間的速度比。圖 3說明ICC隨著機(jī)器人的運(yùn)動(dòng)和的位置改變。一個(gè)車輪之間的速度和車輪到ICC的距離成比例關(guān)系，如圖所示。同樣地，上式可簡(jiǎn)化為:請(qǐng)注意，移動(dòng)機(jī)器人旋轉(zhuǎn)半徑是左，右前輪速度值確定。當(dāng)機(jī)器人耕作跟蹤一條直線時(shí)，R =1，vR = vL。當(dāng)vR != vL，機(jī)器人遵循某種旋轉(zhuǎn)半徑曲線軌跡。因此，速度和加速度的機(jī)器人改變，造成旋轉(zhuǎn)半徑是多種多樣的。當(dāng)移動(dòng)機(jī)器人在A點(diǎn)時(shí)，其坐標(biāo)為，此時(shí)時(shí)間=T，到B，其坐標(biāo)為， 時(shí)間 = t + d t,在時(shí)間= t + d

8、t時(shí)，ICC坐標(biāo)可動(dòng)態(tài)確定為現(xiàn)在，機(jī)器人的運(yùn)動(dòng)位置，時(shí)間 = t + d t,可以來表示根據(jù)ICC和角位置速度Vx，如下：(a) 移動(dòng)機(jī)器人的速度 (b) 機(jī)器人位置的表示形式圖1 一種移動(dòng)機(jī)器人的運(yùn)動(dòng)學(xué)模型圖3 曲率圖4 機(jī)器人移動(dòng)中心現(xiàn)在，移動(dòng)機(jī)器人從A運(yùn)動(dòng)到B地點(diǎn)總距離d和旋轉(zhuǎn)角度u可表示如下：利用這些方程，當(dāng)旋轉(zhuǎn)半徑，運(yùn)動(dòng)距離，以及移動(dòng)機(jī)器人旋轉(zhuǎn)角度事先確定，所需的線性和角速度，可變區(qū)，虛擬現(xiàn)實(shí)和VX可以動(dòng)態(tài)獲取，當(dāng)機(jī)器人是在行駛的曲線路徑運(yùn)行時(shí)。3曲率軌跡3.1 運(yùn)動(dòng)特性曲線曲率，K是定義為移動(dòng)機(jī)器人從一個(gè)點(diǎn)P旋轉(zhuǎn)至Q 時(shí)，Dh 與 Ds比值，如圖4所示。也就是說，曲率的定義是：旋轉(zhuǎn)

9、半徑可以定義為曲率的倒數(shù)，p=1/k,其中k0。從方程（11），可看出，總沿曲線的距離，弧的長(zhǎng)度是與曲率成正比。K是成反比Ds的,曲率K也與曲線半徑成反比。如果k = 0，則曲線半徑，即旋轉(zhuǎn)半徑，成為無限。請(qǐng)注意，使得k = 0意味著一條直線，這是一種無限的半徑。當(dāng)移動(dòng)機(jī)器人沿著彎曲的軌跡前進(jìn)，旋轉(zhuǎn)半徑對(duì)跟蹤誤差產(chǎn)生嚴(yán)重影響。一般來說，移動(dòng)機(jī)器人沿著一條直線（k= 0）比曲線路徑（k!=0）錯(cuò)誤的可能性更小。從理論上說，一個(gè)彎曲的軌跡，可以計(jì)算出均衡器。 （6） - （8），假定純滾動(dòng)和非滑移條件。但是，實(shí)際駕駛可能導(dǎo)致與理論值的一些不同。當(dāng)一個(gè)移動(dòng)機(jī)器人路徑彎曲后，有離心和向心合力。車輪與地

10、面之間的摩擦力，作為ICC的向心力，維護(hù)了移動(dòng)機(jī)器人曲線運(yùn)動(dòng)摩擦力。在理想的條件下滑動(dòng)，跟蹤誤差為零。然而，在實(shí)際情況下，總會(huì)有一個(gè)跟蹤誤差造成的延誤。在離心力的作用，可以制定作為一個(gè)旋轉(zhuǎn)半徑R和速度v函數(shù)：其中m是機(jī)器人的質(zhì)量和c是一個(gè)比例常數(shù)。圖 5說明了移動(dòng)機(jī)器人駕駛的情況，從A出發(fā)，走曲線路徑。在理想的條件下，機(jī)器人，估計(jì)情況會(huì)如B1。然而，在實(shí)際情況下，通過機(jī)器人到達(dá)跟蹤誤差在B2。目前已經(jīng)進(jìn)行，在減少跟蹤誤差小的旋轉(zhuǎn)半徑和高運(yùn)行速度進(jìn)行了許多研究。.圖 6顯示了一個(gè)真正的移動(dòng)機(jī)器人誤差的特點(diǎn)，根據(jù)運(yùn)動(dòng)半徑和速度。右前輪的時(shí)速保持在恒定的，而左車輪被更改，以推動(dòng)在一個(gè)彎曲移動(dòng)的機(jī)器人

11、。隨著左車輪速度增加，以及跟蹤誤差的增加。還要注意的是一個(gè)小的旋轉(zhuǎn)速度，即使保持半徑不變跟蹤誤差也會(huì)增加。從對(duì)圖6的分析，可以得出結(jié)論，一個(gè)一個(gè)較小的旋轉(zhuǎn)半徑和更高的速度移動(dòng)機(jī)器人的跟蹤誤差，同時(shí)提高了移動(dòng)機(jī)器人沿著彎曲的道路運(yùn)動(dòng)。圖5 移動(dòng)機(jī)器人曲線的路徑傳動(dòng)誤差圖6 移動(dòng)速度和曲線半徑的偏差3.2 單曲率軌跡圖7A和b分別代表單曲率和雙曲率軌跡。雙曲率軌跡又一對(duì)稱形狀的拐點(diǎn)。單曲率軌跡保持相同的曲率，而雙曲率軌跡改變其方向和曲率在拐點(diǎn)。圖7C表示了軌跡曲率隨機(jī)變化，即拐點(diǎn)在幾個(gè)地方存在。雖然移動(dòng)機(jī)器人正沿軌跡7c。當(dāng)旋轉(zhuǎn)半徑，運(yùn)動(dòng)方向的改變時(shí)，車輪速度需要改變，按照式（7）。同樣的運(yùn)動(dòng)距離

12、，圖7A顯示了最大的旋轉(zhuǎn)半徑，而其他有不同的小半徑。因此，可以預(yù)見，當(dāng)移動(dòng)機(jī)器人沿著單一軌道曲率旅行，它有最少跟蹤誤差。圖 8顯示了模擬單曲率和雙曲率軌跡形狀。使用公式 （6）-（11），旋轉(zhuǎn)半徑，行駛距離，旋轉(zhuǎn)角度，以及ICC的位置，得到表1。運(yùn)行的總距離單曲率和雙曲率軌跡相同。然而，旋轉(zhuǎn)半徑的單曲率軌跡2倍的雙曲軌道大。具體來說，旋轉(zhuǎn)半徑的單曲率軌跡5.0米，而另外的雙曲率是2.5米，它的拐點(diǎn)在（2.5，2.5）。接近圖6和7的顯示值，導(dǎo)致期望單一曲率的軌跡會(huì)比雙曲軌跡跟蹤誤差小。通過實(shí)時(shí)實(shí)驗(yàn)，單曲率軌跡和雙曲率軌跡跟蹤誤差可以相互定量比較，。 對(duì)移動(dòng)機(jī)器人在最后位置方向，并非只對(duì)雙曲率軌

13、跡，因?yàn)榱硪粋€(gè)轉(zhuǎn)折點(diǎn)曲率軌跡是必要的，以匹配方向移動(dòng)機(jī)器人單曲率軌跡。4.1 預(yù)先假設(shè)根據(jù)不同的運(yùn)動(dòng)物體的狀態(tài)和移動(dòng)機(jī)器人，為移動(dòng)機(jī)器人最優(yōu)軌跡可能會(huì)有所不同。因此，在本文，是一個(gè)移動(dòng)機(jī)器人最優(yōu)軌跡規(guī)劃，其中認(rèn)為對(duì)運(yùn)動(dòng)物體的運(yùn)動(dòng)的限制，以及移動(dòng)機(jī)器人。 首先，移動(dòng)的物體其線速度和角速度，表示如下：(a) 單-曲率 (b) 雙曲率 (c) 復(fù)雜-曲率圖7 曲率類型(a) 單-曲率 (b) 雙曲率圖8單曲率和雙曲率軌跡根據(jù)方程（14）和（15），對(duì)移動(dòng)物體的運(yùn)動(dòng)從最初的位置僅限于直在勻速直線運(yùn)動(dòng)。據(jù)推測(cè)，移動(dòng)機(jī)器人保持靜態(tài)的，開始時(shí)，應(yīng)該有相同的速度和在目前的捕捉運(yùn)動(dòng)物體的方向。 移動(dòng)機(jī)器人最優(yōu)路

14、徑規(guī)劃，主要有兩個(gè)考慮因素：運(yùn)動(dòng)時(shí)間和跟蹤誤差。如果速度加快，最低的行車時(shí)間移動(dòng)機(jī)器人移動(dòng)時(shí)，跟蹤誤差會(huì)增加一個(gè)彎曲的路徑。因此，駕駛時(shí)的最低條件和跟蹤誤差在移動(dòng)機(jī)器人的最小線速度和加速度范圍內(nèi)。其表示如下：其中Vmax是最大允許線速度和amax最大允許加速度。對(duì)于一個(gè)給定的路徑最基本的駕駛時(shí)間，加速移動(dòng)機(jī)器人選擇在允許的范圍內(nèi)加速范圍內(nèi)，最高速度。此外，在移動(dòng)機(jī)器人的最高速度被限制在最小范圍內(nèi)允許的最大范圍內(nèi)跟蹤誤差。4.2 獲得移動(dòng)物體的移動(dòng)機(jī)器人的狀態(tài)由于移動(dòng)機(jī)器人最優(yōu)路徑可以根據(jù)運(yùn)動(dòng)物體的移動(dòng)機(jī)器人的狀態(tài)創(chuàng)建，在移動(dòng)機(jī)器人狀態(tài)和運(yùn)動(dòng)物體的需要定義為成功的移動(dòng)機(jī)器人路徑規(guī)劃準(zhǔn)確。如圖9所

15、示，一個(gè)移動(dòng)物體的位置和移動(dòng)機(jī)器人的定義為兩個(gè)三維笛卡爾變量x和y，以及方向變量h，然后，面向?qū)ο蟮囊苿?dòng)，hobj，表示為運(yùn)動(dòng)物體的初始位置，可以表示為現(xiàn)在，移動(dòng)物體的線速度，vobj，可以計(jì)算如下：在移動(dòng)機(jī)器人的初始位置被表示為在移動(dòng)機(jī)器人的使命要求，它開始捕獲了以固定的初始位置恒定速度運(yùn)動(dòng)的物體。如果移動(dòng)機(jī)器人具有相同的速度，并在最后的位置定位移動(dòng)物體，移動(dòng)物體將被移動(dòng)機(jī)器人輕易抓獲。圖9 移動(dòng)機(jī)器人與移動(dòng)對(duì)象的初始狀態(tài)4.3 確定路徑根據(jù)移動(dòng)機(jī)器人和物體的初始狀態(tài)，無論選中是單或雙曲率軌跡。單一曲率軌道存在的條件是獲得，這是一個(gè)有趣的觀察，這項(xiàng)研究產(chǎn)生的如圖10所示。當(dāng)沿單一曲率移動(dòng)機(jī)器

16、人移動(dòng)的軌跡，從A至D可減少自彎曲運(yùn)動(dòng)延誤，可以跟蹤誤差最小化。因此，在移動(dòng)機(jī)器人可以捕捉運(yùn)動(dòng)物體時(shí)，正是具有相同的速度和移動(dòng)物體。如果軌跡和運(yùn)動(dòng)物體的位置，方向被準(zhǔn)確估計(jì)，預(yù)計(jì)捕捉位置D (xD,yD)為：在這種情況下，C的坐標(biāo)(xC,yC)，可以從運(yùn)動(dòng)物體的初始狀態(tài)和移動(dòng)機(jī)器人的所得如下：其中(xI,yI)代表了運(yùn)動(dòng)物體的初始位置。ICC坐標(biāo)單曲率軌跡，和旋轉(zhuǎn)半徑為R，可以表示如下：還有一些單一曲率軌跡不能產(chǎn)生的情況，由于軌跡取決于移動(dòng)機(jī)器人的狀態(tài)和運(yùn)動(dòng)目標(biāo)。如圖11所示，如果移動(dòng)機(jī)器人與運(yùn)動(dòng)物體的角度和方向的區(qū)別是不積極，單曲率軌跡不能滿足在最后的位置捕獲條件。在這種情況下，雙曲率軌跡被

17、選擇為最佳路徑，而不是單一曲率。在這種情況下，一個(gè)移動(dòng)機(jī)器人軌跡分解為路徑1和路徑2。根據(jù)移動(dòng)對(duì)象和移動(dòng)機(jī)器人，旋轉(zhuǎn)半徑和ICC的坐標(biāo)被決定（見圖12）。從最初的狀態(tài)，坐標(biāo)ICC1和 ICC2, ，表示如下：對(duì)路徑1和路徑2的旋轉(zhuǎn)半徑選擇相同可減少跟蹤誤差，以及旋轉(zhuǎn)半徑可以表示為請(qǐng)注意，移動(dòng)機(jī)器人的方向是在轉(zhuǎn)折點(diǎn)，改變了雙曲率軌跡。4.4設(shè)計(jì)文件的速度移動(dòng)機(jī)器人的速度決定的運(yùn)動(dòng)物體的速度和駕駛距離捕獲的對(duì)象。在單曲率軌跡的移動(dòng)機(jī)器人線速度分為三個(gè)部分：加速，勻速和減速。在移動(dòng)機(jī)器人線速度可以表示如下：其中T是移動(dòng)機(jī)器人的總行車時(shí)間。根據(jù)移動(dòng)機(jī)器人運(yùn)動(dòng)學(xué)，車輪速度，vR 和vL,以及移動(dòng)機(jī)器人角

18、速度hR，確定如下：對(duì)于雙曲軌跡，兩個(gè)速度分布是必要的。也就是說，在拐點(diǎn)的移動(dòng)機(jī)器人暫時(shí)停止和改變的速度分布。5實(shí)驗(yàn)5.1實(shí)驗(yàn)環(huán)境實(shí)驗(yàn)是在智能機(jī)器人實(shí)驗(yàn)室.地板平整，光滑。移動(dòng)機(jī)器人的實(shí)驗(yàn)中使用的是三輪的驅(qū)動(dòng)機(jī)制不同兩個(gè)自由度的移動(dòng)機(jī)器人。在實(shí)施主計(jì)算機(jī)遠(yuǎn)程控制使用串行的通道。在移動(dòng)機(jī)器人有一個(gè) DSP320LF2407A控制板來控制的電機(jī)。一個(gè)10位編碼器安裝在移動(dòng)機(jī)器人每個(gè)車輪。對(duì)于運(yùn)動(dòng)物體的采樣周期是1 / 30秒。對(duì)移動(dòng)機(jī)器人的硬件規(guī)格如表2。表2 移動(dòng)機(jī)器人的硬件列表5.2實(shí)驗(yàn)表明單一曲率軌跡優(yōu)勢(shì)在前兩個(gè)實(shí)驗(yàn)，同樣的移動(dòng)機(jī)器人移動(dòng)的單，雙曲率，曲率軌跡捕獲如圖14所示移動(dòng)對(duì)象。跟蹤誤

19、差測(cè)量和比較圖15。在計(jì)算單曲率和雙曲率軌跡表1可見，用來捕捉移動(dòng)物體。正如15圖所示。為雙曲率軌跡跟蹤誤差的增長(zhǎng)十分迅速，而單軌跡慢慢增加。通過這些實(shí)驗(yàn)，可以得出結(jié)論，一個(gè)單一曲率軌跡是精確跟蹤運(yùn)作的最佳，除非它是不可能的。圖15 尋跡誤差比較5.3實(shí)驗(yàn)的捕獲軌跡允許加速度被設(shè)置為0.1常用和運(yùn)動(dòng)物體的線速度是假設(shè)恒定在0.3米/秒抽樣時(shí)間是0.1秒。基于該算法，單曲率軌跡，計(jì)劃捕捉如圖16A所示移動(dòng)對(duì)象。與單一曲率軌跡的實(shí)驗(yàn)結(jié)果如圖16B所示。以及規(guī)格和單曲率軌道實(shí)驗(yàn)結(jié)果總結(jié)在表3。 （A）理論單曲率曲線 （B）實(shí)際運(yùn)動(dòng)曲線圖17 機(jī)器人捕捉曲線當(dāng)單曲率軌跡不可用，雙曲率軌跡被選擇，而不是

20、單一曲率軌跡最優(yōu)軌跡捕捉移動(dòng)物體。圖 17A說明路徑的移動(dòng)機(jī)器人應(yīng)遵循捕捉運(yùn)動(dòng)物體沿著雙曲軌道上。與雙曲彈道實(shí)驗(yàn)結(jié)果如圖17B所示。以及規(guī)格和雙曲率彈道實(shí)驗(yàn)結(jié)果總結(jié)在表4.通過這些實(shí)驗(yàn)，它再次證實(shí)了雙曲率軌跡具有比單曲率較大的軌跡跟蹤誤差。即使軌跡生成過程不是說明在這一節(jié)中。該算法在第4節(jié)解釋了一個(gè)成功的跟蹤和捕捉重要的作用。表3 單-曲率軌跡的實(shí)驗(yàn)結(jié)果 表4 雙曲率彈道實(shí)驗(yàn)結(jié)果（A）理論雙曲率曲線 （B）實(shí)際運(yùn)動(dòng)曲線圖17 機(jī)器人雙曲率捕捉曲線結(jié)論本文為一個(gè)差分驅(qū)動(dòng)移動(dòng)機(jī)器人最優(yōu)路徑規(guī)劃新算法被提出。其中造成跟蹤移動(dòng)機(jī)器人誤差的因素很多，路徑的曲率是深入分析本文，因?yàn)樗梢圆粓?zhí)行以進(jìn)行任務(wù)的

21、選擇。這項(xiàng)研究表明了精確的彎曲議案單一曲率軌跡最優(yōu)。一個(gè)精確的曲線運(yùn)動(dòng)，運(yùn)動(dòng)物體的捕捉，是真正的實(shí)驗(yàn)說明。在單曲率軌跡優(yōu)勢(shì)已核實(shí)的基礎(chǔ)上從理論和實(shí)際觀測(cè)實(shí)驗(yàn)。由于與航位推算傳感器只能總額估計(jì)誤差的位置移動(dòng)機(jī)器人當(dāng)他們航行，一個(gè)誤差校正算法，以支持精確和及時(shí)的控制。頻繁的糾錯(cuò)過程降低了行駛性能至關(guān)重要，并可能導(dǎo)致不穩(wěn)定的行動(dòng)。提供一個(gè)軌跡這會(huì)導(dǎo)致更少的錯(cuò)誤，是非常有效的精確和快速?gòu)澑櫼苿?dòng)機(jī)器人駕駛差的議案。為了提高移動(dòng)機(jī)器人駕駛的準(zhǔn)確性，在未來的研究中，智能位置估計(jì)計(jì)劃和駕駛控制算法將不得不進(jìn)一步發(fā)展。鳴謝這項(xiàng)工作是由支持MIC和國(guó)際熱帶農(nóng)業(yè)研究所的一部分，通過領(lǐng)先的IT研發(fā)支持項(xiàng)目。A pr

22、ecise curved motion planning for a differential driving mobile robotabstract A single curvature trajectory with a fixed rotation radius is proposed for an optimal trajectory plan for a differential driving mobile robot to capture a moving object. Generally, when the differential driving mobile robot

23、 moves along a path whose rotation radius is not constant, the tracking error of the mobile robot increases with the travel distance. Also, tracking errors increase greatly when the mobile robot follows a trajectory, with a small rotation radius. Based on these two observations, a single curvature t

24、rajectory, which has a constant and large rotation radius, is proposed as an optimal trajectory, in order to minimize the tracking error of the differential driving mobile robot. This paper first reviews the characteristics of a single curvature trajectory. Next, an algorithm to capture a moving obj

25、ect precisely is proposed using the single curvature trajectory. With the pre-determined initial states (i.e., position and orientation of the mobile robot and the final states), the mobile robot is made to capture a moving object.Through simulations and real experiments using a two DOF wheel-based

26、mobile robot, the effectiveness of the proposed algorithm is verified.1. Introduction Research on mobile robots can be globally classified into three categories: path planning, position estimation, and driving control. The trajectory planning of a mobile robot aims at providing an optimal path from

27、an initial position to a targetposition. Optimal trajectory planning for a mobile robot provides a path, which has minimal tracking error and the shortest driving time and distance. Tracking errors of mobile robots cause collisions with obstacles due to deviations from the planned path and also caus

28、e the robot to fail to accomplish the mission successfully. Tracking error can be reduced through feedback control. However, this requires excessive control efforts due to high control gains. Tracking errors also cause an increase of traveling time, as well as travel distance, due to the additional

29、adjustments needed to satisfy the driving states. Therefore, trajectory planning to decrease tracking error is very important and needs to be handled carefully. One of the major reasons for tracking error is the discontinuity of the rotation radius on the path of the differential driving mobile robo

30、t. The rotation radius changes at the connecting point of the straight line route and curved route, or at a point of inflection. At these points, it can be easy for the differential driving mobile robot to secede from its determined orbit due to the rapid change of direction. Therefore, in order to

31、decrease tracking error, the trajectory of the mobile robot must be planned so that the rotation radius is maintained at a constant , if possible. The increase of tracking error due to the small rotation radius interferes with the accurate driving of the mobile robot. The path of the mobile robot ca

32、n be divided into curved and straight-line segments, globally. While tracking error is not generated in the straight-line segment, significant error is produced in the curved segment due to centrifugal and centripetal forces, which cause the robot to slide over the surface. Also, tracking error incr

33、eases when the rotation radius is small. In fact, the straight line segment can be considered as a curved segment whose rotation radius is infinity. As the tracking error becomes larger at the curved segment, the possibility of a tracking error increases with the decrease of the rotation radius of t

34、he curved path. Note that a relatively small error occurs at the straight-line path. Therefore, it is important to maintain simultaneously a large and constant rotation radius in order to decrease the tracking error of the differential driving mobile robot. This paper proposes a single-curvature tra

35、jectory, which has a constant and large rotation radius. In view of the size and discontinuity of the rotation radius,a single-curvature trajectory and a double-curvature trajectory are compared to show that the tracking error increases with the decrease of the rotation radius. Through the tracking

36、experiments along each trajectory, it is proved that a single-curvature trajectory has the least tracking error. With precise trajectory planning, an algorithm for the mobile robot to capture a moving object is proposed. With the pre-specified initial position and orientation of a mobile robot and t

37、he final states, and assuming that the velocity of the moving object is pre-estimated, an optimal capturing path of a mobile robot is produced as a result of this research. In Section 2, the driving characteristics of a mobile robot are analyzed using a kinematics analysis while the mobile robot is

38、making curved motions. The single-curvature trajectory and double-curvature trajectory are described in detail in Section3. In Section4, a curved trajectory formation algorithm, according to a single-curvature trajectory, is introduced with theoretical formulas. Section 5 shows a comparison between

39、a single-curvature and a double-curvature trajectory, with respect to tracking error,in real capturing experiments. Section 6 concludes this paper and provides an agenda for future work.2. Moving characteristics of a differential driving mobile robot To form a trajectory for a differential driving m

40、obile robot, a kinematics analysis first needs to be conducted. Based on the kinematics analysis, the driving characteristics of a mobile robot with a differential driving mechanism are modeled, which provides the theoretical basis for trajectory planning.2.1. Kinematics analysis of the mobile robot

41、As shown in Fig. 1a, a mobile robot with a differential driving mechanism has two wheels on the same axis, and each wheel is controlled by an independent motor. Let us define vL as the velocity of the left wheel, vR as that of the right wheel, and l as the distance between the two wheels. The robots

42、 motion can be determined by the two wheel velocities, vL and vR, and the linear and angular velocities, vl and , of the mobile robot can be described in terms of vL and vR as follows : A kinematics model of a mobile robot with a differential driving mechanism can be described as shown in Fig. 1b. I

43、n two-dimensional X _ Y Cartesian coordinates, the position of the mobile robot is described by (t) and (t), whereas the orientation is represented as (t). Then, and represent the linear velocities, whereas represents the angular velocity. The velocity vector of the mobile robot is defined asNow, th

44、e kinematics model of the mobile robot can be representedas 2.2. Driving principle of the mobile robot Through the kinematics analysis, it can be recognized that the motion states of a mobile robot with a differential driving mechanism change according to the velocities of the two wheels. When a rob

45、ot with multiple wheels rotates about a rotation center instantaneously, this rotation center is defined as the ICC (Instantaneous Center for Curvature). As shown in Fig. 2a, the ICC is located at the cross-section point of the extension-lines of the wheel centers. For a mobile robot with a differen

46、tial driving mechanism, as shown in Fig. 2b, the ICC can be located at any point on the wheel axis, since the two wheel axes are on the same line. In this case, the ICC will be determined by the velocity ratio between the two wheels. Fig. 3 illustrates the ICC along with the robots motion and positi

47、on. There is a proportional relationship between the wheel velocities and the distance from the wheel to the ICC, which is represented as In addition, Eq. (5) can be simply represented as： Note that the rotation radius of the mobile robot is determined by the values of the left and right wheel veloc

48、ities. When the robot is following a straight line, R =1 and vR = vL. When vR != vL, the robot follows a curved trajectory of a certain rotation radius. Therefore, the velocity and acceleration of the robot is changed if the rotation radius is varied. When the mobile robot is moving from A, where th

49、e robot is locatedon at time = t, to B, where the position is at time = t + d t, the coordinates of the ICC can be dynamically determined as Also, the mobile robots position，at time = t + dt, canbe expressed according to the position of the ICC and the angular velocity, vx, as follows:， Now, the tot

50、al distance, d, and the rotation angle, u, of the mobile robots movement from location A to B can be obtained as follows: Using these equations, when the rotation radius, the distance of movement, and the rotation angle of the mobile robot are determined beforehand, the desired linear and angular ve

51、locities, vL, vR, and vx can be dynamically obtained while the robot is moving in a curved path 16.3. Curvature trajectory3.1. Curved motion characteristics The curvature, k, is defined as the ratio of Dh to Ds when a mobile robot is rotating from a point P to Q, as illustrated in Fig. 4. That is, t

52、he curvature is defined as 17The rotation radius can be defined as the inverse of the curvature,p=1/k, where k 0. From Eq. (11), the total traveling distance along the curve, Ds, is the length of the arc and is proportional to the curveradius. Since the curvature, k, is inversely proportional to Ds,

53、 the curvature k is also inversely proportional to the curve-radius. If k = 0, then the curve-radius, that is, the rotation radius, becomes infinite. Note that k = 0 implies a straight line, which is a circle of infinite radius. When the mobile robot is moving along a curved trajectory, the rotation

54、 radius has a severe effect on tracking error. Generally, a mobile robot has a smaller chance of error along a straight line (k = 0) than on a curved path (k 0). Theoretically, a curved trajectory can be calculated with Eqs. (6)(8), assuming pure-rolling and non-slipping conditions. However, practic

55、al driving might result in some divergences from the theoretical values. When a mobile robot is following a curved path, there are combined centrifugal and centripetal forces. The friction force between the surface and the wheels acts as a centripetal force on the ICC and maintains the curved motion

56、 of the mobile robot. Under ideal conditions without slippage, the tracking error becomes zero. However, in practical circumstances, there is always a tracking error caused by slippage. The centrifugal force can be formulated as a function of rotation radius, R, and velocity, v, where m is the mass

57、of the robot and c is a proportional constant. Fig. 5 illustrates a driving situation of a mobile robot, starting from A and following a curved path. Under ideal conditions, the estimated position of the robot becomes B1. However, in practical circumstances, the robot arrives at B2 via a tracking er

58、ror. There have been many studies conducted to reduce the tracking error caused by a small rotation radius and high traveling velocity. Fig. 6 shows the error characteristics of a real mobile robot, according to the traveling radius and speed 19. The speed of the right wheel is maintained at a constant, whereas that of the left wheel is changed in order to move the mob