機械外文文獻翻譯-無人駕駛電動鏟越障車【中文2578字】【PDF+中文WORD】

機械外文文獻翻譯-無人駕駛電動鏟越障車【中文2578字】【PDF+中文WORD】,中文2578字,PDF+中文WORD,機械,外文,文獻,翻譯,無人駕駛,電動,越障,中文,2578,PDF,WORD 無人駕駛電動鏟越障車 摘要 在自然災害發生后會產生大量的廢墟，阻礙了救援人員解救被困人員，延緩了救災行動。動力鏟通常用來清理廢墟殘骸，但這個過程可能需要很多時間。此外，在這種不穩定的條件下，讓救援人員操作重型機械是非常危險的。為了加快進入被困人員區域，可以通過靈活機動的無人駕駛動力鏟臂來執行，而不是將其淘汰，在這項工作中，無人駕駛動力鏟的自主障礙技術是至關重要的。在不同的序列中，優化總能量消耗的方法被選為克服給定步驟障礙的最佳方法，動態仿真結果表明了該方法的有效性。 關鍵詞:動力鏟；障礙超越；無人駕駛；優化 背景 每年世界上許多國家都受到地震、洪水、臺風等自然災害的侵襲，這些災害不僅造成生命損失，而且它們也會產生大量的廢墟，這導致了搜索和救援任務緩慢及救援困難度加大。在受災地區，讓人們操作動力鏟操作清理廢墟，是一項危險的任務，因為這些機器有可能因安裝的不穩定而發生故障，對人們造成傷害。此外，清除所有的障礙并最終進入內部區域需要花費大量的時間。 為了加快救援行動的速度，越過巨大的障礙物，而不是清除它們，這時使用履帶輪，動力鐵鍬能有效地解決這一問題。然而，在使用動力鏟的情況下，有幾個難題需要克服:只有在履帶車的爬坡范圍內的障礙物才能被克服;履帶越障車的力量可以很容易的飽和;當它處于障礙物的頂部時，如果沒有靈巧地移動，它可以翻倒并損壞自己。作為重型機械，在翻倒的時候，動力鏟也很難回到原來的狀態。 以前在挖掘機上的工作可以在[2-5]找到。參考文獻[2]提出了一種挖掘器的動態模型，目的是開發一個用于地面、月球和行星挖掘的自動挖掘控制系統。[3]詳細研究了具有液壓執行機構的挖掘機的運動學。參考文獻[4]主要集中在一個完全自動化卡車裝載任務的系統上。在這個系統中，挖掘機的軟件決定了在哪里挖掘，在哪里傾倒卡車，以及如何快速在這些點之間移動，同時檢測和停止障礙物。研究了開挖過程的性質和控制方法，并在[5]中進行了自動開挖的目的。 在其他相關的工作中，一種自動爬樓梯的履帶機器人被引入[6]。但是，它不使用任何武器援助。參考文獻[7]介紹了一種救援機器人的試驗系統，該系統允許人類操作員在三維碎片環境中提出正確的方向。相比之下，擬議的sys- tem則尋求無需人工干預的自動操作。參考文獻[8]提出了一種可移動的質心(CoM)的輪式機器人，以方便在崎嶇的地形上行走。擬議的系統也考慮通過操縱它的手臂來間接地改變CoM;如何-永遠，主要的焦點是在桶中得到反應力作為支撐來舉起動力鏟履帶。 Fig. 1 Basic parts of a power shovel. The coordinate frame convention is X forward, Y left and Z up X (forward) crawler step platform boom joint power shovel bucket bucket joint axis of platform rotation boom arm Z (up) arm joint 問題陳述 如果有一個類似階梯狀的障礙物，動力鏟應該機動它的手臂以平穩的軌跡爬上障礙物。此外，它還應該以這樣一種方式進行機動，使總能量消耗降到最低。整個過程是自動化的，這樣就消除了人類工人的風險。 b stage 2 Fig. 2 Obstacle surmount stages. The power shovel with dotted lines depicts the initial state while the the one with the regular lines depicts the final state for each stage. P1, P2, P3 and αF denote the parameters of the total maneuver. B and E denote bucket and step edge positions respectively B P3 E initial pose of stage 2 Pb P4 step Pb : bottom center position final pose of stage 2 αF P1 a stage 1 E initial pose of stage 1 Pb Pb : bottom center position P2 step B final pose of stage 1 方法 在提出的方法中，障礙超越操作分為兩個階段。在第一階段，鏟斗保持在動力鏟的前部，并提供所需的反作用力，使爬蟲的正面向上爬升到階梯狀結構;爬蟲的尾部保持與地面水平的接觸。如圖2a所示。第一階段完成后,平臺旋轉180°boom-arm-bucket復合移動到后面的電鏟啟動第二階段。與第一階段類似，吊桶提供了所需的反作用力，以提升爬蟲的尾部，完成第2階段的全部surmount操作。如圖2b所示。在第一和第二階段，水桶保持固定的地面位置，使用摩擦力[1]或由斗齒錨定，這是穩定機動的支點;可根據環境選擇適合的錨固方法。 討論 可以看出，CFSQP結果與完全慢批量模擬得到的結果比較好。事實上，CFSQP已經捕獲了目標函數(能量)的連續性質，因此能夠獲得最高效的param- eters，即使在基于較小參數的情況下，也不能被捕獲。從CFSQP的能量結果來看，這是明顯的，比徹底的慢批量模擬的結果要小。為了使CFSQP運行，必須將修改包含到原始算法中。也就是說，當目標函數的梯度是有限的。 差分逼近,算法傾向于使用附近的點,甚至可以違反給定con?-制度化。這可能會導致ODE崩潰，因為輸入的定義不明確。為了克服這個問題，在測試不確定的點時注入了大量的成本。 吊桿、臂和桶接頭的關節軌跡(圖11、12、13)確認關節平穩過渡。然而，每個數字的不連續性需要特別的說明。第一階段完成后，平臺旋轉到動力鏟的背面開始第二階段。假設這個簡單的操作可以通過恒定的能量來完成，因此為了簡單起見，我們省略了分析。因此，由于序列1和序列2-1之間的最終和初始關節的不匹配，可以看到間斷。 參數P4被認為是常量。 模擬。P4的唯一要求是，當2-2序列完成后，電鏟在提升吊桶后能夠保持穩定。在此之前，只要滿足這一要求，P4就可以被設定為一個經驗值，而不被包含在優化過程中。 open dynamics engine (ODE)[9]包括兩個默認求解器，即(1)Dantzig的agm solver。 (2)連續超松弛(SOR)投影高斯- Seidel (PGS) LCP求解器。在這個工作中，Dantzig的agm solver已經被用于實現a。 數值精確解，即使它大約是一個數量級的慢于或PGS LCP求解器。 從圖14可以看出，關節突在不同的階段經歷一定的瞬態。在第一階段的開始階段，由于兩個原因導致轉矩瞬變:(1)履帶前的接觸與地面接觸，(2)當桶開始推臺階或地面時產生的內力。類似的情況出現在第二階段的開始階段，爬蟲的背部(但由于平臺旋轉而被視為爬蟲的前部)開始向上移動并與地面失去聯系。另一個重要的觀察是重力條件(每一個連桿的質量)在其他術語上占主導地位，比如科里奧利力、向心和慣性項，因為它們的關節速度和加速度相對較小。 作為障礙物的第一步，將一個類似于sim的階梯狀結構作為障礙物。如何——永遠不要忘記，使用它的手臂和水桶來改變地形是有好處的。其結果是，它可以將非結構化的地形鋪在前面，利用臺階切割法等快速方法將其塑造成階梯狀結構，并采用所提出的方法;將地形完全修改成光滑的邊坡需要相當長的時間，這就否定了原來的目的。 未來的工作 提出的方法是解決這一問題的第一步，因此選擇了一個簡單的階梯狀障礙物。由于問題的對稱性，在模擬中可以忽略y坐標運動。此外，臂和桶連接軸相互平行，這使得cor-響應的連接在飛機上移動。這也使我們將三維運動簡化為二維空間。然而，在自然災害之后產生的碎片有非常復雜的形狀。作者希望在未來解決各種障礙的問題，這就需要對全三維運動進行分析?？朔碗s障礙的另一個方面是穩定性問題。電鏟在整個操作過程中應保持其穩定性，在任何情況下都不應傾斜。 在軌跡規劃中采用簡單的高階多項式，因為它簡單易用，沒有遇到任何問題。然而，spline(分段連續多項式)在軌跡規劃中得到了popu- larity，作者希望通過將簡單的多項式在未來改變為樣條函數來觀察其改進。 作為下一步，作者希望在未來使用真實的硬件進行擴展，以確認通過模擬獲得的結果。 5 Surmounting obstacles by arm maneuver for unmanned power shovel Abstract Large debris created after natural disasters restrict access to inner parts of affected regions, and slows down disaster relief operations. Power shovels are often used to clear wreckage but the process can take a lot of time. Moreover, it is dangerous to involve human workers operating heavy machinery in such unstable conditions. To speedup access to inner areas, obstacles can be surmounted with the assistance of carefully maneuvered power shovel arm, instead of removing them. In this work, an autonomous obstacle surmounting technique for an unmanned power shovel is proposed. Out of different sequences, the one that optimizes the total energy consumption is chosen as the best can- didate for surmounting a given step-like obstacle. Dynamic simulation results show the effectiveness of the proposed method. Background Each year many countries in the world are challenged by natural disasters such as earthquakes, floods, tsu- namis, typhoons and so on. While these disasters can cause loss of life, they also generate large amounts of debris, which further reduces access to inner parts of the affected regions. This results in slowing down of search and rescue missions as well as other disaster relief opera- tions. Power shovels are used in disaster stricken areas to remove wreckage and to clear up roads. Neverthe- less, it is a dangerous task to involve human workers to operate such heavy machines in these conditions as there is chance of tip over of these machines due to instabil- ity. Moreover, it can take a lot of time to clear up all the obstacles and finally get access to inner areas. In order to speed up disaster relief operations, large obstacles can be surmounted instead of clearing them. Using crawler wheels, power shovels have the ability to go over objects effectively compared to other vehi- cles. However, there exists several challenges to obsta- cle surmounting with power shovels as follows: only theobstacles that are within the climbing limit of the crawler can be overcome; crawler power can be easily saturated; power shovel can tip over and damage itself if not moved skillfully when it is on top of an obstacle; being heavy machines, power shovels are also difficult to get back to the original state at the event of tip over. To overcome the aforementioned problems, a power shovel can maneuver its arm effectively to assist the obstacle surmount operation. In fact, such arm assistance is being used nowadays to load small power shovels to trucks for transportation. As can be seen on [1], it can be achieved only with great level of skill and competency. Considering this scenario as a starting point, this work presents an autonomous arm maneuver based obstacle surmounting method to overcome a step-like structure for an unmanned power shovel (Fig. 1). Among different maneuver sequences, the best maneuver is chosen based on the minimum total energy consumption. Further- more, a smooth trajectory of the machine is preferred to avoid any vibrations and jerk exerted on itself and on its surroundings. Previous works on excavators can be found at [2–5]. Ref. [2] presents a dynamic model for an excavator with the intention of developing an automated excavation con- trol system for terrestrial, lunar, and planetary excavation. The kinematics of excavators having hydraulic actuatorsare investigated in detail in [3]. Ref. [4] mainly focuses on a system that completely automates the truck loading task. In that system the excavator’s software decides where to dig in the soil, where to dump in the truck, and how to quickly move between these points while detecting and stopping for obstacles. The nature of an excavation process and the way it may be controlled is investigated with the intention of automatic excavation in [5]. Among other related works, an autonomous stair- case climbing tracked mobile robot is introduced in [6]. However, it does not use any arms for assistance. Ref. [7] introduces a pilot system for a rescue robot to let a human operator suggest good directions to traverse on a 3D debris environment. In contrast, the proposed sys- tem seeks autonomous operation without any human intervention. Ref. [8] has proposed a wheeled robot with a movable center of mass (CoM) to ease the traverse over rough terrain. The proposed system also considers change of CoM, indirectly, by maneuvering its arm; how- ever, the main focus is on getting the reaction force at the bucket as a support to lift the power shovel crawler. Fig. 1 Basic parts of a power shovel. The coordinate frame convention is X forward, Y left and Z up X (forward) crawler step platform boom joint power shovel bucket bucket joint axis of platform rotation boom arm Z (up) arm joint Problem statement Given a step-like obstacle, the power shovel should maneuver its arm to climb up the obstacle in a smooth trajectory. Also, it should carry out the maneuver in such a way that the total energy consumption is minimized. The whole process is to be automated so that the risk for the human workers is eliminated. Nomenclature The basic parts of a power shovel are illustrated in Fig. 1; boom, arm and bucket are the main links considered, while each link is attached to the previous link by boom- joint, arm-joint and bucket-joint, respectively. These joints are individually controlled to achieve different poses similar to a serial link robot manipulator. There is a rotating platform, which can rotate around its local z axis (vertical) so that the whole boom-arm-bucket composite can be moved to its front and back, symmetrically. The vehicle stands on a crawler that provides better mobility on unstructured terrain. Methods b stage 2 Fig. 2 Obstacle surmount stages. The power shovel with dotted lines depicts the initial state while the the one with the regular lines depicts the final state for each stage. P1, P2, P3 and αF denote the parameters of the total maneuver. B and E denote bucket and step edge positions respectively B P3 E initial pose of stage 2 Pb P4 step Pb : bottom center position final pose of stage 2 αF P1 a stage 1 E initial pose of stage 1 Pb Pb : bottom center position P2 step B final pose of stage 1 In the proposed method the obstacle surmount operation is divided into two stages. In the 1st stage, the bucket is kept at the front of the power shovel and it provides the required reaction force to lift the front of the crawler to climb up the step-like structure; the rear of the crawler maintains contact with the ground level. This is illus- trated in Fig. 2a. After the 1st stage is completed, the platform rotates 180° to move the boom-arm-bucket composite to the back of the power shovel to initiate the 2nd stage. Similar to the 1st stage, the bucket provides the required reaction force to lift the rear of the crawler to complete the total surmount operation in the 2nd stage. This is illustrated in Fig. 2b. Throughout 1st and 2nd stages, the bucket maintains fixed ground position either by using friction force [1] or anchored by bucket teeth, which acts as a pivot for stable maneuver; the suit- able anchoring method can be chosen depending on the environment. Discussion It can be observed that the CFSQP result compare well with the result obtained in the exhaustive slow batch simulation. In fact, CFSQP had captured the continuous nature of the objective function (energy) and as a result had been able to obtain the most energy efficient param- eters, which cannot be seized even when exhaustive batch simulations are run based on smaller parameter incre- ments. This is evident from CFSQP energy result being smaller than that of the exhaustive slow batch simulations. To make CFSQP running, a modification had to be included into the original algorithm. That is, when the gradient of the objective function is calculated by finite Angle [deg] difference approximation, the algorithm tends to use nearby points, which can even violate the given con- straints. This can make ODE crash due to ill-defined inputs. To overcome this problem, a large cost was injected when ill-defined points were tested. The joint trajectories for boom, arm and bucket joints (Figs. 11, 12, 13) confirm that the joints undergo smooth transition. However, the discontinuity of each figure needs special mention. After the 1st stage has finished the platform rotates to the back of the power shovel to start the 2nd stage. It is assumed that this trivial operation can be done by constant energy and therefore omitted from the analysis for simplicity. As a result, a discontinuity can be seen due to the mismatch of final and initial joint posi- tions between sequence 1 and sequence 2–1. The parameter P4 is considered to be constant in thesimulation. The only requirement for P4 is such that the power shovel should be able to maintain stability once it lifts the bucket after sequence 2–2 is completed. There- fore, as long as this requirement is fulfilled, P4 can be set to an empirical value and not be included in the optimi- zation process. The open dynamics engine (ODE) [9] consists of two default solvers namely, (1) Dantzig’s Agorithm solver, and(2) Successive Over-Relaxation (SOR) Projected Gauss- Seidel (PGS) LCP solver. Dantzig’s Agorithm solver has been used in this work as it attempts to achieve anumerically exact solution, even though it is about one order of magnitude slower than SOR PGS LCP solver. From Fig. 14, it can be observed that the joint tor- ques undergo certain transients at different stages. At the beginning of 1st stage, torque transients occur due to two reasons: (1) front of the crawler looses the contact with ground, and (2) internal forces generated when the bucket starts pushing the step or ground. A similar condition occurs at the beginning of the 2nd stage where the back of the crawler (however, seen as the front of the crawler due to platform rotation) starts moving upwards and looses contact with the ground. Another important observation is that the gravity terms (mass of each link) have dominated over other terms such as Coriolis, centripetal and inertial terms because of the relatively small joint velocities and accelerations. As the first step of obstacle surmount operation a sim- ple step-like structure was chosen as the obstacle. How- ever, one should not forget that power shovels have the advantage of modifying the terrain using its arm and bucket. As a result, it can pave the unstructured terrain in front of it to shape it to a step-like structure using fast methods like bench cut method and employ the proposed method; totally modifying the terrain into a smooth slope would take a considerable amount of time, which negates the original purpose.  無人駕駛電動鏟越障車 摘要 在自然災害發生后會產生大量的廢墟，阻礙了救援人員解救被困人員，延緩了救災行動。動力鏟通常用來清理廢墟殘骸，但這個過程可能需要很多時間。此外，在這種不穩定的條件下，讓救援人員操作重型機械是非常危險的。為了加快進入被困人員區域，可以通過靈活機動的無人駕駛動力鏟臂來執行，而不是將其淘汰，在這項工作中，無人駕駛動力鏟的自主障礙技術是至關重要的。在不同的序列中，優化總能量消耗的方法被選為克服給定步驟障礙的最佳方法，動態仿真結果表明了該方法的有效性。 關鍵詞:動力鏟；障礙超越；無人駕駛；優化 背景 每年世界上許多國家都受到地震、洪水、臺風等自然災害的侵襲，這些災害不僅造成生命損失，而且它們也會產生大量的廢墟，這導致了搜索和救援任務緩慢及救援困難度加大。在受災地區，讓人們操作動力鏟操作清理廢墟，是一項危險的任務，因為這些機器有可能因安裝的不穩定而發生故障，對人們造成傷害。此外，清除所有的障礙并最終進入內部區域需要花費大量的時間。 為了加快救援行動的速度，越過巨大的障礙物，而不是清除它們，這時使用履帶輪，動力鐵鍬能有效地解決這一問題。然而，在使用動力鏟的情況下，有幾個難題需要克服:只有在履帶車的爬坡范圍內的障礙物才能被克服;履帶越障車的力量可以很容易的飽和;當它處于障礙物的頂部時，如果沒有靈巧地移動，它可以翻倒并損壞自己。作為重型機械，在翻倒的時候，動力鏟也很難回到原來的狀態。 以前在挖掘機上的工作可以在[2-5]找到。參考文獻[2]提出了一種挖掘器的動態模型，目的是開發一個用于地面、月球和行星挖掘的自動挖掘控制系統。[3]詳細研究了具有液壓執行機構的挖掘機的運動學。參考文獻[4]主要集中在一個完全自動化卡車裝載任務的系統上。在這個系統中，挖掘機的軟件決定了在哪里挖掘，在哪里傾倒卡車，以及如何快速在這些點之間移動，同時檢測和停止障礙物。研究了開挖過程的性質和控制方法，并在[5]中進行了自動開挖的目的。 在其他相關的工作中，一種自動爬樓梯的履帶機器人被引入[6]。但是，它不使用任何武器援助。參考文獻[7]介紹了一種救援機器人的試驗系統，該系統允許人類操作員在三維碎片環境中提出正確的方向。相比之下，擬議的sys- tem則尋求無需人工干預的自動操作。參考文獻[8]提出了一種可移動的質心(CoM)的輪式機器人，以方便在崎嶇的地形上行走。擬議的系統也考慮通過操縱它的手臂來間接地改變CoM;如何-永遠，主要的焦點是在桶中得到反應力作為支撐來舉起動力鏟履帶。 Fig. 1 Basic parts of a power shovel. The coordinate frame convention is X forward, Y left and Z up X (forward) crawler step platform boom joint power shovel bucket bucket joint axis of platform rotation boom arm Z (up) arm joint 問題陳述 如果有一個類似階梯狀的障礙物，動力鏟應該機動它的手臂以平穩的軌跡爬上障礙物。此外，它還應該以這樣一種方式進行機動，使總能量消耗降到最低。整個過程是自動化的，這樣就消除了人類工人的風險。 b stage 2 Fig. 2 Obstacle surmount stages. The power shovel with dotted lines depicts the initial state while the the one with the regular lines depicts the final state for each stage. P1, P2, P3 and αF denote the parameters of the total maneuver. B and E denote bucket and step edge positions respectively B P3 E initial pose of stage 2 Pb P4 step Pb : bottom center position final pose of stage 2 αF P1 a stage 1 E initial pose of stage 1 Pb Pb : bottom center position P2 step B final pose of stage 1 方法 在提出的方法中，障礙超越操作分為兩個階段。在第一階段，鏟斗保持在動力鏟的前部，并提供所需的反作用力，使爬蟲的正面向上爬升到階梯狀結構;爬蟲的尾部保持與地面水平的接觸。如圖2a所示。第一階段完成后,平臺旋轉180°boom-arm-bucket復合移動到后面的電鏟啟動第二階段。與第一階段類似，吊桶提供了所需的反作用力，以提升爬蟲的尾部，完成第2階段的全部surmount操作。如圖2b所示。在第一和第二階段，水桶保持固定的地面位置，使用摩擦力[1]或由斗齒錨定，這是穩定機動的支點;可根據環境選擇適合的錨固方法。 討論 可以看出，CFSQP結果與完全慢批量模擬得到的結果比較好。事實上，CFSQP已經捕獲了目標函數(能量)的連續性質，因此能夠獲得最高效的param- eters，即使在基于較小參數的情況下，也不能被捕獲。從CFSQP的能量結果來看，這是明顯的，比徹底的慢批量模擬的結果要小。為了使CFSQP運行，必須將修改包含到原始算法中。也就是說，當目標函數的梯度是有限的。 差分逼近,算法傾向于使用附近的點,甚至可以違反給定con?-制度化。這可能會導致ODE崩潰，因為輸入的定義不明確。為了克服這個問題，在測試不確定的點時注入了大量的成本。 吊桿、臂和桶接頭的關節軌跡(圖11、12、13)確認關節平穩過渡。然而，每個數字的不連續性需要特別的說明。第一階段完成后，平臺旋轉到動力鏟的背面開始第二階段。假設這個簡單的操作可以通過恒定的能量來完成，因此為了簡單起見，我們省略了分析。因此，由于序列1和序列2-1之間的最終和初始關節的不匹配，可以看到間斷。 參數P4被認為是常量。 模擬。P4的唯一要求是，當2-2序列完成后，電鏟在提升吊桶后能夠保持穩定。在此之前，只要滿足這一要求，P4就可以被設定為一個經驗值，而不被包含在優化過程中。 open dynamics engine (ODE)[9]包括兩個默認求解器，即(1)Dantzig的agm solver。 (2)連續超松弛(SOR)投影高斯- Seidel (PGS) LCP求解器。在這個工作中，Dantzig的agm solver已經被用于實現a。 數值精確解，即使它大約是一個數量級的慢于或PGS LCP求解器。 從圖14可以看出，關節突在不同的階段經歷一定的瞬態。在第一階段的開始階段，由于兩個原因導致轉矩瞬變:(1)履帶前的接觸與地面接觸，(2)當桶開始推臺階或地面時產生的內力。類似的情況出現在第二階段的開始階段，爬蟲的背部(但由于平臺旋轉而被視為爬蟲的前部)開始向上移動并與地面失去聯系。另一個重要的觀察是重力條件(每一個連桿的質量)在其他術語上占主導地位，比如科里奧利力、向心和慣性項，因為它們的關節速度和加速度相對較小。 作為障礙物的第一步，將一個類似于sim的階梯狀結構作為障礙物。如何——永遠不要忘記，使用它的手臂和水桶來改變地形是有好處的。其結果是，它可以將非結構化的地形鋪在前面，利用臺階切割法等快速方法將其塑造成階梯狀結構，并采用所提出的方法;將地形完全修改成光滑的邊坡需要相當長的時間，這就否定了原來的目的。 未來的工作 提出的方法是解決這一問題的第一步，因此選擇了一個簡單的階梯狀障礙物。由于問題的對稱性，在模擬中可以忽略y坐標運動。此外，臂和桶連接軸相互平行，這使得cor-響應的連接在飛機上移動。這也使我們將三維運動簡化為二維空間。然而，在自然災害之后產生的碎片有非常復雜的形狀。作者希望在未來解決各種障礙的問題，這就需要對全三維運動進行分析。克服復雜障礙的另一個方面是穩定性問題。電鏟在整個操作過程中應保持其穩定性，在任何情況下都不應傾斜。 在軌跡規劃中采用簡單的高階多項式，因為它簡單易用，沒有遇到任何問題。然而，spline(分段連續多項式)在軌跡規劃中得到了popu- larity，作者希望通過將簡單的多項式在未來改變為樣條函數來觀察其改進。 作為下一步，作者希望在未來使用真實的硬件進行擴展，以確認通過模擬獲得的結果。 11