TW202238302A - Deep learning method for controlling the balance of a two-wheeled machine - Google Patents

Deep learning method for controlling the balance of a two-wheeled machine Download PDF

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TW202238302A
TW202238302A TW110109261A TW110109261A TW202238302A TW 202238302 A TW202238302 A TW 202238302A TW 110109261 A TW110109261 A TW 110109261A TW 110109261 A TW110109261 A TW 110109261A TW 202238302 A TW202238302 A TW 202238302A
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TWI767612B (en
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李振興
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崑山科技大學
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Abstract

The present invention relates to a deep learning method for controlling the balance of a two-wheeled machine, which is based on a deep learning method to adjust the controller parameters, and have a learning adjustment mechanism that can widely adapt to changes in environmental parameters, so that the two-wheeled machine can achieve a robust and stable automatic control effect, and increase the practical efficacy in its overall implementation and use.

Description

深度學習控制兩輪機具平衡方法A deep learning method for controlling the balance of two-wheeled implements

本發明係有關於一種深度學習控制兩輪機具平衡方法，尤其是指一種以深度學習的方法調整控制器參數，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，以可使兩輪機具達到強健平衡穩定之自動控制功效，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 method for controlling the balance of two-wheeled equipment, in particular to an adjustment mechanism that uses deep learning to adjust controller parameters and can have learning properties, and can widely adapt to changes in environmental parameters, so that the two wheels can be adjusted. The mechanical equipment achieves strong, balanced and stable automatic control functions, and has more practical features in its overall execution and use.

按，2001年由發明家Dean Kamen發明一種兩輪代步的電動車［賽格威］，這是第一輛能夠自主平衡的運輸工具［或稱為兩輪平衡車］，該兩輪代步的電動車［賽格威］引起很大的迴響，並在全世界造成一股流行趨勢；而兩輪平衡車的重要技術之一就是平衡穩定控制技術，其主要是引用適合的平衡穩定控制技術使兩輪平衡機具達到強健平衡穩定。Press, in 2001, the inventor Dean Kamen invented a two-wheeled electric vehicle [Segway], which is the first vehicle that can balance itself [or called a two-wheeled balance vehicle]. The car [Segway] caused great repercussions and caused a popular trend in the world; and one of the important technologies of the two-wheeled balance car is the balance and stability control technology, which mainly uses the appropriate balance and stability control technology to make the two wheels Wheel balancing implements achieve robust balance and stability.

其中，請參閱公告第M506767號「電動平衡車」，係設有一車輛本體，該車輛本體底部兩端之輪軸上各設有一輪胎，該輪胎係由一輪框、一外輪及一內胎所組成，該外輪係設於該輪框上，該內胎係設於該外輪內，該輪框上設有一氣嘴，該氣嘴係連接至該內胎。該結構主要是透過改變電動平衡車之輪胎係由外輪與內胎組設於輪框上，來解決電動平衡車在使用時因輪胎不具避震效果所存在之缺失。Among them, please refer to the Announcement No. M506767 "Electric Balance Vehicle", which is equipped with a vehicle body, and a tire is provided on the axles at both ends of the bottom of the vehicle body. The tire is composed of a wheel frame, an outer wheel and an inner tube. The outer wheel system is arranged on the wheel frame, the inner tire is arranged in the outer wheel, and an air nozzle is arranged on the wheel frame, and the air nozzle is connected to the inner tire. This structure is mainly to solve the lack of shock-absorbing effect of the tires when the electric balance car is in use by changing the tire system of the electric balance car to be assembled on the wheel frame by the outer wheel and the inner tube.

另，請參閱公告第M500726號「自平衡車之車架機構」，適用於組裝至少兩個車輪，及兩個自平衡機電系統組件，且該等自平衡機電系統組件可分別自動控制該等車輪轉動，以使其保持平衡狀態，該車架機構包含：兩個車架組，分別可安裝一個車輪與一個自平衡機電系統組件，且每一個車架組可被操作而單獨帶動各別之自平衡機電系統組件同步前後傾擺位移；及一個軸承組，連接該等車架組，使該等車架組可各自獨立地前後樞擺。該結構係能方便選擇以雙手操控把手及/或以雙腳踩踏操控踏板的方式，來控制兩輪自平衡車之行進與轉彎。Also, please refer to Announcement No. M500726 "Frame Mechanism of Self-balancing Vehicle", which is suitable for assembling at least two wheels and two self-balancing electromechanical system components, and these self-balancing electromechanical system components can automatically control the wheels respectively Rotate to keep it in a balanced state. The frame mechanism includes: two frame groups, each of which can be installed with a wheel and a self-balancing electromechanical system component, and each frame group can be operated to drive its own a balance electromechanical system component for synchronous front and rear tilt displacement; and a bearing set connecting the frame sets so that the frame sets can independently pivot forward and backward. The structure can conveniently select the way of controlling the handle with both hands and/or stepping on the pedal with both feet to control the traveling and turning of the two-wheeled self-balancing vehicle.

又，請參閱公告第I510394號「自動平衡載具及其轉向控制之方法」其包含：一載具本體，係包含一踩踏板；一第一感測器，係設於該踩踏板上，當一物體觸發該第一感測器時，該第一感測器係產生一第一感測訊號；一第二感測器，係設於該踩踏板上，當該物體觸發該第二感測器時，該第二感測器係產生一第二感測訊號；一控制模組，係接收該第一感測訊號以產生一第一驅動訊號，或接收該第二感測訊號以產生一第二驅動訊號；以及一驅動模組，係包含一第一輪體及一第二輪體，該第一輪體係設於該載具本體之一側，而該第二輪體係相對該第一輪體設於該載具本體之另一側，當該驅動模組對應該第一驅動訊號使該第一輪體與該第二輪體產生一第一速度差時，該載具本體將朝一第一方向轉向，而當該驅動模組對應該第二驅動訊號使該第一輪體與該第二輪體產生一第二速度差時，該載具本體將朝相對該第一方向之一第二方向轉向；其中，該載具本體更包含一升降模組，該升降模組係連結該踩踏板，該控制模組係依據一控制訊號控制該升降模組升降作動，以帶動該踩踏板升降。該結構係有關於一種藉由觸發第一感測器或第二感測器，以使載具本體朝不同方向轉向之技術。Also, please refer to the Announcement No. I510394 "Automatic Balance Vehicle and Its Steering Control Method", which includes: a vehicle body, which includes a pedal; a first sensor, which is arranged on the pedal, when When an object triggers the first sensor, the first sensor generates a first sensing signal; a second sensor is arranged on the pedal, and when the object triggers the second sensing signal When the controller is used, the second sensor generates a second sensing signal; a control module receives the first sensing signal to generate a first driving signal, or receives the second sensing signal to generate a The second driving signal; and a driving module, which includes a first wheel body and a second wheel body, the first wheel system is arranged on one side of the carrier body, and the second wheel system is opposite to the first wheel body The wheel body is arranged on the other side of the carrier body. When the driving module generates a first speed difference between the first wheel body and the second wheel body in response to the first driving signal, the carrier body will move towards a Turning in the first direction, and when the driving module generates a second speed difference between the first wheel body and the second wheel body in response to the second driving signal, the carrier body will face one of the first directions. Turning in the second direction; wherein, the vehicle body further includes a lifting module, the lifting module is connected to the pedal, and the control module controls the lifting movement of the lifting module according to a control signal to drive the pedal lift. The structure relates to a technique for turning the vehicle body in different directions by triggering the first sensor or the second sensor.

此外，現有的兩輪平衡穩定技術尚有使用比例-積分-微分(PID)的控制方法。其中，P代表比例控制項，可以減少系統的上升時間及延遲時間，但卻會增加系統的超越量。I代表積分控制項，可以減少或消除穩態誤差。D代表微分控制項，可以減少系統的最大超越量百分比，但同時卻會增加系統的上升時間及延遲時間。In addition, the existing two-wheel balance stabilization technology still uses a proportional-integral-derivative (PID) control method. Among them, P represents the proportional control item, which can reduce the rise time and delay time of the system, but it will increase the overshoot of the system. I represents the integral control item, which can reduce or eliminate the steady-state error. D represents the differential control item, which can reduce the maximum overshoot percentage of the system, but at the same time it will increase the rise time and delay time of the system.

然而，現有兩輪平衡車雖可達到平衡穩定控制之預期功效，但也在其實際操作施行上發現，該類結構皆係為使用固定參數調整方式，造成若環境條件產生變動，其即無法適應環境條件的變動，相對即導致無法進行穩定平衡控制，致令其在控制方式上仍存在有改進的空間。However, although the existing two-wheeled self-balancing vehicle can achieve the expected effect of balance and stability control, it is also found in its actual operation that this type of structure uses fixed parameter adjustment methods, resulting in that it cannot adapt to changes in environmental conditions. Changes in environmental conditions will relatively lead to the inability to carry out stable balance control, so there is still room for improvement in the control method.

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，針對現有之缺失予以研究改良，提供一種深度學習控制兩輪機具平衡方法，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 has been adhering to many years of rich experience in design, development and actual production in this related industry, researched and improved the existing deficiencies, and provided a method of deep learning to control the balance of two-wheeled machines, in order to achieve better practical value. purpose.

本發明之主要目的在於提供一種深度學習控制兩輪機具平衡方法，其主要係以深度學習的方法調整控制器參數，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，以可使兩輪機具達到強健平衡穩定之自動控制功效，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 method for deep learning to control the balance of two-wheeled implements, which mainly adjusts the controller parameters with the method of deep learning, and can have an adjustment mechanism of learning nature, which can widely adapt to changes in environmental parameters, so that The two-wheeled machine achieves a strong, balanced and stable automatic control function, and has more practical features in its overall execution 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，要控制兩輪機具之車身的平衡，必須先了解兩輪機具的運動模式與相對應的決策，且配合偵測該兩輪機具之車身傾斜角度、車身傾斜角速度及馬達的位置，接著才能進行車身平衡控制方法之設計。First of all, in order to control the balance of the body of the two-wheeled machine, one must first understand the motion mode of the two-wheeled machine and the corresponding decision-making, and cooperate with the detection of the body tilt angle, body tilt angular velocity and motor position of the two-wheeled machine, and then Carry out the design of the body balance control method.

請參閱第一圖兩輪機具之車身傾斜狀態示意圖所示，G代表重心、O代表軸心、L代表地面，該兩輪機具之車身部分係以馬達軸心為中心作前後擺動，若假設車身垂直地面的角度為0度，由三軸加速器及陀螺儀可以量得車身擺動的角度。兩輪機具一開始必須保持車身與地面垂直，放開後有三種情況，分別是靜止、前傾與後傾；其簡單的控制方法如下：Please refer to the schematic diagram of the tilted state of the body of the two-wheeled machine in Figure 1. G represents the center of gravity, O represents the axis, and L represents the ground. The body part of the two-wheeled machine swings back and forth around the axis of the motor. The angle vertical to the ground is 0 degrees, and the swing angle of the vehicle body can be measured by the three-axis accelerometer and gyroscope. At the beginning, the two-wheeled equipment must keep the vehicle body vertical to the ground. After releasing it, there are three situations, which are static, forward tilt and backward tilt; the simple control method is as follows:

1.直立：若車身重心落在左右兩輪與地面接觸點連線中心位置，且車身保持平衡不動，則車輪靜止且不作任何動作。1. Upright: If the center of gravity of the vehicle body falls on the center of the line connecting the left and right wheels with the ground, and the vehicle body is kept in balance, the wheels are still and do not make any movement.

2.前傾：若車身重心偏向前，車身將向前傾斜，則控制車輪前進，依據車輪轉動與車身傾斜的相對角度及相對角速度大小，控制車輪前進的力量，以維持車身的平衡。2. Forward tilt: If the center of gravity of the vehicle body is tilted forward, the vehicle body will tilt forward, then control the wheel to move forward, and control the force of the wheel to move forward according to the relative angle and relative angular velocity between the rotation of the wheel and the body tilt, so as to maintain the balance of the vehicle body.

3.後傾：若車身重心偏向後，車身將向後傾斜，則控制車輪後退，依據車輪轉動與車身傾斜的相對角度及相對角速度大小，控制車輪後退的力量，以維持車身的平衡。3. Rear tilt: If the center of gravity of the vehicle body is tilted backward, the vehicle body will tilt backward, then control the wheels to move backward. According to the relative angle and relative angular velocity between the rotation of the wheels and the tilt of the vehicle body, control the force of the wheels moving backward to maintain the balance of the vehicle body.

請再一併參閱第二圖兩輪機具之立體簡化結構示意圖、第三圖兩輪機具之側視簡化結構示意圖及第四圖兩輪機具之俯視簡化結構示意圖所示，

Figure 02_image001
是重力加速度，
Figure 02_image003
是輪子的重量，
Figure 02_image005
是輪子的半徑，
Figure 02_image007
是輪子的轉動慣量，
Figure 02_image009
是兩輪機具之機身的質量，
Figure 02_image011
是兩輪機具之機身的寬度，
Figure 02_image013
是兩輪機具之機身的深度，
Figure 02_image015
是兩輪機具之機身的高度，
Figure 02_image017
為馬達軸到重心的長度，
Figure 02_image019
為傾斜角度［pitch］轉動慣量，
Figure 02_image021
為偏轉角度［yaw］的轉動慣量，
Figure 02_image023
為馬達的轉動慣量，
Figure 02_image025
是齒輪箱比值；左輪的轉動角度是
Figure 02_image027
，右輪的轉動角度是
Figure 02_image029
，左右輪的平均角度為
Figure 02_image031
，所以
Figure 02_image033
；左馬達的轉動角度是
Figure 02_image035
，右馬達的轉動角度是
Figure 02_image037
，兩輪機具之機身的傾斜角度［pitch］為
Figure 02_image039
，兩輪機具偏轉角度［yaw］為
Figure 02_image041
。 Please also refer to the three-dimensional simplified structural diagram of the two-wheeled machine tool in Figure 2, the simplified structural schematic diagram of the side view of the two-wheeled machine tool in Figure 3, and the simplified structural schematic diagram of the top view of the two-wheeled machine tool in Figure 4,
Figure 02_image001
is the acceleration of gravity,
Figure 02_image003
is the weight of the wheel,
Figure 02_image005
is the radius of the wheel,
Figure 02_image007
is the moment of inertia of the wheel,
Figure 02_image009
is the mass of the body of the two-wheeled machine,
Figure 02_image011
is the width of the fuselage of the two-wheeled machine,
Figure 02_image013
is the depth of the fuselage of the two-wheeled machine,
Figure 02_image015
is the height of the fuselage of the two-wheeled machine,
Figure 02_image017
is the length from the motor shaft to the center of gravity,
Figure 02_image019
is the moment of inertia of the tilt angle [pitch],
Figure 02_image021
is the moment of inertia of deflection angle [yaw],
Figure 02_image023
is the moment of inertia of the motor,
Figure 02_image025
is the gearbox ratio; the rotation angle of the left wheel is
Figure 02_image027
, the rotation angle of the right wheel is
Figure 02_image029
, the average angle of the left and right wheels is
Figure 02_image031
,so
Figure 02_image033
;The rotation angle of the left motor is
Figure 02_image035
, the rotation angle of the right motor is
Figure 02_image037
, the inclination angle [pitch] of the fuselage of the two-wheeled implement is
Figure 02_image039
, the deflection angle [yaw] of the two-wheel implement is
Figure 02_image041
.

以下進一步具體說明本發明深度學習控制兩輪機具平衡方法，請再一併參閱第五圖本發明之步驟流程示意圖所示，其包括下列步驟：The following further specifically describes the deep learning method of the present invention to control the balance of two-wheeled implements. Please also refer to the fifth figure as shown in the schematic flow chart of the steps of the present invention, which includes the following steps:

步驟一(S01)：測量一兩輪機具的輪胎轉動角度、傾斜角度［pitch］及偏轉角度［yaw］，以判斷所述兩輪機具處於直立、前傾、後傾、左轉或右轉狀態；Step 1 (S01): Measure the tire rotation angle, inclination angle [pitch] and deflection angle [yaw] of a two-wheeled implement to determine whether the two-wheeled implement is in an upright, forward, backward, left-turned or right-turned state ;

步驟二(S02)：對所述兩輪機具的左右輪的平均角度變數

Figure 02_image043
及兩輪機具的傾斜角度［pitch］變數
Figure 02_image045
進行深度學習控制，進而得到第一控制輸出的電壓控制值； Step 2 (S02): the average angle variable of the left and right wheels of the two-wheel implement
Figure 02_image043
And the tilt angle [pitch] variable of the two-wheeled implement
Figure 02_image045
performing deep learning control, and then obtaining the voltage control value of the first control output;

步驟三(S03)：對所述兩輪機具的偏轉角度［yaw］變數

Figure 02_image047
以極點設置法［pole assignment］進行狀態回授控制，以得到第二控制輸出的電壓控制值； Step 3 (S03): Change the deflection angle [yaw] of the two-wheel implement
Figure 02_image047
Perform state feedback control with pole assignment method to obtain the voltage control value of the second control output;

步驟四(S04)：將所述第一控制輸出的電壓控制值加上所述第二控制輸出的電壓控制值，除以二，即得到右輪驅動馬達的電壓控制值，以控制右輪驅動馬達的轉速與轉向；將所述第一控制輸出的電壓控制值減去所述第二控制輸出的電壓控制值，除以二，即得到左輪驅動馬達的電壓控制值，以控制左輪驅動馬達的轉速與轉向。Step 4 (S04): Add the voltage control value of the first control output to the voltage control value of the second control output, and divide by two to obtain the voltage control value of the right wheel drive motor to control the right wheel drive The rotation speed and steering of the motor; the voltage control value of the first control output minus the voltage control value of the second control output is divided by two to obtain the voltage control value of the left wheel drive motor to control the left wheel drive motor speed and steering.

使用拉格朗奇方法［Lagrangian］推導兩輪機具的動態方程式，假設傾斜角很小時(

Figure 02_image049
)可以簡化如下： Use the Lagrangian method [Lagrangian] to derive the dynamic equation of the two-wheeled implement, assuming that the inclination angle is small (
Figure 02_image049
) can be simplified as follows:

Figure 02_image051
(1)
Figure 02_image051
(1)

Figure 02_image053
Figure 02_image055
(2)
Figure 02_image053
Figure 02_image055
(2)

Figure 02_image057
(3)
Figure 02_image057
(3)

座標系統的變數如下，

Figure 02_image059
代表
Figure 02_image061
角度方向的力矩［Torque］，
Figure 02_image062
代表
Figure 02_image064
角度方向的力矩［Torque］，
Figure 02_image065
代表
Figure 02_image067
角度方向的力矩［Torque］，
Figure 02_image068
代表左右馬達的端電壓，
Figure 02_image070
是齒輪箱比值，
Figure 02_image071
是力矩常數，
Figure 02_image073
為馬達的摩擦係數，
Figure 02_image075
是輪子與地的摩擦係數，
Figure 02_image077
代表反電動勢常數，
Figure 02_image079
代表電樞電阻。 The variables of the coordinate system are as follows,
Figure 02_image059
represent
Figure 02_image061
Angular moment [Torque],
Figure 02_image062
represent
Figure 02_image064
Angular moment [Torque],
Figure 02_image065
represent
Figure 02_image067
Angular moment [Torque],
Figure 02_image068
Represents the terminal voltage of the left and right motors,
Figure 02_image070
is the gearbox ratio,
Figure 02_image071
is the moment constant,
Figure 02_image073
is the friction coefficient of the motor,
Figure 02_image075
is the coefficient of friction between the wheel and the ground,
Figure 02_image077
represents the back EMF constant,
Figure 02_image079
Represents the armature resistance.

將電壓公式代入(1)-(3)式線性方程式中，可以得到以下公式：Substituting the voltage formula into the linear equation (1)-(3), the following formula can be obtained:

Figure 02_image081
(4)
Figure 02_image081
(4)

其中

Figure 02_image083
矩陣如下： in
Figure 02_image083
The matrix is as follows:

Figure 02_image085
，
Figure 02_image085
,

Figure 02_image087
，
Figure 02_image087
,

Figure 02_image089
，
Figure 02_image089
,

Figure 02_image091
，
Figure 02_image091
,

而且

Figure 02_image093
、
Figure 02_image095
。 and
Figure 02_image093
,
Figure 02_image095
.

Figure 02_image097
是左馬達產生的力矩，
Figure 02_image099
是右馬達產生的力矩，
Figure 02_image101
是機身偏轉角度(yaw)，
Figure 02_image067
角度方向的力矩［Torque］如下：
Figure 02_image097
is the torque produced by the left motor,
Figure 02_image099
is the torque produced by the right motor,
Figure 02_image101
is the airframe deflection angle (yaw),
Figure 02_image067
The torque [Torque] in the angular direction is as follows:

Figure 02_image102
Figure 02_image104
(5)
Figure 02_image102
Figure 02_image104
(5)

其中

Figure 02_image106
。 in
Figure 02_image106
.

根據(3)式及(5)式，化簡可得：According to formula (3) and formula (5), simplification can be obtained:

Figure 02_image108
(6)
Figure 02_image108
(6)

其中參數如下，The parameters are as follows,

Figure 02_image110
，
Figure 02_image112
，
Figure 02_image114
Figure 02_image110
,
Figure 02_image112
,
Figure 02_image114

由(4)式展開可得，求解

Figure 02_image116
及
Figure 02_image118
，得： From formula (4), it can be obtained that the solution
Figure 02_image116
and
Figure 02_image118
,have to:

Figure 02_image120
Figure 02_image122
Figure 02_image120
Figure 02_image122

Figure 02_image124
(7)
Figure 02_image124
(7)

Figure 02_image126
Figure 02_image128
Figure 02_image126
Figure 02_image128

Figure 02_image130
(8)
Figure 02_image130
(8)

由(6)式展開可得：Expanded from formula (6), we can get:

Figure 02_image132
(9)
Figure 02_image132
(9)

由(9)式能得知可以用

Figure 02_image134
來控制機身偏轉角度［yaw］
Figure 02_image136
，由(7)式及(8)式能得知可以用
Figure 02_image138
來控制左右輪的平均角度
Figure 02_image140
及機身傾斜角度［pitch］
Figure 02_image141
。 From formula (9), it can be known that the
Figure 02_image134
to control the body deflection angle [yaw]
Figure 02_image136
, from formula (7) and formula (8), it can be known that it can be used
Figure 02_image138
to control the average angle of the left and right wheels
Figure 02_image140
and body tilt angle [pitch]
Figure 02_image141
.

由

Figure 02_image134
及
Figure 02_image138
的值可算出所需的右輪馬達控制電壓
Figure 02_image142
及左輪馬達控制電壓
Figure 02_image144
。 Depend on
Figure 02_image134
and
Figure 02_image138
The value of the required right wheel motor control voltage can be calculated
Figure 02_image142
and left wheel motor control voltage
Figure 02_image144
.

令狀態變數

Figure 02_image146
為左右輪的平均角度
Figure 02_image140
，狀態變數
Figure 02_image148
為機身傾斜角度［pitch］
Figure 02_image141
，狀態變數
Figure 02_image150
為
Figure 02_image152
，狀態變數
Figure 02_image154
為
Figure 02_image156
，狀態變數
Figure 02_image158
為機身偏轉角度［yaw］
Figure 02_image136
，狀態變數
Figure 02_image160
為
Figure 02_image162
，
Figure 02_image138
的值為
Figure 02_image164
，
Figure 02_image166
的值為
Figure 02_image168
，則系統的狀態空間方程式為： Let the state variable
Figure 02_image146
is the average angle of the left and right wheels
Figure 02_image140
, the state variable
Figure 02_image148
is the inclination angle of the fuselage [pitch]
Figure 02_image141
, the state variable
Figure 02_image150
for
Figure 02_image152
, the state variable
Figure 02_image154
for
Figure 02_image156
, the state variable
Figure 02_image158
is the body deflection angle [yaw]
Figure 02_image136
, the state variable
Figure 02_image160
for
Figure 02_image162
,
Figure 02_image138
The value is
Figure 02_image164
,
Figure 02_image166
The value is
Figure 02_image168
, then the state-space equation of the system is:

Figure 02_image170
(10)
Figure 02_image170
(10)

Figure 02_image172
(11)
Figure 02_image172
(11)

其中參數如下，The parameters are as follows,

Figure 02_image174
，
Figure 02_image176
Figure 02_image178
，
Figure 02_image180
，
Figure 02_image174
,
Figure 02_image176
Figure 02_image178
,
Figure 02_image180
,

Figure 02_image182
，
Figure 02_image182
,

Figure 02_image184
，
Figure 02_image186
Figure 02_image188
，
Figure 02_image190
，
Figure 02_image184
,
Figure 02_image186
Figure 02_image188
,
Figure 02_image190
,

Figure 02_image192
，
Figure 02_image192
,

而所需的右輪馬達控制電壓

Figure 02_image194
及左輪馬達控制電壓
Figure 02_image196
為： while the required right wheel motor control voltage
Figure 02_image194
and left wheel motor control voltage
Figure 02_image196
for:

Figure 02_image198
，
Figure 02_image200
。
Figure 02_image198
,
Figure 02_image200
.

就(10)式而言，狀態回授控制器可以改寫如下：As far as (10) is concerned, the state feedback controller can be rewritten as follows:

Figure 02_image202
Figure 02_image202

Figure 02_image204
Figure 02_image204

Figure 02_image206
(12)
Figure 02_image206
(12)

其中

Figure 02_image208
，
Figure 02_image210
，
Figure 02_image212
，
Figure 02_image214
。 in
Figure 02_image208
,
Figure 02_image210
,
Figure 02_image212
,
Figure 02_image214
.

由(12)式，可以說狀態回授控制器等效於［equivalent］ PD控制。將(12)式分成兩個PD控制的分量如下；From (12), it can be said that the state feedback controller is equivalent to [equivalent] PD control. Divide (12) into two PD control components as follows;

Figure 02_image216
(13)
Figure 02_image216
(13)

則狀態回授控制等效於雙PD控制。Then the state feedback control is equivalent to the dual PD control.

對於一個可穩定［stabilizable］及可偵測［detectable］線性非時變系統，For a stable [stabilizable] and detectable [detectable] linear time-invariant system,

Figure 02_image218
(14)
Figure 02_image218
(14)

其中

Figure 02_image220
是狀態向量，
Figure 02_image222
是控制輸入，
Figure 02_image224
是系統矩陣，
Figure 02_image226
是控制輸入矩陣，則狀態回授控制為， in
Figure 02_image220
is the state vector,
Figure 02_image222
is the control input,
Figure 02_image224
is the system matrix,
Figure 02_image226
is the control input matrix, then the state feedback control is,

Figure 02_image228
(15)
Figure 02_image228
(15)

因為系統是可穩定［stabilizable］及可偵測［detectable］線性非時變系統，則系統可以用狀態回授控制器達到穩定控制的目的。以下將使用雙PD控制達到穩定控制的目的。Because the system is a stable [stabilizable] and detectable [detectable] linear time-invariant system, the system can use the state feedback controller to achieve the purpose of stable control. The following will use dual PD control to achieve the purpose of stable control.

至於(11)式則單獨另外設計控制器，就(11)式而言，在狀態回授控制器如下：As for formula (11), the controller is designed separately. As far as formula (11) is concerned, the state feedback controller is as follows:

Figure 02_image230
(16)
Figure 02_image230
(16)

將(16)式代入(11)式，則可以得到：Substituting formula (16) into formula (11), we can get:

Figure 02_image232
(17)
Figure 02_image232
(17)

則受控系統(17)的特性方程式［characteristic equation］為：Then the characteristic equation of the controlled system (17) is:

Figure 02_image234
(18)
Figure 02_image234
(18)

若要設計系統的極點［poles］於

Figure 02_image236
，
Figure 02_image238
，則設計系統的特性方程式為： To design the poles [poles] of the system at
Figure 02_image236
,
Figure 02_image238
, then the characteristic equation of the design system is:

Figure 02_image240
(19)
Figure 02_image240
(19)

比較(18)式及(19)式，可得控制器為：Comparing formula (18) and formula (19), the controller can be obtained as:

Figure 02_image242
，
Figure 02_image244
(20)
Figure 02_image242
,
Figure 02_image244
(20)

根據(13)式就可以求得

Figure 02_image246
，根據(20)式就可以求得
Figure 02_image248
，再根據下式 According to (13), it can be obtained
Figure 02_image246
, according to (20) can get
Figure 02_image248
, and then according to the following formula

Figure 02_image250
，
Figure 02_image251
，
Figure 02_image250
,
Figure 02_image251
,

即可以求得

Figure 02_image253
及
Figure 02_image254
，進而可以控制兩輪機具的穩定平衡。 that can be obtained
Figure 02_image253
and
Figure 02_image254
, which in turn can control the stable balance of the two-wheel implement.

另，就該步驟二(S02)之深度學習控制而言，該數位控制器需要調節的控制參數如下：In addition, as far as the deep learning control of step 2 (S02) is concerned, the control parameters that the digital controller needs to adjust are as follows:

Figure 02_image256
，
Figure 02_image256
,

Figure 02_image258
是狀態回授控制參數，
Figure 02_image258
is the state feedback control parameter,

利用深度學習的方法調整該控制參數，深度學習是使用多層類神經網路作為控制方法，請再一併參閱第六圖本發明之多層類神經網路架構示意圖所示，其中，變數符號

Figure 02_image260
是深度學習類神經網路的輸入節點，
Figure 02_image262
、
Figure 02_image264
是該受控系統的量測輸出第k個取樣，變數符號
Figure 02_image266
是該輸入節點的偏值，變數符號
Figure 02_image268
、
Figure 02_image270
各是第1層、第2層的隱藏節點，隱藏層有2層以上；變數符號
Figure 02_image272
、
Figure 02_image274
是該隱藏節點的偏值，變數符號
Figure 02_image276
是輸出節點，該自動控制系統需要調節的控制參數為
Figure 02_image256
，是狀態回授控制參數，其中該輸出節點代表意思如下： Utilize the method of deep learning to adjust the control parameters. Deep learning uses multi-layer neural network as the control method. Please refer to the schematic diagram of the multi-layer neural network architecture of the present invention in Figure 6. Among them, the variable symbols
Figure 02_image260
is the input node of deep learning neural network,
Figure 02_image262
,
Figure 02_image264
is the kth sample of the measured output of the controlled system, and the symbol of the variable is
Figure 02_image266
is the bias value of the input node, variable symbol
Figure 02_image268
,
Figure 02_image270
Each is the hidden node of the first layer and the second layer, and the hidden layer has more than two layers; the variable symbol
Figure 02_image272
,
Figure 02_image274
is the bias value of the hidden node, variable symbol
Figure 02_image276
is the output node, and the control parameters that the automatic control system needs to adjust are
Figure 02_image256
, is the state feedback control parameter, where the output node represents the following meanings:

Figure 02_image278
，
Figure 02_image280
，
Figure 02_image282
，
Figure 02_image284
，
Figure 02_image278
,
Figure 02_image280
,
Figure 02_image282
,
Figure 02_image284
,

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

令參數符號

Figure 02_image286
是該輸入節點與該第1層隱藏節點間的權值，參數符號
Figure 02_image288
是該第1層隱藏節點與該第2層隱藏節點間的權值，參數符號
Figure 02_image290
是該第2層隱藏節點與該輸出節點間的權值， Let parameter symbol
Figure 02_image286
is the weight between the input node and the hidden node of the first layer, parameter symbol
Figure 02_image288
is the weight between the hidden node of the first layer and the hidden node of the second layer, parameter symbol
Figure 02_image290
is the weight between the second layer hidden node and the output node,

該第1層隱藏節點與該輸入節點的關係如下：The relationship between the layer 1 hidden node and the input node is as follows:

Figure 02_image292
，該
Figure 02_image294
係為函數符號，而該等號左右兩式係單一純量，
Figure 02_image296
是第1層隱藏節點
Figure 02_image298
的計算值，
Figure 02_image300
，啟動函數
Figure 02_image302
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 02_image304
,
Figure 02_image306
。
Figure 02_image292
,Should
Figure 02_image294
is a function symbol, and the left and right sides of the equal sign are single scalars,
Figure 02_image296
is the layer 1 hidden node
Figure 02_image298
the calculated value of
Figure 02_image300
, start the function
Figure 02_image302
Use the following bipolar sigmoid function to scale the output appropriately to the value range -1 to 1,
Figure 02_image304
,
Figure 02_image306
.

該第2層隱藏節點與該第1層隱藏節點的關係如下：The relationship between the second layer hidden node and the first layer hidden node is as follows:

Figure 02_image308
，該
Figure 02_image310
係為函數符號，而該等號左右兩式係單一純量，
Figure 02_image312
是第二層隱藏層節點
Figure 02_image314
的計算值，
Figure 02_image316
。
Figure 02_image308
,Should
Figure 02_image310
is a function symbol, and the left and right sides of the equal sign are single scalars,
Figure 02_image312
is the second hidden layer node
Figure 02_image314
the calculated value of
Figure 02_image316
.

該輸出節點與該第2層隱藏節點的關係如下：The relationship between the output node and the layer 2 hidden node is as follows:

Figure 02_image318
，該
Figure 02_image320
係為函數符號，而該等號左右兩式係單一純量，
Figure 02_image322
是輸出層節點
Figure 02_image324
的計算值，
Figure 02_image326
。
Figure 02_image318
,Should
Figure 02_image320
is a function symbol, and the left and right sides of the equal sign are single scalars,
Figure 02_image322
is the output layer node
Figure 02_image324
the calculated value of
Figure 02_image326
.

該輸入節點

Figure 02_image328
連接到左右輪的平均角度
Figure 02_image031
，該輸入節點
Figure 02_image330
連接到機身的傾斜角度［pitch］為
Figure 02_image039
，使用倒傳遞法求每一層的權值，訓練的目的是要使誤差平方達到最小，誤差的平方為： The input node
Figure 02_image328
Attached to the average angle of the left and right wheels
Figure 02_image031
, the input node
Figure 02_image330
The angle of inclination [pitch] attached to the fuselage is
Figure 02_image039
, using the reverse transfer method to find the weight of each layer, the purpose of training is to minimize the square of the error, the square of the error is:

Figure 02_image332
，該
Figure 02_image334
代表誤差的平方，該
Figure 02_image336
代表誤差平方根，
Figure 02_image338
是左右輪的平均角度參考輸入，
Figure 02_image340
是機身傾斜角度［pitch］參考輸入，
Figure 02_image342
、
Figure 02_image344
是該受控系統的量測輸出第k個取樣。
Figure 02_image332
,Should
Figure 02_image334
represents the square of the error, the
Figure 02_image336
stands for the square root of the error,
Figure 02_image338
is the average angle reference input of the left and right wheels,
Figure 02_image340
is the body tilt angle [pitch] reference input,
Figure 02_image342
,
Figure 02_image344
is the kth sample of the measured output of the controlled system.

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

Figure 02_image346
，
Figure 02_image346
,

Figure 02_image348
，
Figure 02_image348
,

Figure 02_image350
為數學上的差量，該第一層隱藏層到該第二層隱藏層為：
Figure 02_image350
is the mathematical difference, the first hidden layer to the second hidden layer is:

Figure 02_image352
，
Figure 02_image352
,

Figure 02_image354
，
Figure 02_image354
,

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

Figure 02_image356
，
Figure 02_image356
,

Figure 02_image358
，
Figure 02_image358
,

其中

Figure 02_image360
為學習速率常數。 in
Figure 02_image360
is the learning rate constant.

偏微分

Figure 02_image362
，
Figure 02_image364
，
Figure 02_image366
，
Figure 02_image368
，
Figure 02_image370
及
Figure 02_image372
的計算如下。 partial differential
Figure 02_image362
,
Figure 02_image364
,
Figure 02_image366
,
Figure 02_image368
,
Figure 02_image370
and
Figure 02_image372
The calculation of is as follows.

Figure 02_image374
，
Figure 02_image374
,

Figure 02_image376
，
Figure 02_image376
,

Figure 02_image378
Figure 02_image380
，
Figure 02_image378
Figure 02_image380
,

Figure 02_image382
Figure 02_image384
，
Figure 02_image382
Figure 02_image384
,

Figure 02_image386
Figure 02_image388
Figure 02_image390
，
Figure 02_image386
Figure 02_image388
Figure 02_image390
,

Figure 02_image392
Figure 02_image394
Figure 02_image396
，
Figure 02_image392
Figure 02_image394
Figure 02_image396
,

其中in

Figure 02_image398
，
Figure 02_image400
，
Figure 02_image402
，
Figure 02_image398
,
Figure 02_image400
,
Figure 02_image402
,

Figure 02_image404
，
Figure 02_image406
，
Figure 02_image404
,
Figure 02_image406
,

Figure 02_image408
，
Figure 02_image410
，
Figure 02_image408
,
Figure 02_image410
,

Figure 02_image412
，
Figure 02_image414
，
Figure 02_image412
,
Figure 02_image414
,

Figure 02_image416
，
Figure 02_image418
，
Figure 02_image416
,
Figure 02_image418
,

Figure 02_image420
，
Figure 02_image422
，
Figure 02_image420
,
Figure 02_image422
,

在實用上，偏微分

Figure 02_image424
可以用
Figure 02_image426
來近似，其中
Figure 02_image428
且
Figure 02_image430
。因此偏微分
Figure 02_image432
，
Figure 02_image433
，
Figure 02_image434
，
Figure 02_image436
，
Figure 02_image438
及
Figure 02_image440
可以改寫如下，
Figure 02_image442
為狀態變數： In practice, partial differential
Figure 02_image424
Can use
Figure 02_image426
to approximate, where
Figure 02_image428
and
Figure 02_image430
. So the partial differential
Figure 02_image432
,
Figure 02_image433
,
Figure 02_image434
,
Figure 02_image436
,
Figure 02_image438
and
Figure 02_image440
can be rewritten as follows,
Figure 02_image442
For state variables:

Figure 02_image444
，
Figure 02_image444
,

Figure 02_image446
，
Figure 02_image446
,

Figure 02_image448
，
Figure 02_image448
,

Figure 02_image450
，
Figure 02_image450
,

Figure 02_image452
，
Figure 02_image452
,

Figure 02_image454
，
Figure 02_image454
,

該輸出節點、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

Figure 02_image456
，
Figure 02_image458
，
Figure 02_image460
。 in
Figure 02_image456
,
Figure 02_image458
,
Figure 02_image460
.

因此權值的更新公式可以更改如下，

Figure 02_image462
為狀態變數： Therefore, the update formula of the weight can be changed as follows,
Figure 02_image462
For state variables:

Figure 02_image464
，
Figure 02_image464
,

Figure 02_image466
，
Figure 02_image466
,

Figure 02_image468
，
Figure 02_image468
,

Figure 02_image470
，
Figure 02_image470
,

Figure 02_image472
，
Figure 02_image472
,

Figure 02_image474
，
Figure 02_image474
,

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

Figure 02_image476
，
Figure 02_image476
,

Figure 02_image478
，
Figure 02_image478
,

Figure 02_image480
，
Figure 02_image480
,

Figure 02_image482
，
Figure 02_image482
,

Figure 02_image484
，
Figure 02_image484
,

Figure 02_image486
，
Figure 02_image486
,

其中，動力［momentum］因子的範圍為

Figure 02_image488
。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
Figure 02_image488
. Adding momentum [momentum] can prevent the neural network from falling into the local minimum when learning and calculating.

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，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，以可使兩輪機具達到強健平衡穩定之自動控制功效，而在其整體施行使用上更增實用功效特性者。From the above, the description of the use and implementation of the present invention shows that, compared with the prior art, the present invention mainly adjusts the controller parameters by means of deep learning, which can have a learning adjustment mechanism and can be widely used. Adapting to changes in environmental parameters, so as to achieve a strong, balanced and stable automatic control function for two-wheeled machines, and to increase practical performance characteristics 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 aforementioned 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 never been seen in similar products, nor has it been disclosed before the application, and it has fully complied with the provisions of the Patent Law In accordance with the requirements, it is very convenient to file an application for a patent for invention in accordance with the law, and sincerely ask for the review and approval of the patent.

S01:步驟一S01: Step 1

S02:步驟二S02: Step 2

S03:步驟三S03: Step 3

S04:步驟四S04: Step 4

第一圖：兩輪機具之車身傾斜狀態示意圖Figure 1: Schematic diagram of the tilted state of the body of the two-wheeled machine

第二圖：兩輪機具之立體簡化結構示意圖Figure 2: Schematic diagram of a three-dimensional simplified structure of a two-wheeled machine tool

第三圖：兩輪機具之側視簡化結構示意圖Figure 3: Simplified schematic diagram of the side view of the two-wheeled machine tool

第四圖：兩輪機具之俯視簡化結構示意圖Figure 4: Simplified structural schematic diagram of a top view of a two-wheeled machine tool

第五圖：本發明之步驟流程示意圖Figure 5: Schematic diagram of the steps of the present invention

第六圖：本發明之多層類神經網路架構示意圖Figure 6: Schematic diagram of the multi-layer neural network architecture of the present invention

S01:步驟一 S01: Step 1

S02:步驟二 S02: Step 2

S03:步驟三 S03: Step 3

S04:步驟四 S04: Step 4

Claims (8)

一種深度學習控制兩輪機具平衡方法，其主要係包括下列步驟： 步驟一(S01)：測量一兩輪機具的輪胎轉動角度、傾斜角度［pitch］及偏轉角度［yaw］，以判斷所述兩輪機具處於直立、前傾、後傾、左轉或右轉狀態； 步驟二(S02)：對所述兩輪機具的左右輪的平均角度變數
Figure 03_image043
及兩輪機具的傾斜角度［pitch］變數
Figure 03_image045
進行深度學習控制，進而得到第一控制輸出的電壓控制值； 步驟三(S03)：對所述兩輪機具的偏轉角度［yaw］變數
Figure 03_image047
以極點設置法［pole assignment］進行狀態回授控制，以得到第二控制輸出的電壓控制值； 步驟四(S04)：將所述第一控制輸出的電壓控制值加上所述第二控制輸出的電壓控制值，除以二，即得到右輪驅動馬達的電壓控制值，以控制右輪驅動馬達的轉速與轉向；將所述第一控制輸出的電壓控制值減去所述第二控制輸出的電壓控制值，除以二，即得到左輪驅動馬達的電壓控制值，以控制左輪驅動馬達的轉速與轉向。 A deep learning method for controlling the balance of two-wheeled equipment, which mainly includes the following steps: Step 1 (S01): Measure the tire rotation angle, inclination angle [pitch] and deflection angle [yaw] of a two-wheeled equipment to determine the The wheel equipment is in the state of standing upright, leaning forward, tilting backward, turning left or turning right; Step 2 (S02): the average angle variable of the left and right wheels of the two-wheel equipment
Figure 03_image043
And the tilt angle [pitch] variable of the two-wheeled implement
Figure 03_image045
Perform deep learning control, and then obtain the voltage control value of the first control output; Step 3 (S03): Change the deflection angle [yaw] of the two-wheel implement
Figure 03_image047
Performing state feedback control with a pole assignment method to obtain a voltage control value of the second control output; Step 4 (S04): adding the voltage control value of the first control output to the second control output The voltage control value of the right wheel drive motor is divided by two to obtain the voltage control value of the right wheel drive motor to control the speed and steering of the right wheel drive motor; the voltage control value of the first control output is subtracted from the second control output The voltage control value of the left wheel drive motor is divided by two to obtain the voltage control value of the left wheel drive motor to control the speed and steering of the left wheel drive motor. 如請求項1所述深度學習控制兩輪機具平衡方法，其中，使用拉格朗奇方法［Lagrangian］推導兩輪機具的動態方程式，假設傾斜角很小時(
Figure 03_image049
)可以簡化如下：
Figure 03_image001
是重力加速度，
Figure 03_image003
是輪子的重量，
Figure 03_image005
是輪子的半徑，
Figure 03_image007
是輪子的轉動慣量，
Figure 03_image009
是兩輪機具之機身的質量，
Figure 03_image011
是兩輪機具之機身的寬度，
Figure 03_image013
是兩輪機具之機身的深度，
Figure 03_image015
是兩輪機具之機身的高度，
Figure 03_image017
為馬達軸到重心的長度，
Figure 03_image019
為傾斜角度［pitch］轉動慣量，
Figure 03_image021
為偏轉角度［yaw］的轉動慣量，
Figure 03_image023
為馬達的轉動慣量，
Figure 03_image025
是齒輪箱比值；左輪的轉動角度是
Figure 03_image027
，右輪的轉動角度是
Figure 03_image029
，左右輪的平均角度為
Figure 03_image033
；左馬達的轉動角度是
Figure 03_image035
，右馬達的轉動角度是
Figure 03_image037
，兩輪機具之機身的傾斜角度［pitch］為
Figure 03_image039
，兩輪機具偏轉角度［yaw］為
Figure 03_image041
；座標系統的變數如下，
Figure 03_image059
代表
Figure 03_image061
角度方向的力矩［Torque］，
Figure 03_image062
代表
Figure 03_image064
角度方向的力矩［Torque］，
Figure 03_image065
代表
Figure 03_image067
角度方向的力矩［Torque］，
Figure 03_image068
代表左右馬達的端電壓，
Figure 03_image070
是齒輪箱比值，
Figure 03_image071
是力矩常數，
Figure 03_image073
為馬達的摩擦係數，
Figure 03_image075
是輪子與地的摩擦係數，
Figure 03_image077
代表反電動勢常數，
Figure 03_image079
代表電樞電阻；
Figure 03_image051
(1)
Figure 03_image053
Figure 03_image055
(2)
Figure 03_image057
(3) 將電壓公式代入(1)-(3)式線性方程式中，可以得到以下公式：
Figure 03_image081
(4) 其中
Figure 03_image083
矩陣如下：
Figure 03_image085
，
Figure 03_image087
，
Figure 03_image089
，
Figure 03_image091
， 而且
Figure 03_image093
、
Figure 03_image095
；
Figure 03_image097
是左馬達產生的力矩，
Figure 03_image099
是右馬達產生的力矩，
Figure 03_image101
是機身偏轉角度(yaw)，
Figure 03_image067
角度方向的力矩［Torque］如下：
Figure 03_image102
Figure 03_image104
(5) 其中
Figure 03_image106
； 根據(3)式及(5)式，化簡可得：
Figure 03_image108
(6) 其中參數如下，
Figure 03_image110
，
Figure 03_image112
，
Figure 03_image114
由(4)式展開可得，求解
Figure 03_image116
及
Figure 03_image118
，得：
Figure 03_image120
Figure 03_image122
Figure 03_image124
(7)
Figure 03_image126
Figure 03_image128
Figure 03_image130
(8) 由(6)式展開可得：
Figure 03_image132
(9) 由(9)式能得知可以用
Figure 03_image134
來控制機身偏轉角度［yaw］
Figure 03_image136
，由(7)式及(8)式能得知可以用
Figure 03_image138
來控制左右輪的平均角度
Figure 03_image140
及機身傾斜角度［pitch］
Figure 03_image141
。 As described in claim item 1, the method of deep learning to control the balance of two-wheeled equipment, wherein the dynamic equation of the two-wheeled equipment is derived using the Lagrangian method [Lagrangian], assuming that the inclination angle is small (
Figure 03_image049
) can be simplified as follows:
Figure 03_image001
is the acceleration of gravity,
Figure 03_image003
is the weight of the wheel,
Figure 03_image005
is the radius of the wheel,
Figure 03_image007
is the moment of inertia of the wheel,
Figure 03_image009
is the mass of the body of the two-wheeled machine,
Figure 03_image011
is the width of the fuselage of the two-wheeled machine,
Figure 03_image013
is the depth of the fuselage of the two-wheeled machine,
Figure 03_image015
is the height of the fuselage of the two-wheeled machine,
Figure 03_image017
is the length from the motor shaft to the center of gravity,
Figure 03_image019
is the moment of inertia of the tilt angle [pitch],
Figure 03_image021
is the moment of inertia of deflection angle [yaw],
Figure 03_image023
is the moment of inertia of the motor,
Figure 03_image025
is the gearbox ratio; the rotation angle of the left wheel is
Figure 03_image027
, the rotation angle of the right wheel is
Figure 03_image029
, the average angle of the left and right wheels is
Figure 03_image033
;The rotation angle of the left motor is
Figure 03_image035
, the rotation angle of the right motor is
Figure 03_image037
, the inclination angle [pitch] of the fuselage of the two-wheeled implement is
Figure 03_image039
, the deflection angle [yaw] of the two-wheel implement is
Figure 03_image041
; The variables of the coordinate system are as follows,
Figure 03_image059
represent
Figure 03_image061
Angular moment [Torque],
Figure 03_image062
represent
Figure 03_image064
Angular moment [Torque],
Figure 03_image065
represent
Figure 03_image067
Angular moment [Torque],
Figure 03_image068
Represents the terminal voltage of the left and right motors,
Figure 03_image070
is the gearbox ratio,
Figure 03_image071
is the moment constant,
Figure 03_image073
is the friction coefficient of the motor,
Figure 03_image075
is the coefficient of friction between the wheel and the ground,
Figure 03_image077
represents the back EMF constant,
Figure 03_image079
represents the armature resistance;
Figure 03_image051
(1)
Figure 03_image053
Figure 03_image055
(2)
Figure 03_image057
(3) Substituting the voltage formula into the linear equation (1)-(3), the following formula can be obtained:
Figure 03_image081
(4) of which
Figure 03_image083
The matrix is as follows:
Figure 03_image085
,
Figure 03_image087
,
Figure 03_image089
,
Figure 03_image091
, and
Figure 03_image093
,
Figure 03_image095
;
Figure 03_image097
is the torque produced by the left motor,
Figure 03_image099
is the torque produced by the right motor,
Figure 03_image101
is the airframe deflection angle (yaw),
Figure 03_image067
The torque [Torque] in the angular direction is as follows:
Figure 03_image102
Figure 03_image104
(5) of which
Figure 03_image106
; According to formula (3) and formula (5), simplification can be obtained:
Figure 03_image108
(6) The parameters are as follows,
Figure 03_image110
,
Figure 03_image112
,
Figure 03_image114
From formula (4), it can be obtained that the solution
Figure 03_image116
and
Figure 03_image118
,have to:
Figure 03_image120
Figure 03_image122
Figure 03_image124
(7)
Figure 03_image126
Figure 03_image128
Figure 03_image130
(8) Expanded from formula (6), we can get:
Figure 03_image132
(9) It can be known from formula (9) that it can be used
Figure 03_image134
to control the body deflection angle [yaw]
Figure 03_image136
, from formula (7) and formula (8), it can be known that it can be used
Figure 03_image138
to control the average angle of the left and right wheels
Figure 03_image140
and body tilt angle [pitch]
Figure 03_image141
. 如請求項2所述深度學習控制兩輪機具平衡方法，其中，由
Figure 03_image134
及
Figure 03_image138
的值可算出所需的右輪馬達控制電壓
Figure 03_image142
及左輪馬達控制電壓
Figure 03_image144
， 令狀態變數
Figure 03_image146
為左右輪的平均角度
Figure 03_image140
，狀態變數
Figure 03_image148
為機身傾斜角度［pitch］
Figure 03_image141
，狀態變數
Figure 03_image150
為
Figure 03_image152
，狀態變數
Figure 03_image154
為
Figure 03_image156
，狀態變數
Figure 03_image158
為機身偏轉角度［yaw］
Figure 03_image136
，狀態變數
Figure 03_image160
為
Figure 03_image162
，
Figure 03_image138
的值為
Figure 03_image164
，
Figure 03_image166
的值為
Figure 03_image168
，則系統的狀態空間方程式為：
Figure 03_image170
(10)
Figure 03_image172
(11) 其中參數如下，
Figure 03_image174
，
Figure 03_image176
Figure 03_image178
，
Figure 03_image180
，
Figure 03_image182
，
Figure 03_image184
，
Figure 03_image186
Figure 03_image188
，
Figure 03_image190
，
Figure 03_image192
， 而所需的右輪馬達控制電壓
Figure 03_image194
及左輪馬達控制電壓
Figure 03_image196
為：
Figure 03_image198
，
Figure 03_image200
。 As described in claim item 2, the deep learning control two-wheel implement balance method, wherein, by
Figure 03_image134
and
Figure 03_image138
The value of the required right wheel motor control voltage can be calculated
Figure 03_image142
and left wheel motor control voltage
Figure 03_image144
, let the state variable
Figure 03_image146
is the average angle of the left and right wheels
Figure 03_image140
, the state variable
Figure 03_image148
is the inclination angle of the fuselage [pitch]
Figure 03_image141
, the state variable
Figure 03_image150
for
Figure 03_image152
, the state variable
Figure 03_image154
for
Figure 03_image156
, the state variable
Figure 03_image158
is the body deflection angle [yaw]
Figure 03_image136
, the state variable
Figure 03_image160
for
Figure 03_image162
,
Figure 03_image138
The value is
Figure 03_image164
,
Figure 03_image166
The value is
Figure 03_image168
, then the state-space equation of the system is:
Figure 03_image170
(10)
Figure 03_image172
(11) where the parameters are as follows,
Figure 03_image174
,
Figure 03_image176
Figure 03_image178
,
Figure 03_image180
,
Figure 03_image182
,
Figure 03_image184
,
Figure 03_image186
Figure 03_image188
,
Figure 03_image190
,
Figure 03_image192
, while the required right wheel motor control voltage
Figure 03_image194
and left wheel motor control voltage
Figure 03_image196
for:
Figure 03_image198
,
Figure 03_image200
. 如請求項3所述深度學習控制兩輪機具平衡方法，其中， 該狀態回授控制器可將(10)式改寫如下：
Figure 03_image491
Figure 03_image204
Figure 03_image206
(12) 其中
Figure 03_image208
，
Figure 03_image210
，
Figure 03_image212
，
Figure 03_image214
， 由(12)式，可以說狀態回授控制器等效於［equivalent］ PD控制，將(12)式分成兩個PD控制的分量如下；
Figure 03_image216
(13) 則狀態回授控制等效於雙PD控制。 As described in claim item 3, the deep learning control two-wheel implement balance method, wherein, the state feedback controller can rewrite formula (10) as follows:
Figure 03_image491
Figure 03_image204
Figure 03_image206
(12) of which
Figure 03_image208
,
Figure 03_image210
,
Figure 03_image212
,
Figure 03_image214
, From formula (12), it can be said that the state feedback controller is equivalent to [equivalent] PD control, and formula (12) is divided into two components of PD control as follows;
Figure 03_image216
(13) The state feedback control is equivalent to dual PD control. 如請求項4所述深度學習控制兩輪機具平衡方法，其中，對於一個可穩定［stabilizable］及可偵測［detectable］線性非時變系統，
Figure 03_image218
(14) 其中
Figure 03_image220
是狀態向量，
Figure 03_image222
是控制輸入，
Figure 03_image224
是系統矩陣，
Figure 03_image226
是控制輸入矩陣，則狀態回授控制為，
Figure 03_image228
(15) 因為系統是可穩定［stabilizable］及可偵測［detectable］線性非時變系統，則系統可以用狀態回授控制器達到穩定控制的目的。 As described in claim item 4, the deep learning control method for two-wheel implement balance, wherein, for a stable [stabilizable] and detectable [detectable] linear non-time-varying system,
Figure 03_image218
(14) of which
Figure 03_image220
is the state vector,
Figure 03_image222
is the control input,
Figure 03_image224
is the system matrix,
Figure 03_image226
is the control input matrix, then the state feedback control is,
Figure 03_image228
(15) Because the system is a stable [stabilizable] and detectable [detectable] linear time-invariant system, the system can use the state feedback controller to achieve the purpose of stable control. 如請求項4所述深度學習控制兩輪機具平衡方法，其中，對該(11)式單獨另外設計控制器，就(11)式而言，在狀態回授控制器如下：
Figure 03_image230
(16) 將(16)式代入(11)式，則可以得到：
Figure 03_image232
(17) 則受控系統(17)的特性方程式［characteristic equation］為：
Figure 03_image234
(18) 若要設計系統的極點［poles］於
Figure 03_image236
，
Figure 03_image238
，則設計系統的特性方程式為：
Figure 03_image240
(19) 比較(18)式及(19)式，可得控制器為：
Figure 03_image242
，
Figure 03_image244
(20) 根據(13)式就可以求得
Figure 03_image246
，根據(20)式就可以求得
Figure 03_image248
，再根據下式
Figure 03_image250
，
Figure 03_image251
， 即可以求得
Figure 03_image253
及
Figure 03_image254
，進而可以控制兩輪機具的穩定平衡。 As described in claim item 4, the deep learning control two-wheel implement balance method, wherein, the controller is separately designed for the (11) formula, and as far as the (11) formula is concerned, the state feedback controller is as follows:
Figure 03_image230
(16) Substituting (16) into (11), we can get:
Figure 03_image232
(17) Then the characteristic equation [characteristic equation] of the controlled system (17) is:
Figure 03_image234
(18) To design the poles [poles] of the system at
Figure 03_image236
,
Figure 03_image238
, then the characteristic equation of the design system is:
Figure 03_image240
(19) Comparing formula (18) and formula (19), the controller can be obtained as:
Figure 03_image242
,
Figure 03_image244
(20) According to formula (13), it can be obtained
Figure 03_image246
, according to (20) can get
Figure 03_image248
, and then according to the following formula
Figure 03_image250
,
Figure 03_image251
, which can be obtained
Figure 03_image253
and
Figure 03_image254
, which in turn can control the stable balance of the two-wheel implement. 如請求項1所述深度學習控制兩輪機具平衡方法，其中，就該步驟二(S02)之深度學習控制而言，數位控制器需要調節的控制參數如下：
Figure 03_image256
，
Figure 03_image258
是狀態回授控制參數， 利用深度學習的方法調整該控制參數，深度學習是使用多層類神經網路作為控制方法，其中，變數符號
Figure 03_image260
是深度學習類神經網路的輸入節點，
Figure 03_image262
、
Figure 03_image264
是該受控系統的量測輸出第k個取樣，變數符號
Figure 03_image266
是該輸入節點的偏值，變數符號
Figure 03_image268
、
Figure 03_image270
各是第1層、第2層的隱藏節點，隱藏層有2層以上；變數符號
Figure 03_image272
、
Figure 03_image274
是該隱藏節點的偏值，變數符號
Figure 03_image276
是輸出節點，該自動控制系統需要調節的控制參數為
Figure 03_image256
，是狀態回授控制參數，其中該輸出節點代表意思如下：
Figure 03_image278
，
Figure 03_image280
，
Figure 03_image282
，
Figure 03_image284
， 該深度學習類神經網路的權值如下： 令參數符號
Figure 03_image286
是該輸入節點與該第1層隱藏節點間的權值，參數符號
Figure 03_image288
是該第1層隱藏節點與該第2層隱藏節點間的權值，參數符號
Figure 03_image290
是該第2層隱藏節點與該輸出節點間的權值， 該第1層隱藏節點與該輸入節點的關係如下：
Figure 03_image292
，該
Figure 03_image294
係為函數符號，而該等號左右兩式係單一純量，
Figure 03_image296
是第1層隱藏節點
Figure 03_image298
的計算值，
Figure 03_image300
，啟動函數
Figure 03_image302
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 03_image304
,
Figure 03_image306
； 該第2層隱藏節點與該第1層隱藏節點的關係如下：
Figure 03_image308
，該
Figure 03_image310
係為函數符號，而該等號左右兩式係單一純量，
Figure 03_image312
是第二層隱藏層節點
Figure 03_image314
的計算值，
Figure 03_image316
； 該輸出節點與該第2層隱藏節點的關係如下：
Figure 03_image318
，該
Figure 03_image320
係為函數符號，而該等號左右兩式係單一純量，
Figure 03_image322
是輸出層節點
Figure 03_image324
的計算值，
Figure 03_image326
； 該輸入節點
Figure 03_image328
連接到左右輪的平均角度
Figure 03_image031
，該輸入節點
Figure 03_image330
連接到機身的傾斜角度［pitch］為
Figure 03_image039
，使用倒傳遞法求每一層的權值，訓練的目的是要使誤差平方達到最小，誤差的平方為：
Figure 03_image332
，該
Figure 03_image334
代表誤差的平方，該
Figure 03_image336
代表誤差平方根，
Figure 03_image338
是左右輪的平均角度參考輸入，
Figure 03_image340
是機身傾斜角度［pitch］參考輸入，
Figure 03_image342
、
Figure 03_image344
是該受控系統的量測輸出第k個取樣； 權值用以下的方法來更新，輸入層到該第一層隱藏層為：
Figure 03_image346
，
Figure 03_image348
，
Figure 03_image350
為數學上的差量，該第一層隱藏層到該第二層隱藏層為：
Figure 03_image352
，
Figure 03_image354
， 該第二層隱藏層到輸出層為：
Figure 03_image356
，
Figure 03_image358
， 其中
Figure 03_image360
為學習速率常數。 As described in claim item 1, the deep learning control two-wheel implement balance method, wherein, in terms of the deep learning control of step 2 (S02), the control parameters that need to be adjusted by the digital controller are as follows:
Figure 03_image256
,
Figure 03_image258
is the state feedback control parameter, and the control parameter is adjusted by the method of deep learning, which uses a multi-layer neural network as the control method, where the variable symbol
Figure 03_image260
is the input node of deep learning neural network,
Figure 03_image262
,
Figure 03_image264
is the kth sample of the measured output of the controlled system, and the symbol of the variable is
Figure 03_image266
is the bias value of the input node, variable symbol
Figure 03_image268
,
Figure 03_image270
Each is the hidden node of the first layer and the second layer, and the hidden layer has more than two layers; the variable symbol
Figure 03_image272
,
Figure 03_image274
is the bias value of the hidden node, variable symbol
Figure 03_image276
is the output node, and the control parameters that the automatic control system needs to adjust are
Figure 03_image256
, is the state feedback control parameter, where the output node represents the following meanings:
Figure 03_image278
,
Figure 03_image280
,
Figure 03_image282
,
Figure 03_image284
, the weights of this deep learning neural network are as follows: Let the parameter symbol
Figure 03_image286
is the weight between the input node and the hidden node of the first layer, parameter symbol
Figure 03_image288
is the weight between the hidden node of the first layer and the hidden node of the second layer, parameter symbol
Figure 03_image290
is the weight between the hidden node of the second layer and the output node, and the relationship between the hidden node of the first layer and the input node is as follows:
Figure 03_image292
,Should
Figure 03_image294
is a function symbol, and the left and right sides of the equal sign are single scalars,
Figure 03_image296
is the layer 1 hidden node
Figure 03_image298
the calculated value of
Figure 03_image300
, start the function
Figure 03_image302
Use the following bipolar sigmoid function to scale the output appropriately to the value range -1 to 1,
Figure 03_image304
,
Figure 03_image306
; The relationship between the hidden node of the second layer and the hidden node of the first layer is as follows:
Figure 03_image308
,Should
Figure 03_image310
is a function symbol, and the left and right sides of the equal sign are single scalars,
Figure 03_image312
is the second hidden layer node
Figure 03_image314
the calculated value of
Figure 03_image316
; The relationship between the output node and the hidden node of the second layer is as follows:
Figure 03_image318
,Should
Figure 03_image320
is a function symbol, and the left and right sides of the equal sign are single scalars,
Figure 03_image322
is the output layer node
Figure 03_image324
the calculated value of
Figure 03_image326
; The input node
Figure 03_image328
Attached to the average angle of the left and right wheels
Figure 03_image031
, the input node
Figure 03_image330
The angle of inclination [pitch] attached to the fuselage is
Figure 03_image039
, using the reverse transfer method to find the weight of each layer, the purpose of training is to minimize the square of the error, the square of the error is:
Figure 03_image332
,Should
Figure 03_image334
represents the square of the error, the
Figure 03_image336
stands for the square root of the error,
Figure 03_image338
is the average angle reference input of the left and right wheels,
Figure 03_image340
is the body tilt angle [pitch] reference input,
Figure 03_image342
,
Figure 03_image344
is the kth sample of the measured output of the controlled system; the weights are updated in the following way, from the input layer to the first hidden layer:
Figure 03_image346
,
Figure 03_image348
,
Figure 03_image350
is the mathematical difference, the first hidden layer to the second hidden layer is:
Figure 03_image352
,
Figure 03_image354
, the second hidden layer to the output layer is:
Figure 03_image356
,
Figure 03_image358
, in
Figure 03_image360
is the learning rate constant. 如請求項7所述深度學習控制兩輪機具平衡方法，其中，偏微分
Figure 03_image362
，
Figure 03_image364
，
Figure 03_image366
，
Figure 03_image368
，
Figure 03_image370
及
Figure 03_image372
的計算如下：
Figure 03_image374
，
Figure 03_image376
，
Figure 03_image378
Figure 03_image380
，
Figure 03_image382
Figure 03_image384
，
Figure 03_image386
Figure 03_image388
Figure 03_image390
，
Figure 03_image392
Figure 03_image394
Figure 03_image396
， 其中
Figure 03_image398
，
Figure 03_image400
，
Figure 03_image402
，
Figure 03_image404
，
Figure 03_image406
，
Figure 03_image408
，
Figure 03_image410
，
Figure 03_image412
，
Figure 03_image414
，
Figure 03_image416
，
Figure 03_image418
，
Figure 03_image420
，
Figure 03_image422
， 在實用上，偏微分
Figure 03_image424
可以用
Figure 03_image426
來近似，其中
Figure 03_image428
且
Figure 03_image430
。因此偏微分
Figure 03_image432
，
Figure 03_image433
，
Figure 03_image434
，
Figure 03_image436
，
Figure 03_image438
及
Figure 03_image440
可以改寫如下，
Figure 03_image442
為狀態變數：
Figure 03_image444
，
Figure 03_image446
，
Figure 03_image448
，
Figure 03_image450
，
Figure 03_image452
，
Figure 03_image454
， 該輸出節點、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 03_image456
，
Figure 03_image458
，
Figure 03_image460
。 因此權值的更新公式可以更改如下，
Figure 03_image462
為狀態變數：
Figure 03_image464
，
Figure 03_image466
，
Figure 03_image468
，
Figure 03_image470
，
Figure 03_image472
，
Figure 03_image474
， 學習法則可以修改為以下公式，
Figure 03_image476
，
Figure 03_image478
，
Figure 03_image480
，
Figure 03_image482
，
Figure 03_image484
，
Figure 03_image486
， 其中，動力［momentum］因子的範圍為
Figure 03_image488
，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。 As described in claim item 7, the deep learning control two-wheel implement balance method, wherein, the partial differential
Figure 03_image362
,
Figure 03_image364
,
Figure 03_image366
,
Figure 03_image368
,
Figure 03_image370
and
Figure 03_image372
is calculated as follows:
Figure 03_image374
,
Figure 03_image376
,
Figure 03_image378
Figure 03_image380
,
Figure 03_image382
Figure 03_image384
,
Figure 03_image386
Figure 03_image388
Figure 03_image390
,
Figure 03_image392
Figure 03_image394
Figure 03_image396
, in
Figure 03_image398
,
Figure 03_image400
,
Figure 03_image402
,
Figure 03_image404
,
Figure 03_image406
,
Figure 03_image408
,
Figure 03_image410
,
Figure 03_image412
,
Figure 03_image414
,
Figure 03_image416
,
Figure 03_image418
,
Figure 03_image420
,
Figure 03_image422
, in practice, the partial differential
Figure 03_image424
Can use
Figure 03_image426
to approximate, where
Figure 03_image428
and
Figure 03_image430
. So the partial differential
Figure 03_image432
,
Figure 03_image433
,
Figure 03_image434
,
Figure 03_image436
,
Figure 03_image438
and
Figure 03_image440
can be rewritten as follows,
Figure 03_image442
For state variables:
Figure 03_image444
,
Figure 03_image446
,
Figure 03_image448
,
Figure 03_image450
,
Figure 03_image452
,
Figure 03_image454
, the slight change of the output node, the second hidden layer node and the first hidden layer node is: where
Figure 03_image456
,
Figure 03_image458
,
Figure 03_image460
. Therefore, the update formula of the weight can be changed as follows,
Figure 03_image462
For state variables:
Figure 03_image464
,
Figure 03_image466
,
Figure 03_image468
,
Figure 03_image470
,
Figure 03_image472
,
Figure 03_image474
, the learning rule can be modified as the following formula,
Figure 03_image476
,
Figure 03_image478
,
Figure 03_image480
,
Figure 03_image482
,
Figure 03_image484
,
Figure 03_image486
, where the range of the momentum [momentum] factor is
Figure 03_image488
, plus momentum [momentum] can make the learning and calculation of the neural network not fall into the local minimum.
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