TWI808852B - Method for stable control of six-axis robotic arm by deep learning - Google Patents

Method for stable control of six-axis robotic arm by deep learning Download PDF

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TWI808852B
TWI808852B TW111128793A TW111128793A TWI808852B TW I808852 B TWI808852 B TW I808852B TW 111128793 A TW111128793 A TW 111128793A TW 111128793 A TW111128793 A TW 111128793A TW I808852 B TWI808852 B TW I808852B
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李振興
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崑山科技大學
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Abstract

The invention relates to a method for stable control of a six-axis robotic arm by deep learning. Primarily, the six-axis robotic arm comprises a first axis, a second axis, a third axis, a fourth axis, a fifth axis and a sixth axis. The parameters of a controller are adjusted by deep learning, and a state feedback controller is mainly used, so that an adjustment mechanism with learning nature can be widely adapted to the changes of environmental parameters to achieve the effect of automatic control, so as to increase the practicality and efficiency for the whole implementation.

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六軸機器手臂深度學習穩定控制方法A deep learning stabilization control method for a six-axis robotic arm

本發明係有關於一種六軸機器手臂深度學習穩定控制方法，尤其是指一種具有學習性質的調整機制，可以廣泛的適應環境參數之改變，以達到自動控制之功效，而在其整體施行使用上更增實用功效特性者。The present invention relates to a deep learning stabilization control method for a six-axis robotic arm, in particular to an adjustment mechanism with a learning nature, which can widely adapt to changes in environmental parameters to achieve the effect of automatic control, and has more practical features in its overall implementation and use.

按，機器手臂是工業自動化進程中的重要角色，機器手臂的定位越精準，更能增加生產效率及工安防護應用，而人工智慧可為機器手臂達到穩定並強健的控制，此即為現今以人工智慧調整控制器的技術。其中，六軸機器手臂係為一種常見的機械手臂，其涵蓋了X、Y、Z三個方向軸以及U、V、W三個旋轉軸，該六軸機器手臂幾乎沒有運作死角，於使用操作上非常具有彈性，可對目標進行各種角度、方向的加工，使得其被廣為是用在各種自動化工廠中，能被應用在包括焊接、卯接、切削加工、去毛邊、噴漆、上下料搬運、零件組裝、拋光等，且因為COVID-19疫情關係，零接觸成為常態，更為加速工業機器手臂取代人力，個別產業發展也促使工業機器手臂需求攀升，如半導體、綠電、電動車產業，國防工業，資通訊等領域也需要利用工業機器手臂與工具機整合技術。Press, the robot arm is an important role in the process of industrial automation. The more precise the positioning of the robot arm, the more it can increase production efficiency and industrial safety protection applications, and artificial intelligence can achieve stable and robust control for the robot arm. This is the current technology of adjusting the controller with artificial intelligence. Among them, the six-axis robot arm is a common robot arm, which covers the three axes of X, Y, and Z and the three rotation axes of U, V, and W. The six-axis robot arm has almost no dead angle in operation, and is very flexible in use and operation. It can process objects in various angles and directions, making it widely used in various automated factories. The development of individual industries also drives up the demand for industrial robotic arms, such as semiconductor, green electricity, electric vehicle industry, national defense industry, information and communication and other fields, which also need to use the integration technology of industrial robotic arms and machine tools.

該類機器手臂已經有使用運動學推導出各關節轉動角度與機器手臂終端位置姿勢的關係，軌跡規劃是規劃機器手臂在工作空間的行動路徑及運動位置、速度及加速度，將行走的點用逆運動學公式後，將直角座標轉為關節轉動角度，即可對各軸作角度軌跡控制，軌跡控制的方法有點對點控制、函數補間控制、設定點追蹤控制三種。機器手臂的運動可分為正運動學［Forward kinematics］和逆運動學［Inverse kinematics］兩方面；正運動學是由各關節的轉動角度去計算機器手臂終端位置［直角座標］，逆運動學則是由機器手臂終端位置［直角座標］去計算各關節的轉動角度，逆運動學的解有很多組，所以需依機器手臂實際轉動角度和位置姿態選擇出適當的解。This type of robot arm has already used kinematics to derive the relationship between the rotation angle of each joint and the terminal position and posture of the robot arm. Trajectory planning is to plan the action path, motion position, speed, and acceleration of the robot arm in the workspace. After using the inverse kinematics formula for the walking point, convert the Cartesian coordinates into the joint rotation angle, and then control the angular trajectory of each axis. There are three methods of trajectory control: point-to-point control, function interpolation control, and set point tracking control. The motion of the robot arm can be divided into two aspects: forward kinematics and inverse kinematics. Forward kinematics calculates the terminal position of the robot arm [cartesian coordinates] from the rotation angle of each joint, and inverse kinematics calculates the rotation angle of each joint from the terminal position of the robot arm [cartesian coordinates]. There are many sets of solutions for inverse kinematics, so it is necessary to choose an appropriate solution based on the actual rotation angle, position and posture of the robot arm.

而現今對於機器手臂穩定控制的方法有很多種類，包括模糊控制、強健控制等；強健控制的缺點在於需要對於機器手臂的參數有詳細的資料，但是強健控制可以達到最保守的穩定控制的設計；另，模糊控制則可以不用有機器手臂的參數詳細資料，可是必須有專家的經驗設計才能達到最完美的控制。Nowadays, there are many kinds of methods for the stability control of robotic arms, including fuzzy control, robust control, etc.; the disadvantage of robust control is that detailed information on the parameters of the robotic arm is required, but robust control can achieve the most conservative design of stable control; in addition, fuzzy control does not require detailed information on the parameters of the robotic arm, but it must be designed with expert experience to achieve the most perfect control.

緣是，發明人有鑑於此，秉持多年該相關行業之豐富設計開發及實際製作經驗，針對現有之結構及缺失再予以研究改良，進而提供一種六軸機器手臂深度學習穩定控制方法，以期達到更佳實用價值性之目的者。The reason is that, in view of this, the inventor, with years of rich experience in design, development and actual production in this related industry, researches and improves the existing structure and defects, and then provides a six-axis robot arm deep learning stability control method, in order to achieve better practical value.

本發明之主要目的在於提供一種六軸機器手臂深度學習穩定控制方法，主要係以深度學習的方法調整控制器參數，且利用狀態回授控制器為主，使得能具有學習性質的調整機制，可以廣泛的適應環境參數之改變，以達到自動控制之功效，而在其整體施行使用上更增實用功效特性者。The main purpose of the present invention is to provide a deep learning and stable control method for a six-axis robot arm, which mainly uses deep learning to adjust controller parameters, and uses a state feedback controller as the main method, so that the adjustment mechanism can have a learning property, and can widely adapt to changes in environmental parameters to achieve the effect of automatic control, and it has more practical features in its overall implementation and use.

為令本發明所運用之技術內容、發明目的及其達成之功效有更完整且清楚的揭露，茲於下詳細說明之，並請一併參閱所揭之圖式及圖號：In order to have a more complete and clear disclosure of the technical content used in the present invention, the purpose of the invention and the effects achieved, it will be described in detail below, and please also refer to the disclosed drawings and drawing numbers:

首先，請參閱第一圖本發明之六軸機器手臂關節示意圖及第二圖本發明之六軸機器手臂的D-H模型圖所示，本發明之六軸機器手臂(1)主要係包括有第一軸(11)、第二軸(12)、第三軸(13)、第四軸(14)、第五軸(15)及第六軸(16)，而該六軸機器手臂(1)各軸之參數即如下表所示： 軸 θ α(red) 一 θ 1 π/2 0 二 θ 2 0 0 三 θ 3 π/2 0 四 θ 4 -π/2 0 五 θ 5 π/2 0 0 六 θ 6 0 0 First, please refer to the schematic diagram of the joints of the six-axis robot arm of the present invention in the first figure and the DH model diagram of the six-axis robot arm of the present invention in the second figure, the six-axis robot arm (1) of the present invention mainly includes the first axis (11), the second axis (12), the third axis (13), the fourth axis (14), the fifth axis (15) and the sixth axis (16), and the parameters of each axis of the six-axis robot arm (1) are shown in the following table: axis θ α(red) one θ 1 π/2 0 two θ 2 0 0 three θ 3 π/2 0 Four θ 4 -π/2 0 five θ 5 π/2 0 0 six θ 6 0 0

而D-H座標系統方法是一種為關節鏈中的每一個桿件建立坐標系統的矩陣方式，利用D-H參數法［Denavit-Hartenberg］求得該六軸機器手臂(1)軸與軸之間的相對關係，θ i［關節角度］、 ［連桿分出］、 ［連桿長度］、α i［連桿扭轉］稱為D-H參數。 The DH coordinate system method is a matrix method to establish a coordinate system for each member in the joint chain. The relative relationship between the axes of the six-axis robot arm (1) is obtained by using the DH parameter method [Denavit-Hartenberg], θi [joint angle], [Connecting rod separation], [Connecting rod length], α i [Connecting rod torsion] are called DH parameters.

使得該六軸機器手臂(1)之動力學模型如下：The dynamic model of the six-axis robotic arm (1) is as follows:

M(q) ​+C(q , ​) ​+G (q)+ = ，                              (1) M(q) +C(q , ) +G (q)+ = , (1)

其中，q是關節(角)位移向量， 是關節力矩向量， 為干擾力矩向量， 是機器手臂的 質量矩陣， 是 離心力和科氏力矩陣， 是 重力向量， 為 庫倫摩擦力與黏滯摩擦力向量。 where q is the joint (angular) displacement vector, is the joint torque vector, is the disturbance torque vector, It's a robotic arm mass matrix, yes Centrifugal and Coriolis force matrices, yes gravity vector, for Coulomb and viscous friction vectors.

請再一併參閱第三圖本發明之六軸機器手臂的關節空間控制架構圖所示，該六軸機器手臂(1)若以關節角度做為控制量的運動，即為關節空間控制，在實際操作空間中所下的指令，利用逆運動學，透過控制器經由致動器驅動驅動器進行動作，以經由轉換得到關節空間後，進入該六軸機器手臂(1)內部，帶動該六軸機器手臂(1)進行運動，並從傳感器回授各軸關節角度做角度上的控制，而於該六軸機器手臂(1)運動中，各個關節之間互相獨立，互相不受影響。Please also refer to the third figure of the joint space control architecture diagram of the six-axis robotic arm of the present invention. If the six-axis robotic arm (1) moves with joint angles as the control amount, it is joint space control. The commands given in the actual operating space use inverse kinematics to move through the controller through the actuator to drive the driver. During the movement of the six-axis robot arm (1), each joint is independent of each other and is not affected by each other.

設 、 、 為控制參考輸入［desire input］，分別是角度、角速度及角加速度， 、 、 為誤差量［error］，而 、 、 為當前關節狀態，也就是感測器讀回來的值。在式(1)中， 是該六軸機器手臂(1)的力矩控制輸入，假設 干擾力矩為零， 庫倫摩擦力與黏滯摩擦力為零，則該六軸機器手臂(1)的動態方程式表示如下式(2)所示。 set up , , For control reference input [desire input], which are angle, angular velocity and angular acceleration respectively, , , is the error amount [error], and , , It is the current joint state, that is, the value read back by the sensor. In formula (1), is the torque control input of the six-axis robotic arm (1), assuming The disturbance torque is zero, Coulomb friction and viscous friction are zero, then the dynamic equation of the six-axis robotic arm (1) is expressed as the following formula (2).

M(q) ​+C(q , ​) ​+G (q) =u，                                             (2) M(q) +C(q , ) +G (q) = u, (2)

若控制變量設計為下式(3)：If the control variable is designed as the following formula (3):

，                                                  (3) , (3)

該式(3)中的誤差為：The error in the formula (3) is:

， ,

， ,

， ,

、 分別為第一個狀態回授比例控制常數及第二個狀態回授微分控制常數；當設計控制輸入u為下式(4)： , are respectively the first state feedback proportional control constant and the second state feedback differential control constant; when the design control input u is the following formula (4):

+ ，                   (4) + , (4)

將(4)式代入(2)式則可以得到閉迴路動態方程式為下式(5)：Substituting formula (4) into formula (2), the closed-loop dynamic equation can be obtained as the following formula (5):

，                                                  (5) , (5)

意指時間趨近於無限大∞，則 、 、 都會趨近於零［漸近穩定］，則即可得到第四圖所示之關節空間動態模型狀態回授控制方塊圖。 It means that time tends to infinity ∞, then , , will tend to zero [asymptotically stable], then the state feedback control block diagram of the joint space dynamic model shown in the fourth figure can be obtained.

請再一併參閱第五圖本發明之六軸機器手臂的操作空間控制架構圖所示，在操作空間控制中，所面對到的系統空間是實際工作的空間，並非關節空間，透過該控制器經由該致動器驅動該驅動器進行動作，令該驅動器帶動該六軸機器手臂(1)進行運動，並從該傳感器回授各軸關節角度做角度上的控制，使得從參考指令到回授信號都是在操作空間中，所以在操作空間到該六軸機器手臂(1)中必須做轉換，讓指令可以進入該六軸機器手臂(1)做執行。Please also refer to Figure 5 for the control structure diagram of the six-axis robotic arm of the present invention. In the control of the operating space, the system space faced is the actual working space, not the joint space. Through the controller, the actuator drives the driver to move the six-axis robot arm (1), and the sensor feeds back the joint angles of each axis to control the angle, so that the reference command and the feedback signal are all in the operation space. Therefore, a conversion must be made between the operation space and the six-axis robot arm (1). , so that the command can enter the six-axis robotic arm (1) for execution.

解析雅可比矩陣［Analytical Jacobian 矩陣］定義為 ，X指的是該六軸機器手臂(1)端點相對於基座座標的姿態，表示為三個位移量及三個旋轉量，X與 的關係如下式(6)： Analytical Jacobian matrix [Analytical Jacobian matrix] is defined as , X refers to the attitude of the end point of the six-axis robotic arm (1) relative to the coordinates of the base, expressed as three displacements and three rotations, X and The relationship is as follows (6):

，                                                                    (6) , (6)

設 、 、 為控制參考指令輸入， 、 、 為誤差量， 、 、 為目前關節狀態，也就是感測器讀回來的值， 為設計控制變量，式(2)中， 是該六軸機器手臂(1)的力矩控制輸入。將式(6)等號兩邊對時間做一次微分可得到下式(7)： set up , , For control reference command input, , , is the amount of error, , , is the current joint state, that is, the value read back by the sensor, is the design control variable, in formula (2), is the torque control input of the six-axis robotic arm (1). Differentiate the time on both sides of the equation (6) to get the following equation (7):

，                                                            (7)將該式(7)整理為下式(8)： , (7) organize the formula (7) into the following formula (8):

，                                                       (8) , (8)

可以將控制變量y設計為下式(9)：The control variable y can be designed as the following formula (9):

，                                  (9) , (9)

在式(9)中，誤差值為以下表示式，In formula (9), the error value is the following expression,

， ,

， ,

， ,

將式(9)的y帶入式(2)的 ，即可以設計出下式(10)： Put y in formula (9) into formula (2) , that is, the following formula (10) can be designed:

(10) (10)

則操作空間控制的閉迴路系統動態方程表示如式(11)所示，Then the dynamic equation expression of the closed-loop system of operating space control is shown in formula (11),

，                                                (11) , (11)

而可設計 控制器［狀態回授控制器］使得 達到漸進穩定，意思是當 。 can be designed The controller [state feedback controller] makes asymptotically stable, meaning that when .

請再一併參閱第六圖本發明之深度學習方法控制方塊圖所示，予以加入深度學習的方法調整狀態回授控制器參數 及微調量 ；請再一併參閱第七圖本發明之多層類神經網路架構示意圖所示，利用深度學習的方法調整方程式(11)式的控制參數 及 。深度學習是使用多層類神經網路作為控制方法，變數符號 是深度學習類神經網路的輸入節點，符號 是輸入節點的偏值，符號 、 各是第1層、第2層的隱藏節點，隱藏層有2層以上，因為深度學習需要比較多的隱藏層才會有良好的效果。符號 、 是隱藏節點的偏值，變數符號 是輸出節點。 是狀態回授控制器。 是保持系統效能的微調量。 、 ，誤差為 ， ， 。輸入 、 、 輸出 、 、 Please also refer to Figure 6 as shown in the control block diagram of the deep learning method of the present invention, and add the method of deep learning to adjust the parameters of the state feedback controller and fine-tuning ; Please also refer to the seventh figure as shown in the schematic diagram of the multi-layer neural network architecture of the present invention, using the method of deep learning to adjust the control parameters of the equation (11) and . Deep learning is the use of multi-layer neural networks as a control method, variable notation is the input node of the deep learning neural network, the symbol is the bias value of the input node, the symbol , Each is the hidden node of the first layer and the second layer, and the hidden layer has more than 2 layers, because deep learning requires more hidden layers to have a good effect. symbol , is the bias value of the hidden node, variable sign is the output node. is the state feedback controller. is the amount of fine-tuning to maintain system performance. , , the error is , , . enter , , output , ,

其中輸入節點代表意思如下：The input node represents the following meanings:

、 ，                                               (12) , , (12)

輸出節點代表意思如下：The meaning of the output node is as follows:

， ， ，                                (13) , , , (13)

控制輸入 為 control input for

+ +ɛ，            (14) + +ɛ, (14)

深度學習類神經網路的權值如下：The weights of the deep learning neural network are as follows:

令符號 是輸入節點與第1層隱藏節點間的權值，符號 是第1層隱藏節點與第2層隱藏節點間的權值，符號 是第2層隱藏節點與輸出節點間的權值。 order symbol is the weight between the input node and the hidden node of the first layer, symbol is the weight between hidden nodes in layer 1 and hidden nodes in layer 2, symbol is the weight between the layer 2 hidden node and the output node.

第1層隱藏節點與輸入節點的關係如下：The relationship between layer 1 hidden nodes and input nodes is as follows:

，                                         (15) , (15)

於上述(15)式中，該 係為符號，而該等號左右兩式係單一純量， In the above formula (15), the is a symbol, and the left and right sides of the equal sign are a single scalar,

，                                                   (16) , (16)

啟動函數 使用如下的雙極S型函數，將輸出適當的縮放到值域-1到1之間， start function Use the following bipolar sigmoid function to scale the output appropriately to the value range -1 to 1,

, ，                                         (17) , , (17)

第2層隱藏節點與第1層隱藏節點的關係如下：The relationship between hidden nodes in layer 2 and hidden nodes in layer 1 is as follows:

，                                (18) , (18)

於上述(18)式中，該 係為符號，而該等號左右兩式係單一純量， In the above formula (18), the is a symbol, and the left and right sides of the equal sign are a single scalar,

，                                                 (19) , (19)

輸出節點與第2層隱藏節點的關係如下：The relationship between output nodes and layer 2 hidden nodes is as follows:

，                                    (20) , (20)

於上述(20)式中，該 係為符號，而該等號左右兩式係單一純量， In the above formula (20), the is a symbol, and the left and right sides of the equal sign are a single scalar,

，                                                           (21) , (twenty one)

使用倒傳遞法求每一層的權值。Use the backward pass method to find the weight of each layer.

訓練的目的是要使誤差平方達到最小，誤差的平方為：The purpose of training is to minimize the square of the error, the square of the error is:

，                                                          (22) , (twenty two)

權值用以下的方法來更新，輸入層到第一層隱藏層為：The weights are updated in the following way, from the input layer to the first hidden layer:

，                                            (23) , (twenty three)

，                                                        (24) , (twenty four)

為數學上的差量，第一層隱藏層到第二層隱藏層為： For the mathematical difference, the first hidden layer to the second hidden layer is:

，                                         (25) , (25)

，                                                        (26) , (26)

第二層隱藏層到輸出層為：The second hidden layer to the output layer is:

，                                          (27) , (27)

，                                                       (28) , (28)

其中 為學習速率常數。偏微分 ， ， ， ， 及 的計算如下。 in is the learning rate constant. partial differential , , , , and The calculation of is as follows.

，                      (29) , (29)

，                                  (30) , (30)

(31) (31)

，      (32) , (32)

，                                                            (33) , (33)

，                                                            (34) , (34)

其中in

， ， ，                       (35) , , , (35)

其中， ， ， ， in, , , ,

， ，                     (36) , , (36)

， ，       (37) , , (37)

， ，                                          (38) , , (38)

， ，   (39) , , (39)

， ，                                     (40) , , (40)

在實用上，偏微分 可以用 來近似，其中 且 。因此偏微分 ， ， ， ， 及 可以改寫如下： In practice, partial differential Can use to approximate, where and . So the partial differential , , , , and can be rewritten as follows:

，                                          (41) , (41)

，                                                        (42) , (42)

，                                    (43) , (43)

，                                                   (44) , (44)

，                                          (45) , (45)

，                                                   (46) , (46)

輸出節點、第二層隱藏層節點與第一層隱藏層節點的微量變動為：The slight changes of the output node, the second hidden layer node and the first hidden layer node are:

其中 ， ， 。 in , , .

因此權值的更新公式可以更改如下：Therefore, the update formula of the weight can be changed as follows:

，                                         (47) , (47)

，                                                         (48) , (48)

，                                    (49) , (49)

，                                                   (50) , (50)

，                                           (51) , (51)

，                                                      (52) , (52)

學習法則可以修改為以下公式，The learning rule can be modified as the following formula,

輸出層和第2隱藏層的權值更新公式：The weight update formula of the output layer and the second hidden layer:

，                         (53) , (53)

輸出層和第2隱藏層的偏值更新公式：The bias value update formula of the output layer and the second hidden layer:

，                                               (54) , (54)

第2隱藏層和第1隱藏層的權值更新公式：The weight update formulas of the second hidden layer and the first hidden layer:

，                   (55) , (55)

第2隱藏層和第1隱藏層的偏值更新公式：The bias update formulas of the second hidden layer and the first hidden layer:

，                                         (56) , (56)

第1隱藏層和輸入層的權值更新公式：The weight update formula of the first hidden layer and input layer:

，                         (57) , (57)

第1隱藏層和輸入層的偏值更新公式：The partial value update formula of the first hidden layer and input layer:

，                                           (58) , (58)

其中，動力［momentum］因子的範圍為 。加上動力［momentum］可以使類神經網路的學習計算時不會掉入局部最小值。 Among them, the range of the dynamic [momentum] factor is . Adding momentum [momentum] can prevent the neural network from falling into the local minimum when learning and calculating.

如此一來，即可使該可調控制參數 及 調整達到深度學習的模式，進而具有自動控制的目的。 In this way, the tunable control parameter can be and Adjust the mode to achieve deep learning, and then have the purpose of automatic control.

藉由以上所述，本發明之使用實施說明可知，本發明與現有技術手段相較之下，本發明主要係以深度學習的方法調整控制器參數，且利用狀態回授控制器為主，使得能具有學習性質的調整機制，可以廣泛的適應環境參數之改變，以達到自動控制之功效，而在其整體施行使用上更增實用功效特性者。Based on the above description and the description of the implementation of the present invention, it can be seen that the present invention is compared with the prior art methods. The present invention mainly uses the method of deep learning to adjust the controller parameters, and mainly uses the state feedback controller, so that the adjustment mechanism with learning properties can be widely adapted to the change of environmental parameters, so as to achieve the effect of automatic control, and it has more practical features in its overall implementation and use.

然而前述之實施例或圖式並非限定本發明之產品結構或使用方式，任何所屬技術領域中具有通常知識者之適當變化或修飾，皆應視為不脫離本發明之專利範疇。However, the above-mentioned embodiments or drawings do not limit the product structure or usage of the present invention, and any appropriate changes or modifications by those with ordinary knowledge in the technical field shall be considered as not departing from the patent scope of the present invention.

綜上所述，本發明實施例確能達到所預期之使用功效，又其所揭露之具體構造，不僅未曾見諸於同類產品中，亦未曾公開於申請前，誠已完全符合專利法之規定與要求，爰依法提出發明專利之申請，懇請惠予審查，並賜准專利，則實感德便。To sum up, the embodiment of the present invention can indeed achieve the expected use effect, and the specific structure disclosed by it has not only been seen in similar products, but also has not been disclosed before the application, and it has fully complied with the provisions and requirements of the Patent Law. It is really convenient to file an application for a patent for invention according to the law, and earnestly ask for the review and approval of the patent.

1:六軸機器手臂1: Six-axis robot arm

11:第一軸11: The first axis

12:第二軸12: Second axis

13:第三軸13: The third axis

14:第四軸14: Fourth axis

15:第五軸15: Fifth axis

16:第六軸16: Sixth axis

第一圖：本發明之六軸機器手臂關節示意圖Figure 1: Schematic diagram of the joints of the six-axis robotic arm of the present invention

第二圖：本發明之六軸機器手臂的D-H模型圖Figure 2: D-H model diagram of the six-axis robotic arm of the present invention

第三圖：本發明之六軸機器手臂的關節空間控制架構圖Figure 3: The structure diagram of the joint space control of the six-axis robotic arm of the present invention

第四圖：本發明關節空間動態模型狀態回授控制方塊圖Figure 4: The state feedback control block diagram of the joint space dynamic model of the present invention

第五圖：本發明之六軸機器手臂的操作空間控制架構圖Figure 5: The control structure diagram of the operating space of the six-axis robotic arm of the present invention

第六圖：本發明之深度學習方法控制方塊圖Figure 6: Control block diagram of the deep learning method of the present invention

第七圖：本發明之多層類神經網路架構示意圖Figure 7: Schematic diagram of the multi-layer neural network architecture of the present invention

1:六軸機器手臂 1: Six-axis robot arm

11:第一軸 11: The first axis

12:第二軸 12: Second axis

13:第三軸 13: The third axis

14:第四軸 14: Fourth axis

15:第五軸 15: Fifth axis

16:第六軸 16: Sixth axis

Claims (3)

一種六軸機器手臂深度學習穩定控制方法，其主要係令六軸機器手臂主要係包括有第一軸、第二軸、第三軸、第四軸、第五軸及第六軸，該六軸機器手臂軸與軸之間的相對關係，θ i〔關節角度〕、d i 〔連桿分出〕、a i 〔連桿長度〕、α i〔連桿扭轉〕稱為D-H參數；使得該六軸機器手臂之動力學模型如下：
Figure 111128793-A0305-02-0019-1
 其中，q是關節(角)位移向量，τ是關節力矩向量，τd為干擾力矩向量，M(q)是機器手臂的n×n質量矩陣，C(q,
Figure 111128793-A0305-02-0019-83
)是n×n離心力和科氏力矩陣，G(q)是n×1重力向量，F(
Figure 111128793-A0305-02-0019-75
)為n×1庫倫摩擦力與黏滯摩擦力向量；設q d 、
Figure 111128793-A0305-02-0019-76
、
Figure 111128793-A0305-02-0019-77
為控制參考輸入〔desire input〕，分別是角度、角速度及角加速度，q e 、
Figure 111128793-A0305-02-0019-78
、
Figure 111128793-A0305-02-0019-79
為誤差量〔error〕，而q、
Figure 111128793-A0305-02-0019-80
、
Figure 111128793-A0305-02-0019-104
為當前關節狀態，在式(1)中，u=τ是該六軸機器手臂的力矩控制輸入，假設τd干擾力矩為零，F(
Figure 111128793-A0305-02-0019-84
)庫倫摩擦力與黏滯摩擦力為零，則該六軸機器手臂的動態方程式表示如下式(2)所示：
Figure 111128793-A0305-02-0019-2
 若控制變量設計為下式(3)：
Figure 111128793-A0305-02-0019-3
 K 1、K 2分別為第一個狀態回授比例控制常數及第二個狀態回授微分控制常數；當設計控制輸入u為下式(4)：
Figure 111128793-A0305-02-0020-4
 將(4)式代入(2)式則可以得到閉迴路動態方程式為下式(5)：
Figure 111128793-A0305-02-0020-5
 即時間趨近於無限大∞，則q e 、
Figure 111128793-A0305-02-0020-85
、
Figure 111128793-A0305-02-0020-86
都會趨近於零〔漸近穩定〕；解析雅可比矩陣〔Analytical Jacobian矩陣〕定義為J A ，X指的是該六軸機器手臂端點相對於基座座標的姿態，表示為三個位移量及三個旋轉量，X與J A 的關係如下式(6)：
Figure 111128793-A0305-02-0020-6
 設X d 、
Figure 111128793-A0305-02-0020-87
、
Figure 111128793-A0305-02-0020-88
為控制參考指令輸入，X e 、
Figure 111128793-A0305-02-0020-89
、
Figure 111128793-A0305-02-0020-90
為誤差量，X、
Figure 111128793-A0305-02-0020-94
、
Figure 111128793-A0305-02-0020-95
為目前關節狀態，
Figure 111128793-A0305-02-0020-71
為設計控制變量，式(2)中，u=τ是該六軸機器手臂的力矩控制輸入，將式(6)等號兩邊對時間做一次微分可得到下式(7)：
Figure 111128793-A0305-02-0020-7
 將該式(7)整理為下式(8)：
Figure 111128793-A0305-02-0020-8
 將控制變量y設計為下式(9)：
Figure 111128793-A0305-02-0020-9
 將式(9)的y帶入式(2)的
Figure 111128793-A0305-02-0020-96
，即設計出下式(10)：
Figure 111128793-A0305-02-0021-10
 則操作空間控制的閉迴路系統動態方程表示如式(11)所示，
Figure 111128793-A0305-02-0021-11
 而可設計K 1 、K 2控制器〔狀態回授控制器〕使得X e 達到漸進穩定，即當t→∞時，X e →0；該六軸機器手臂予以加入深度學習的方法調整狀態回授控制器參數K 1 、K 2及微調量
Figure 111128793-A0305-02-0021-18
；利用深度學習的方法調整方程式(11)式的控制參數K 1 、K 2及
Figure 111128793-A0305-02-0021-19
；深度學習是使用多層類神經網路作為控制方法，變數符號{X i |i=1,2}是深度學習類神經網路的輸入節點，符號θ X 是輸入節點的偏值，符號{H h1|h 1=1~n 1}、{H h2|h 2=1~n 2}各是第1層、第2層的隱藏節點，隱藏層有2層以上；符號
Figure 111128793-A0305-02-0021-20
、
Figure 111128793-A0305-02-0021-21
是隱藏節點的偏值，變數符號{Y j |j=1~3}是輸出節點，K 1 、K 2是狀態回授控制器，
Figure 111128793-A0305-02-0021-13
是保持系統效能的微調量，X 1=Xe(k)、
Figure 111128793-A0305-02-0021-12
，誤差為X e =X d -X，
Figure 111128793-A0305-02-0021-14
，
Figure 111128793-A0305-02-0021-15
，輸入X d 、
Figure 111128793-A0305-02-0021-97
、
Figure 111128793-A0305-02-0021-98
，輸出X、
Figure 111128793-A0305-02-0021-99
、
Figure 111128793-A0305-02-0021-100
；其中輸入節點代表意思如下：X 1=Xe(k)、
Figure 111128793-A0305-02-0021-16
，輸出節點代表意思如下：Y 1=K1，Y 2=K2，
Figure 111128793-A0305-02-0021-17
， 控制輸入u為
Figure 111128793-A0305-02-0022-22
 深度學習類神經網路的權值如下：令符號
Figure 111128793-A0305-02-0022-26
是輸入節點與第1層隱藏節點間的權值，符號
Figure 111128793-A0305-02-0022-27
是第1層隱藏節點與第2層隱藏節點間的權值，符號
Figure 111128793-A0305-02-0022-28
是第2層隱藏節點與輸出節點間的權值；第1層隱藏節點與輸入節點的關係如下：
Figure 111128793-A0305-02-0022-23
 該netH 1係為符號，而該等號左右兩式係單一純量，H 1[h 1]=f(netH 1[h 1])，啟動函數f(.)使用如下的雙極S型函數，將輸出適當的縮放到值域-1到1之間，
Figure 111128793-A0305-02-0022-24
，α
Figure 111128793-A0305-02-0022-101
R，第2層隱藏節點與第1層隱藏節點的關係如下：
Figure 111128793-A0305-02-0022-25
 該netH 2係為符號，而該等號左右兩式係單一純量，H 2[h 2]=f(netH 2[h 2])，輸出節點與第2層隱藏節點的關係如下：
Figure 111128793-A0305-02-0023-29
 該netY j 係為符號，而該等號左右兩式係單一純量，Y j =f(netY j )，使用倒傳遞法求每一層的權值；誤差的平方為：
Figure 111128793-A0305-02-0023-30
 權值用以下的方法來更新，輸入層到第一層隱藏層為：
Figure 111128793-A0305-02-0023-31
 △為數學上的差量，第一層隱藏層到第二層隱藏層為：
Figure 111128793-A0305-02-0023-32
 第二層隱藏層到輸出層為：
Figure 111128793-A0305-02-0023-72
 其中η為學習速率常數，偏微分
Figure 111128793-A0305-02-0023-34
，
Figure 111128793-A0305-02-0023-35
，
Figure 111128793-A0305-02-0023-36
，
Figure 111128793-A0305-02-0023-37
，
Figure 111128793-A0305-02-0023-38
及
Figure 111128793-A0305-02-0023-39
的計算如下；
Figure 111128793-A0305-02-0023-40
Figure 111128793-A0305-02-0024-41
 其中：
Figure 111128793-A0305-02-0024-42
 其中，x 1=X e ，
Figure 111128793-A0305-02-0024-43
，x 3=1，
Figure 111128793-A0305-02-0024-44
 偏微分
Figure 111128793-A0305-02-0025-45
可以用
Figure 111128793-A0305-02-0025-46
來近似，其中△X e =X e (k)-X e (k-1)且△u=u(k)-u(k-1)；因此偏微分
Figure 111128793-A0305-02-0025-47
，
Figure 111128793-A0305-02-0025-48
，
Figure 111128793-A0305-02-0025-49
，
Figure 111128793-A0305-02-0025-50
，
Figure 111128793-A0305-02-0025-51
及
Figure 111128793-A0305-02-0025-52
可以改寫如下：
Figure 111128793-A0305-02-0025-53
-δY j ．H 2[h 2]．x j ，
Figure 111128793-A0305-02-0025-54
-δY j ．x j ，
Figure 111128793-A0305-02-0025-55
-δH 2[h 2]．x j ．H 1[h 1]，
Figure 111128793-A0305-02-0025-56
-δH 2[h 2]．x j ，
Figure 111128793-A0305-02-0025-57
-δH 1[h 1]．x j ．X i ，
Figure 111128793-A0305-02-0025-58
-δH 1[h 1]．x j ，輸出節點、第二層隱藏層節點與第一層隱藏層節點的微量變動為：其中
Figure 111128793-A0305-02-0025-59
，
Figure 111128793-A0305-02-0025-60
 因此權值的更新公式可以更改如下：
Figure 111128793-A0305-02-0025-61
Figure 111128793-A0305-02-0026-63
 △θ X =ηδH 1[h 1]．x j ，學習法則可以修改為以下公式，輸出層和第2隱藏層的權值更新公式：
Figure 111128793-A0305-02-0026-64
 輸出層和第2隱藏層的偏值更新公式：
Figure 111128793-A0305-02-0026-65
 第2隱藏層和第1隱藏層的權值更新公式：
Figure 111128793-A0305-02-0026-66
 第2隱藏層和第1隱藏層的偏值更新公式：
Figure 111128793-A0305-02-0026-67
 第1隱藏層和輸入層的權值更新公式：
Figure 111128793-A0305-02-0026-68
 第1隱藏層和輸入層的偏值更新公式：△θ X =ηδH 1[h 1]．x j +λ△θ X ，其中，動力〔momentum〕因子的範圍為0
Figure 111128793-A0305-02-0026-102
|λ|
Figure 111128793-A0305-02-0026-103
1，加上動力〔momentum〕可以使類神經網路的學習計算時不會掉入局部最小值。 A six-axis robot arm deep learning stability control method, which mainly makes the six-axis robot arm mainly include the first axis , the second axis, the third axis , the fourth axis, the fifth axis and the sixth axis, and the relative relationship between the axes of the six-axis robot arm .
Figure 111128793-A0305-02-0019-1
 Among them, q is the joint (angular) displacement vector, τ is the joint torque vector, τ d is the disturbance torque vector, M(q) is the n×n mass matrix of the robot arm, C(q ,
Figure 111128793-A0305-02-0019-83
) is n×n centrifugal force and Coriolis force matrix, G(q) is n×1 gravity vector, F(
Figure 111128793-A0305-02-0019-75
) is n×1 Coulomb friction force and viscous friction force vector; let q d ,
Figure 111128793-A0305-02-0019-76
,
Figure 111128793-A0305-02-0019-77
For the control reference input [desire input], they are angle, angular velocity and angular acceleration respectively, q e ,
Figure 111128793-A0305-02-0019-78
,
Figure 111128793-A0305-02-0019-79
is the error amount [error], and q ,
Figure 111128793-A0305-02-0019-80
,
Figure 111128793-A0305-02-0019-104
is the current joint state, in formula (1), u=τ is the torque control input of the six-axis robotic arm, assuming that τ d disturbance torque is zero, F(
Figure 111128793-A0305-02-0019-84
) Coulomb friction and viscous friction are zero, then the dynamic equation of the six-axis robotic arm is expressed as the following formula (2):
Figure 111128793-A0305-02-0019-2
 If the control variable is designed as the following formula (3):
Figure 111128793-A0305-02-0019-3
 K 1 and K 2 are respectively the first state feedback proportional control constant and the second state feedback differential control constant; when the design control input u is the following formula (4):
Figure 111128793-A0305-02-0020-4
 Substituting formula (4) into formula (2), the closed-loop dynamic equation can be obtained as the following formula (5):
Figure 111128793-A0305-02-0020-5
 That is, the time tends to infinity ∞, then q e ,
Figure 111128793-A0305-02-0020-85
,
Figure 111128793-A0305-02-0020-86
will tend to zero [asymptotically stable]; the analytical Jacobian matrix [Analytical Jacobian matrix] is defined as J A , X refers to the attitude of the end point of the six-axis robot arm relative to the coordinates of the base, expressed as three displacements and three rotations, the relationship between X and J A is as follows (6):
Figure 111128793-A0305-02-0020-6
 Let X d ,
Figure 111128793-A0305-02-0020-87
,
Figure 111128793-A0305-02-0020-88
Input for control reference command, X e ,
Figure 111128793-A0305-02-0020-89
,
Figure 111128793-A0305-02-0020-90
is the error amount, X,
Figure 111128793-A0305-02-0020-94
,
Figure 111128793-A0305-02-0020-95
is the current joint state,
Figure 111128793-A0305-02-0020-71
In order to design the control variable, in formula (2), u=τ is the torque control input of the six-axis robot arm, and the following formula (7) can be obtained by differentiating both sides of the equal sign of formula (6) with respect to time:
Figure 111128793-A0305-02-0020-7
 The formula (7) is organized into the following formula (8):
Figure 111128793-A0305-02-0020-8
 The control variable y is designed as the following formula (9):
Figure 111128793-A0305-02-0020-9
 Put y in formula (9) into formula (2)
Figure 111128793-A0305-02-0020-96
, that is, the following formula (10) is designed:
Figure 111128793-A0305-02-0021-10
 Then the dynamic equation expression of the closed-loop system of operating space control is shown in formula (11),
Figure 111128793-A0305-02-0021-11
 However, K 1 and K 2 controllers [state feedback controller] can be designed to make X e reach asymptotic stability, that is, when t → ∞, X e → 0; the six-axis robot arm is added with deep learning method to adjust state feedback controller parameters K 1 , K 2 and fine-tuning amount
Figure 111128793-A0305-02-0021-18
; Adjust the control parameters K 1 , K 2 and
Figure 111128793-A0305-02-0021-19
;Deep learning uses a multi-layer neural network as a control method . The variable symbol { X i | i = 1,2 } is the input node of the deep learning neural network, and the symbol θ X is the bias value of the input node.
Figure 111128793-A0305-02-0021-20
,
Figure 111128793-A0305-02-0021-21
is the bias value of the hidden node, the variable symbol { Y j | j =1~3} is the output node, K 1 and K 2 are the state feedback controllers,
Figure 111128793-A0305-02-0021-13
is the amount of fine-tuning to maintain system performance, X 1 =X e ( k ),
Figure 111128793-A0305-02-0021-12
, the error is X e = X d - X ,
Figure 111128793-A0305-02-0021-14
,
Figure 111128793-A0305-02-0021-15
, input X d ,
Figure 111128793-A0305-02-0021-97
,
Figure 111128793-A0305-02-0021-98
, output X,
Figure 111128793-A0305-02-0021-99
,
Figure 111128793-A0305-02-0021-100
; The meaning of the input node is as follows: X 1 =X e ( k ),
Figure 111128793-A0305-02-0021-16
, the meaning of the output node is as follows: Y 1 =K 1 , Y 2 =K 2 ,
Figure 111128793-A0305-02-0021-17
, the control input u is
Figure 111128793-A0305-02-0022-22
 The weights of the deep learning neural network are as follows: Let the symbol
Figure 111128793-A0305-02-0022-26
is the weight between the input node and the hidden node of the first layer, symbol
Figure 111128793-A0305-02-0022-27
is the weight between hidden nodes in layer 1 and hidden nodes in layer 2, symbol
Figure 111128793-A0305-02-0022-28
is the weight between the hidden node of the second layer and the output node; the relationship between the hidden node and the input node of the first layer is as follows:
Figure 111128793-A0305-02-0022-23
 The netH 1 is a symbol, and the left and right sides of the equal sign are a single scalar, H 1 [ h 1 ]= f ( netH 1 [ h 1 ]), the starting function f (.) uses the following bipolar Sigmoid function to properly scale the output to the value range between -1 and 1,
Figure 111128793-A0305-02-0022-24
, α
Figure 111128793-A0305-02-0022-101
R , the relationship between the hidden nodes of the second layer and the hidden nodes of the first layer is as follows:
Figure 111128793-A0305-02-0022-25
 The netH 2 is a symbol, and the left and right sides of the equal sign are a single scalar, H 2 [ h 2 ]= f ( netH 2 [ h 2 ]), the relationship between the output node and the hidden node of the second layer is as follows:
Figure 111128793-A0305-02-0023-29
 The netY j is a symbol, and the left and right sides of the equal sign are a single scalar, Y j = f ( netY j ), use the backward transfer method to find the weight of each layer; the square of the error is:
Figure 111128793-A0305-02-0023-30
 The weights are updated in the following way, from the input layer to the first hidden layer:
Figure 111128793-A0305-02-0023-31
 △ is the difference in mathematics, from the first hidden layer to the second hidden layer is:
Figure 111128793-A0305-02-0023-32
 The second hidden layer to the output layer is:
Figure 111128793-A0305-02-0023-72
 where η is the learning rate constant, partial differential
Figure 111128793-A0305-02-0023-34
,
Figure 111128793-A0305-02-0023-35
,
Figure 111128793-A0305-02-0023-36
,
Figure 111128793-A0305-02-0023-37
,
Figure 111128793-A0305-02-0023-38
and
Figure 111128793-A0305-02-0023-39
is calculated as follows;
Figure 111128793-A0305-02-0023-40
Figure 111128793-A0305-02-0024-41
 in:
Figure 111128793-A0305-02-0024-42
 where x 1 = X e ,
Figure 111128793-A0305-02-0024-43
, x 3 =1,
Figure 111128793-A0305-02-0024-44
 partial differential
Figure 111128793-A0305-02-0025-45
Can use
Figure 111128793-A0305-02-0025-46
to approximate, where △ X e = X e ( k )- X e ( k -1) and △ u = u ( k )- u ( k -1); therefore the partial differential
Figure 111128793-A0305-02-0025-47
,
Figure 111128793-A0305-02-0025-48
,
Figure 111128793-A0305-02-0025-49
,
Figure 111128793-A0305-02-0025-50
,
Figure 111128793-A0305-02-0025-51
and
Figure 111128793-A0305-02-0025-52
can be rewritten as follows:
Figure 111128793-A0305-02-0025-53
- δY j . H 2 [ h 2 ]. x j ,
Figure 111128793-A0305-02-0025-54
- δY j . x j ,
Figure 111128793-A0305-02-0025-55
- δH 2 [ h 2 ]. x j . H 1 [ h 1 ],
Figure 111128793-A0305-02-0025-56
- δH 2 [ h 2 ]. x j ,
Figure 111128793-A0305-02-0025-57
- δH 1 [ h 1 ]. x j . X i ,
Figure 111128793-A0305-02-0025-58
- δH 1 [ h 1 ]. x j , the slight change of the output node, the second hidden layer node and the first hidden layer node is: where
Figure 111128793-A0305-02-0025-59
,
Figure 111128793-A0305-02-0025-60
 Therefore, the update formula of the weight can be changed as follows:
Figure 111128793-A0305-02-0025-61
Figure 111128793-A0305-02-0026-63
 △ θ X = ηδH 1 [ h 1 ]. x j , the learning rule can be modified as the following formula, the weight update formula of the output layer and the second hidden layer:
Figure 111128793-A0305-02-0026-64
 The bias value update formula of the output layer and the second hidden layer:
Figure 111128793-A0305-02-0026-65
 The weight update formulas of the second hidden layer and the first hidden layer:
Figure 111128793-A0305-02-0026-66
 The bias update formulas of the second hidden layer and the first hidden layer:
Figure 111128793-A0305-02-0026-67
 The weight update formula of the first hidden layer and input layer:
Figure 111128793-A0305-02-0026-68
 The partial update formula of the first hidden layer and input layer: △ θ X = ηδH 1 [ h 1 ]. x j + λ △ θ X , where the range of the dynamic [momentum] factor is 0
Figure 111128793-A0305-02-0026-102
| λ |
Figure 111128793-A0305-02-0026-103
1. Adding momentum [momentum] can prevent the learning and calculation of the neural network from falling into the local minimum. 如請求項1所述六軸機器手臂深度學習穩定控制方法，其中，該式(3)中的誤差為：q e =q d -q，
Figure 111128793-A0305-02-0027-69
 As described in claim item 1, the deep learning stability control method for a six-axis robot arm, wherein the error in the formula (3) is: q e = q d - q ,
Figure 111128793-A0305-02-0027-69
 如請求項1所述六軸機器手臂深度學習穩定控制方法，其中，該式(9)中的誤差值：X e =X d -X，
Figure 111128793-A0305-02-0027-70
 As described in the request item 1, the deep learning stability control method of the six-axis robot arm, wherein the error value in the formula (9): X e = X d - X ,
Figure 111128793-A0305-02-0027-70
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103331756A (en) * 2013-06-04 2013-10-02 浙江工业大学 Mechanical arm motion control method
CN113927596A (en) * 2021-10-07 2022-01-14 西北工业大学 Time-varying output constraint robot teleoperation finite time control method based on width neural learning
CN114310965A (en) * 2022-01-18 2022-04-12 上海景吾酷租科技发展有限公司 Mechanical arm impedance control method and system without joint torque measurement
CN114750137A (en) * 2022-05-19 2022-07-15 合肥工业大学 RBF network-based upper limb exoskeleton robot motion control method

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103331756A (en) * 2013-06-04 2013-10-02 浙江工业大学 Mechanical arm motion control method
CN113927596A (en) * 2021-10-07 2022-01-14 西北工业大学 Time-varying output constraint robot teleoperation finite time control method based on width neural learning
CN114310965A (en) * 2022-01-18 2022-04-12 上海景吾酷租科技发展有限公司 Mechanical arm impedance control method and system without joint torque measurement
CN114750137A (en) * 2022-05-19 2022-07-15 合肥工业大学 RBF network-based upper limb exoskeleton robot motion control method

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