KR100222763B1 - Linear output apparatus for controlling position of robot and method thereof - Google Patents

Abstract

The present invention relates to a linear output control apparatus and a method for controlling the position of a robot that allows the robot to move to a desired position in a short time with respect to an unknown variable using only position information in a rigid or flexible joint robot system requiring high precision. The first output control unit for controlling the robot's motor to operate the robot according to the set control input signal, and determine whether the current position signal output from the robot is in a normal state to modify and set the control input of the first output control unit. Determines and outputs the initial control input of the first output controller according to the requested control input modification request unit and the initial position of the robot, and if there is a control input modification request from the control input correction request unit according to the current position signal and the reference position input. The control input correction unit for modifying and setting the control input, and the robot indexes from the current position to the reference position. The second output control unit for controlling the motor of the robot so as to asymmetrically, and if the difference between the current position signal and the reference position input is greater than the micro-movement reference, the robot is repeatedly controlled by the first output controller, the current position signal and the reference When the difference in the position signal is less than the micro-movement reference, the robot is characterized in that it comprises a switching unit for switching to be controlled by the second output control unit.

Description

Linear output control device for position control of robot and its method

The present invention relates to a linear output control device and a method for controlling the position of a robot, and in particular, in a rigid or flexible joint robot system requiring high precision, the robot moves to a desired position in a short time with respect to an unknown variable using only position information. The present invention relates to a linear output control apparatus for position control of a robot and a method thereof.

Traditionally, the actual controller of a robot used in an industrial field has been implemented using a PID (proportional differential derivative) controller, and most robots used in these days control position using a PD (proportional differential) controller. To do this, you need to know all the states of the robot. Position sensors and speed sensors are essential. However, in a working environment that is always exposed to external noise, the speed sensor is sensitive to noise, and the controller implemented using PID (proportional differential) control and the controller implemented using PD (proportional differential) control are the derivative elements D. Derivative factors can cause malfunctions and adversely affect the desired response.

In order to overcome this problem, a lot of researches have been made to configure a controller that guarantees the stability of the whole area with only a position sensor without a speed sensor. FIG. 1 is a block diagram schematically showing the configuration of a system including a control device that ensures stability of the whole area with only position information. As shown here, the robot 11 includes a motor 12 for driving the robot; , And a motor amplifier 13 for driving the motor by applying a signal to the motor, and an encoder 14 for detecting the rotation angle of the motor and outputting position information of the robot as the motor rotates. The input is a reference position (X _d ), which is the target position to which the robot is to move, and if the reference position is input to the control device 15, the control device outputs a control signal for driving the robot's motor so that the robot's reference is determined according to the position information of the robot. Make sure the location is reached.

Among many studies to construct a controller that guarantees full area stability with only a position sensor without a speed sensor, in particular, Amit Ailon has developed a Lyapunov Stability non-linear system for set-point regulation. By using the iterative control method based on the theory and the Convergence Mapping Theorem, we proposed a linear output feedback controller that is robust to unknown variables and ensures full area stability (Automatica, Vol. 32, No. 10, pp. 1455-1461, 1996). 2 is a block diagram showing the configuration of the control device. As shown here, the control input modification requester 22 receives the current position information of the robot output from the robot and determines and outputs the control input modification time. A control input modifier 23 which receives the current position information of the robot and the reference position input and the control input modification timing of the robot and modifies the control input when the control input modification time arrives; and the current position information of the robot and the modified control input. On the basis of the signal is composed of an output controller 24 for outputting a control signal for controlling the motor of the robot so that the robot moves in accordance with the modified control input.

The operation of this control device is explained as follows. First, input an arbitrary reference position that the robot wants to move. In the control input corrector 23, the initial control input of the output controller is determined based on the initial position of the robot, and when the initial control input is input to the output controller 24, the output controller is operated to operate the robot by this initial control input. 24) inputs a signal to the robot to control the motor of the robot. The robot starts by this signal, and after a certain period of time, the robot's output returns to its normal state. The control input modification requester 22 determines whether the output of the robot is in a normal state and outputs an eternal modification timing signal for correcting the control input when the robot is in the normal state. When the control input corrector 23 modifies the control input correction timing signal into a new control input and applies it to the output controller 24, the output controller 24 operates on the new control input to control the motor of the robot. Output the signal to the robot. The robot 21 operates on this new signal and after a certain period of time, the output of the robot is brought back to a normal state. By repeating this process, the robot's output approaches the reference position.

The theoretical background of the operation of the control device will be described as follows. First, when modeling the n-link flexible joint robot with linear torsion spring, a model having n degree of freedom can be obtained as shown in Equation 1 (Spong and Vidyasagar, 1989).

Rⁿ는 각각 링크와 모터의 각도를 표시하고, D(q₁)는 강성 링크의 관성행렬을 표시하며, J

0는 기어의 링크측에 반영된 액츄에이터 관성의 대각행렬이다.

은 코리올리스(Coriolis)와 원심력을 나타내며, g(q₁)는 중력을 나타내고, K

0는 관절 경도계수를 포함하는 대각행렬이다. 그리고 u

Rⁿ는 인가되는 토크벡터이다. 수학식 1의 상태공간은 다음의 수학식 2와 같이 주어진다.Where q ₁ , q ₂

R ⁿ denotes the angle of the link and the motor, respectively, D (q ₁ ) denotes the inertia matrix of the rigid link, and J

0 is the diagonal matrix of actuator inertia reflected on the link side of the gear.

Denotes Coriolis and centrifugal force, g (q ₁ ) denotes gravity, and K

0 is a diagonal matrix containing the joint hardness factor. And u

R ⁿ is the torque vector to be applied. The state space of Equation 1 is given by Equation 2 below.

이고, 모터각이 유일한 측정가능한 위치 정보이며, 수학식 2는 제2도에서의 유연관절 로봇(21)의 모델이 된다. 수학식 2의 시스템을 위한 선형의 n차원 출력제어기는 다음의 수학식 3과 같다.From here

Where motor angle is the only measurable position information, and Equation 2 is a model of the flexible joint robot 21 in FIG. The linear n-dimensional output controller for the system of Equation 2 is shown in Equation 3 below.

0 및 벡터 v

Rⁿ

0가 결정된다. 수학식 3은 제2도의 출력제어기(24)를 유연관절 로봇에 대하여 표현한 것이다.Where the constant matrices S = S ^T and R = R ^T

0 and vector v

R ⁿ

0 is determined. Equation 3 expresses the output controller 24 of FIG. 2 with respect to the flexible joint robot.

In the case of a rigid robot, Equation 2 is reduced to Equation 4 below. That is, Equation 4 is a model of the rigid robot 21 of FIG.

In this case, since the measurable position signal is x ₁ , Equation 3 is expressed by Equation 5 below.

은 x의 유클리안 놈(Euclidean Norm)을 표시하고

는 행렬 A의 유도 놈(Induced Norm)을 표시한다. 즉,

이며

는

의 가장 큰 고유치이다. 수학식 5는 강성 로봇의 경우에 제2도의 출력제어기(24)를 표현한 것이다.

Denotes the Euclidean Norm of x,

Denotes the induced norm of matrix A. In other words,

And

Is

Is the largest eigenvalue of. Equation 5 represents the output controller 24 of FIG. 2 in the case of a rigid robot.

가 평등유계가 있으면 다음의 수학식 6의 β가 존재한다.Scalar function

If there is an equality system, β of the following Equation 6 exists.

0이라고 가정한다. 다음으로 수학식 7을 고려한다.Β always here

Assume 0 Next, consider Equation 7.

Here, S and R are selected as in Equation 7 below.

를 가지며,

은 수학식 4와 수학식 5의 페루프 시스템의 유일한 평형점이 된다. 역으로, 모든 기준위치 x_1d(로봇의 셋-포인트)에 대하여 수학식 7은 유일한 해

를 가지며 유연관절 로봇의 모델에서도 수학식 7과 수학식 8은 다음과 같이 대체된다.Equation 7 is the only solution for all constant vectors v _d

Has,

Is the only equilibrium point of the Peruvian systems of equations (4) and (5). Conversely, for every reference position x _1d (the set-point of the robot), equation (7) is the only solution

In the model of the flexible joint robot, Equations 7 and 8 are replaced as follows.

가 존재하고,

은 수학식 2와 수학식 3의 페루프 시스템의 유일한 평형점이 된다. 역으로 모든 x_1d에 대하여 수학식 9는 유일한 해

를 가진다.Unique solution to Equation 9 for all v _d under the condition of Equation 10

Is present,

Is the only equilibrium point of the Peruvian systems of equations (2) and (3). Conversely, for every x _1d Equation 9 is the only solution

Has

이 존재한다.Considering the Peruvian systems of Equations 4 and 5, and selecting {S, R} to satisfy Equation 8, the equation of Equation 11

This exists.

을 다음의 수학식 12와 같이 정의하면Here, {x ₁ , v} satisfies Equation 7. x _1d is called a given constant vector

Is defined as in Equation 12

The following results can be obtained. That is, in the case of the rigid robot given the spirit T _r (v) is defined by Equation 7 and Equation 8 and Equation 11 and Equation 12, the matrix {S, R} is T _r of the equation (13) It can be determined to be a Global Contraction M apping with a unique fixed point v ^* .

This means the following equation (14).

{v _n } is defined by Equation 15,

S and R are selected according to equation (16).

2β로 가정하고, 임의의 v₀에 대하여 {v_i}는 수학식 15에 의하여 생성된다고 가정하며, 수학식 4와 수학식 5의 페루프 시스템을 고려하면 주어진 초기위치와 각 v_i에 대하여 시스템의 궤적φ_vi(·)는

의 점으로 수렴하고

이 된다. {

}의 극한은 x_1d이다. 평형점을 향한 시스템의 동작을

로 표현하고, 주어진 x₁ ⁱ에 대하여 수학식 11과 수학식 12 및 수학식 15로부터

이며, v_i+1의 계산은 측정가능한 신호에 근거하고

에 의하여 나타내면 다음과 같이 정리할 수 있다, 즉, r

0은 (r₁+1)/r₁

ρ을 만족하는 임의의 수인 ρ

1, r

max {r1,

, 2ρβ}의 상수를 선택하고, S, R이 수학식 16에 의하여 주어지면 임의의 상수 벡터 v₀

Rⁿ는 다음의 제1체인을 기동시킨다.r

Assume 2β, and for any v ₀ , {v _i } is generated by Equation 15. Considering the Peruvian systems of Equations 4 and 5, the system for a given initial position and each v _i The locus of φ _vi (·) is

Converge to the point of

Becomes {

} The limit is x _1d . System behavior towards the equilibrium point

And for Equation x ₁ ⁱ from Equations 11 and 12 and 15

And the calculation of v _{i + 1} is based on the measurable signal

Can be summarized as follows: r

0 is (r ₁ +1) / r ₁

ρ is any number satisfying ρ

1, r

max {r1,

, 2ρβ}, and if S and R are given by Eq _.

R ⁿ activates the following first chain.

가 존재하며, 여기서

이고 v^*은 {v_i}의 극한이며, x_1d은 {x₁ ⁱ}의 극한이다.And

Exists, where

And v ^* is the limit of {v _i } and x _1d is the limit of {x ₁ ⁱ }.

의 식에 의하여 새롭게 수정되는 제어입력 v(t)를 나타낸 것이다.If a relatively large r is selected, the constant η _r becomes a small number from above, and as a result, as shown in FIG. 3 (a), {x ₁ ⁱ } quickly converges to the vector x _1d . 3 (b)

The control input v (t) is newly modified by the following equation.

이 존재한다.In the case of a flexible joint robot, considering the Peruvian systems of Equations 2 and 3 and selecting {S, R} to satisfy Equation 10, the equation of Equation 17

This exists.

을 다음의 수학식 18과 같이 정의한다.Here, {x ₁ , v} satisfies Equation 7. The reference position x _1d is called the given constant vector

Is defined as in Equation 18 below.

라 가정할 때 행렬 {S, R}은 T_f이 수학식 19의 유일한 고정점 v^*를 갖는 글로벌 수렴 사상이 되도록 결정될 수 있다.From above, we can get the following result. That is, considering the event T _f (v) defined by Equations 9 and 10 and 16 and 17,

Assume that the matrix {S, R} can be determined such that T _f is a global convergence event with only fixed point v ^* of equation (19).

This means (20).

If {x _n } is defined by Equation 21,

ρ을 만족하는 임의의 양수인 ρ

1, r

max {r₁,

, 6ρβ,

}의 상수를 선택하고, S, R이 수학식 16에 의하여 주어지면 임의의 상수 벡터 v₀

Rⁿ는 다음의 제2체인을 기동시킨다.As in the rigid robot, we can arrange as follows. That is, r ₁ is (r ₁ +1) / r ₁

ρ is any positive integer that satisfies ρ

1, r

max {r ₁ ,

, 6ρβ,

} And, if S and R are given by Eq _.

R ⁿ activates the following second chain.

And

이고 v^*은 {v_i}의 극한이고 x_1d은 {x₁ ⁱ}의 극한이다.here

And v ^* is the limit of {v _i } and x _1d is the limit of {x ₁ ⁱ }.

2ξβ을 보장하고 따라서 η_f

1이 된다. 그러나 앞서의 강성 로봇에서와 달리 {x₁ ⁱ}가 벡터 x_1d에 수렴하는 비율을 상수 r의 증가에 의하여 임의로 빠르게 할 수 없다. 그 이유는 상대적으로 큰 r에 대하여 ζ의 분모뿐만 아니라 분자로 r차수이기 때문이다. 그러나λ_min(K)

3β이면 r을 증가하여 {x₁ ⁱ}의 수렴 비율을 비교적 크게된다.the choice of r is γ

Guarantees 2ξβ and therefore η _f

It becomes 1. However, unlike in the above-mentioned rigid robot, the rate at which {x ₁ ⁱ } converges to the vector x _1d cannot be arbitrarily increased by increasing the constant r. This is because, for a relatively large r, not only the denominator of ζ, but also the r order in the molecule. Λ _min (K)

If 3β, r is increased and the convergence ratio of {x ₁ ⁱ } becomes relatively large.

The asymptotic convergence of the system to the equilibrium point is related to the infinite time course. Therefore, some modifications are necessary to realize the control of the rigid robot and the flexible joint robot in the actual robot. As a result, the control ensures that there is a full range ultimate bound for the operating point where the system's time response is desired. Also, the response of all systems converges to the equilibrium point within a finite time.

This control device is linear and simple, so it is easy to implement as a real robot controller, so it is suitable for use in industry and can be applied to flexible-joint robots with unknown variables. There is a problem that it takes a long time to reach the desired position in.

The present invention is to solve such a conventional problem, an object of the present invention is to move the robot to a desired position in a fast time with respect to an unknown variable using only the position information in a rigid or flexible joint robot system that requires high precision The present invention provides a linear output control device for position control of a robot.

Another object of the present invention is a linear output control method for controlling the position of the robot to move the robot to a desired position in a short time with respect to an unknown variable using only position information in a rigid or flexible joint robot system requiring high precision In providing.

1 is a block diagram schematically showing the configuration of a system including an apparatus for controlling the position of a robot with only position information.

2 is a block diagram showing the configuration of a conventional control apparatus for controlling the position of a robot with only position information.

FIG. 3 (a) is a graph showing the output of the robot by the control device of FIG. 2 and the control input signal input to the output controller of FIG.

4 is a block diagram showing the configuration of a linear output control apparatus for position control of a robot according to the present invention.

5 is a graph showing the output of the robot by the control device of FIG.

6 is a flowchart illustrating a linear output control method for position control of a robot according to the present invention.

* Explanation of symbols for main parts of the drawings

41: robot 42: control input modification request

43: control input corrector 44: first output controller

45: second output controller 46: switch

In order to achieve the above object, the present invention provides a robot for controlling a robot having a drive motor and an encoder for detecting an angle of rotation as the drive motor rotates and outputting a current position signal of the robot to an input reference position. A linear output control device for position control, comprising: receiving a current position signal and a control input signal and outputting a signal for controlling the motor of the robot to operate the robot according to the input control input signal and outputting the first output controller and the robot; The control input modification request unit for outputting a control input modification timing signal for requesting to determine whether the current position signal is normal and to set and correct the current control input input to the first output Determine and output the initial control input input to the first output controller according to the initial position and receive the control input modification timing signal. If there is a control input modification request from the control input modification request unit, the robot receives the current position signal and the reference position signal based on the current position signal and the reference position input, and the robot receives the current position signal and the reference position signal. The second output control unit for controlling the motor of the robot to exponentially approach the position, and the difference between the current position signal and the reference position input by receiving the current position signal, the reference position signal, the control input correction timing signal and the fine motion reference signal Is larger than the micro-movement reference, the robot is repeatedly controlled by the first output controller, and when the difference between the current position signal and the reference position signal is smaller than the micro-movement reference signal, the robot is switched to be controlled by the second output controller. It is characterized by comprising a part.

In addition, to achieve the above object, the present invention, to control the robot to move to the input reference position having a drive motor, and the encoder to detect the rotation angle as the drive motor rotates to output the current position signal of the robot In the linear output control method for position control of a robot, (1) a step of inputting a reference position to which the robot is to be moved and a reference signal to which the robot is switched to fine motion, and determining an initial control input of the robot according to the initial position of the robot And (2) outputting a control input correction timing signal requesting that the current position signal outputted from the robot is in a normal state and correcting and setting the control input when it is in a normal state; and (3) and (2) Modifying and setting the control input based on the current position signal and the reference position input in accordance with the control input modification timing signal in the step of (4) the current position (3) controlling the robot's motor so that the robot operates according to the modified control input signal with respect to the input of the tangled force signal modified in this step; (5) the current position signal and the reference position signal, and (3) Comparing the current position signal of the robot with the reference position input of the robot on the basis of the control input modification timing signal of step (1) and the fine motion reference signal of step (1), and (6) comparing the step (5) As a result, if the difference between the current position signal and the reference position input is larger than the fine motion reference of step (1), repeat steps (2)-(4). If the difference between the current position signal and the reference location is smaller than the fine motion reference, And controlling the motor of the robot so that the robot exponentially approaches the current position signal and the reference position signal from the current position to the reference position.

Hereinafter, the configuration and operation of the embodiment of the linear output control apparatus according to the present invention will be described in detail with reference to the accompanying drawings.

4 is a block diagram showing the configuration of a linear output control device for position control of a robot according to the present invention. As shown here, the present invention of a robot is detected by detecting a rotation angle as the driving motor and the driving motor rotate. The robot 41 having an encoder for outputting a position signal and the state of the current position signal output from the robot are checked to determine whether the output state of the robot is in a normal state, and when the state is normal, the first output controller 44. A control input modification requester 42 for outputting a control input modification timing signal for requesting to modify the current control input of the controller, and an initial control input input to the first output controller 44 according to the initial position of the robot and then outputting the same. The robot starts and if the control input modification request is received from the control input modification request, the robot is controlled according to the current position signal and the reference position input. The control input modifier 43 for correcting and outputting the force, the current position signal and the control input signal of the control input modifier 43, and the robot motor is repeatedly operated so that the robot operates on the input control input signal. A first output controller 44 for controlling and a second output controller 45 for controlling the motor of the robot so that the robot receives the current position signal and the reference position signal exponentially from the current position to the reference position; The robot receives the micro-movement reference signal as the reference for selecting the first output controller or the second output controller, compares the current position signal with the reference position signal, and if the difference is greater than the micro-movement reference, the robot repeats the operation by the first output controller. And a switch 46 for switching the robot to be controlled by the second output controller when the difference between the current position signal and the reference position signal is smaller than the micro motion reference signal. There.

Referring to the operation of the present invention configured as described above are as follows.

Basically, the linear output control device for position control of a robot according to the present invention is composed of two stages. First, a step of 'rough motion' for converging the robot into a region as close as possible to an operating point of a desired reference position, followed by a robot for control purposes It consists of a 'fine motion' step that allows it to move almost accurately to the desired operating point. In the step of 'rough operation', as described above, the robot 41 and the control input modifying requester 42, the control input correcting unit 43, the first output controller 44 and the switching unit 46 are used. A loop is formed, and the components forming the loop are repeatedly modified by a control input signal inputted to the first output controller 44 to control the robot to approach the operating point. Converges to an approximate region, i.e., an approximated region determined by the micro-operation reference signal input to the switch 46. FIG. The step of coarse motion is different from the conventional control described above, in which a switch is added to the control loop in the component, and the switch 46 is input with a fine motion reference signal for determining the switching between coarse motion and fine motion. Is that. Therefore, in the operation, the control step of the coarse motion of the present invention is repeatedly controlled to the approximate area determined by the fine motion reference signal with respect to the desired operation point, while the control operation of the coarse motion of the present invention is repeated. do. As a result, in the related art, it takes a lot of time by repeating infinitely to the operating point, but the present invention shortens the required time by repeatedly controlling only a predetermined area. Once in a certain approximation region, the micro motion that moves to the operation point, which is the target point by 'fine motion', is looped by the robot 41, the second output controller 45, and the switch 46. The loop is formed by the second output controller 45 and the switch 46 forming the loop, and according to the operation of the second output controller 45 forming the loop, the robot exponentially functions from the current position to the desired position. Go to the enemy.

The theoretical background of an embodiment of the present invention will be described below with reference to the second output controller. As a result of performing the control of the coarse motion mode, when the state vector of the robot enters the region close to the desired operating point, it is possible to construct a linear control-observer that guarantees the subfield exponential stability of the system only by measuring the position of the link. Moreover, the eigenvalues of the linearized system can be arbitrarily assigned on the complex plane.

Using the above result and the previous result, the following control method is suggested. In other words, when a real-time control processor based on convergence mapping is implemented, it drives the robot to an approximate region of a desired operating point. Thereafter, the processor changes modes so that a new output controller 45 is executed and the robot converges exponentially to the final target point. For this purpose, considering the system of Equation 4 and the following Equation 22,

R^n×n는 추후결정될 상수행렬이고

은 시스템의 입력이며 출력 사상은 다음과 같다.Where H

R ^{n × n} is the constant matrix to be determined later

Is the input to the system and the output map is

Consider the output feedback of equation (24) for equation (23).

은 추후결정될 상수행렬이다. L을 다음의 수학식 25로 분할하면,here

Is the constant matrix to be determined later. Dividing L by the following equation (25),

(22) becomes (26).

Consider the linear function of Equation 27 below.

로 표시된다. 그리고

는 수학식 26의 평형점이다.For all non-singular matrices H, a block l _{ij in} which the left matrix of Equation 27 is non-singular may be selected. If H is regular and L chooses that the left square matrix of equation 27 is reversible, then {H, L} is an acceptable pair. Given acceptable pairs {H, L} are the only solutions of

Is displayed. And

Is the equilibrium point of equation (26).

를 결정하고 g(x_1d)가 미지의 벡터라는 사실은 여기서 관계가 없다.If {H, L} is an acceptable pair, then the constant vector x _1d is the equilibrium point.

The fact that g (x _1d ) is an unknown vector is irrelevant here.

에 의하여 수학식 22와 수학식 23의 시스템은 다음과 같이 쓸 수 있다.

The system of Equations 22 and 23 can be written as follows.

와

를 정의하면 다음식을 얻을 수 있다.Suppose we know exactly g (x _1d ) for a while,

Wow

If we define, we get

라고 가정한다. 수학식 24에 Γ를 대체하고 수학식 30과 수학식 31를 사용하여 테일러 공식을 평형점 Φ_d의 주위에서

에 적용하면 수학식 27은 수학식 32가 된다.The matrices A and B are independent of the vectors of {w ₁ , w ₂ }. An acceptable partner {H, L} is selected and the equilibrium point of the

Assume that Substitute Γ in Equation 24 and use Equation 30 and Equation 31 to form the Taylor formula around the equilibrium point Φ _d .

When applied to Equation 27 becomes Equation 32.

는

을 만족한다.here

Is

To satisfy.

In future developments, we use the following linear equation:

은 i+1, …, 4n에 대하여 Rea{λ_i}

0인 미리 결정된 서로 다른 복소수이고 임의의 σ

0를 선택한다. 그러면

로 표현되는 (A+BLC)의 고유치가 다음의 수학식 34을 만족하는 수학식 25의 형태의 행렬 L이 존재한다.In Equation 30 and Equation 31, assuming that the elements of A and B are correctly known, the regular matrix H is arbitrarily selected.

Is i + 1,... , Rea {λ _i } for 4n

Is a predetermined different complex number of zeros and an arbitrary σ

Select 0. then

There is a matrix L in the form of Equation 25 in which the eigenvalue of (A + BLC) represented by Eq.

0이 충분히 작게 선택하면 {H, L}이 수용가능하며,

를 갖는 원래의 비선형 시스템인 수학식 28은 적어도 부분영역에서 지수함수적 안정하다.Moreover if σ

If 0 is chosen small enough, {H, L} is acceptable,

Equation 28, which is the original non-linear system with a, is exponentially stable at least in the partial region.

To prove this, a random regular matrix H is selected and matrices A and B of Equations 30 and 31 are determined thereby. First, to show that {A, B} and {A, C} are controllable and observable, we obtain

이고,

여기서 dim(Φ)=4n, dim(Γ)=2n, dim(Υ)=3n이며, 이것은 dim(Φ)≤dim(Γ)+dim(Υ)-1=5n-1임을 의미한다.From here

ego,

Where dim (Φ) = 4n, dim (Γ) = 2n, dim (Υ) = 3n, which means that dim (Φ) ≦ dim (Γ) + dim (Υ) -1 = 5n-1.

0에 대하여 (A+BLC)는 후르비츠(Hurwitz)이고 또한 정규이다. 달리 말하면 수학식 35의 행렬은 가역이다.Next we prove that {H, L}, which means that Equation 27 has a unique solution, is acceptable. At least small enough ρ

For 0 (A + BLC) is Hurwitz and is also normal. In other words, the matrix of Equation 35 is invertible.

이다. 그리하여 수학식 35에서 마지막 3n행은 선형적으로 독립이다. 이 사실을 사용하고 H가 정규하다는 것을 이용하여 다음을 밝힐 수 있다.From here

to be. Thus, the last 3n rows in (35) are linearly independent. Using this fact and using the fact that H is normal, we can

가

를 갖는 수학식 28의 평형점이라는 것을 의미한다. 그러나 수학식 33이 Φ_d근처에서 수학식 28의 선형근사이며 1차근사에서 안정화 정리는 원래의 비선형 페루프시스템의 부분영역 점근적안정성을 보장한다. 또한 부분영역 지수함수적 안정성도 보장한다.Given that H is normal, the previous equation ensures that {H, L} is acceptable. The final conclusion is

end

It means that the equilibrium point of the equation (28) having a. However, Eq 33 is a linear approximation of Eq 28 near Φ _d and the stabilization theorem in the first approximation ensures partial region asymptotic stability of the original nonlinear Perup system. It also guarantees subregion exponential stability.

F is called the stabilization matrix, and considering the Liapunov determinant for an arbitrary symmetric finite matrix Q, there is only one symmetric finite matrix P that satisfies the following equation.

이며 여기서

는 E의 추정치를 나타낸다. 앞에서 행렬 L은

가 후르비츠이도록 선택할 수 있다.

이고

이라 정의하면

이다. P를 임의의 양의 유한행렬 Q에 대한 수학식 36의 해라하고 다음의 수학식 37을 정의한다.Considering Equation 30 and Equation 31

Where

Represents an estimate of E. The matrix L in front of

You can choose to be Fruitwitz.

ego

If you define

to be. Let P be the equation (36) for any positive finite matrix Q and define the following equation (37).

Along the trajectory of Equation 32 (simplified Φ _d ≡ 0)

Can be obtained.

ego

Therefore, the conclusion of Equation 39 can be obtained.

가 최대값이 된다.

를 감안하면 다음의 결론을 얻는다.Q = _4n for all {P, Q} satisfying Equation 36

Is the maximum value.

Given this, the following conclusions are drawn.

이고, 수학식 41를 만족하는 a

0과 충분히 작은 k

0이 존재한다.From here

And satisfies Equation 41

0 and small enough k

0 is present.

는 B_a에서인

의 추정치이고 다음의 수학식 42를 만족한다.here

Is in B _a sign

Is an estimate of and satisfies the following equation (42).

가

를 만족하면(a는 수학식 41에 의하여 주어진다.) 프로세서는

를 갖는 수학식 26에 의하여 표현되는 새로운 모드의 동작을 시작한다. 그리고 새로운 출력제어기(제2출력제어기)가 작동하여 로봇은 최종목표 위치에 지수함수적으로 수렴한다. 그리하여 이러한 서브동작은 두가지의 모드를 결합함으로써 이루어 질 수 있다. 그 과정의 첫 번째 단계는 종래의 제어와 동일하며 이에 관련하여 제1출력제어기(44)는 수학식 5에 의하여 주어진다. 과정의 두 번째 단계는 미세동작과 관련한 것으로 수학식 26에 의하여 주어지는 제2출력제어기(45)의 동작으로 이루어진다.If the initial condition belongs to B _a , the system converges exponentially to the final position. The final conclusion can be combined with conventional controllers. First, if the conventional controller is applied, the controller is given by Equation 5 and the state vector of the robot.

end

(A is given by Equation 41), the processor

Starts a new mode of operation represented by Equation 26 with And a new output controller (second output controller) is activated, the robot converges exponentially to the final target position. Thus this sub-operation can be achieved by combining the two modes. The first step of the process is the same as the conventional control and in this regard the first output controller 44 is given by equation (5). The second step of the process is related to the fine motion and consists of the operation of the second output controller 45 given by Eq.

0은 (r₁+1)/r₁

ρ을 만족하는 임의의 수인 ρ

1, r

max{r1,

, 2ρβ}의 상수를 선택하고 S, R이 수학적 16에 의하여 주어진다고 가정한다. B_a는 원하는 최종위치에 중심을 두고 수학식 42를 만족하는 충분히 작은 영역이라면 임의의 상수 벡터 v

Rⁿ은 다음의 제3체인을 기동시킨다.To sum it up, r ₁

0 is (r ₁ +1) / r ₁

ρ is any number satisfying ρ

1, r

max {r1,

, 2ρβ} and assume that S and R are given by B _a is any constant vector v if it is small enough to be centered at the desired final position and satisfy Eq.

R ⁿ activates the following third chain.

In real time control, the vision that modified the first chain must be realized in the third chain. This is because, first, asymptotic convergence is related to the infinite time process and second, the x ₂ (·) signal is not measurable. The revised version solves this problem.

In the case of the flexible joint robot, the same as in the previous case, the detailed proof is omitted and only the result is described.

As in the case of the rigid robot, when the robot's state vector enters the region sufficiently close to the desired operating point as a result of the coarse motion control, only the position measurement of the link and the rotor is used, and the exponential stability of the partial region of the system is guaranteed. Furthermore, it is possible to construct a linear output controller in which the eigenvalues of the linearized Perup system are assigned anywhere in the complex plane. With these results, consider what was previously disclosed for rigid robots. First, a real-time control processor based on convergent thought theorem can be realized, and the flexible joint robot is driven to an approximate area of the desired operating point, thereby enabling the processor to operate a new output controller. The robot converges exponentially at the final target point. Using Equation 2 and considering the following system

R^n×n는 추후결정될 상수행렬이고

는 시스템의 입력이며, 출력 사상은 다음과 같다.Where H

R ^{n × n} is the constant matrix to be determined later

Is the input of the system and the output mapping is

Considering the following output feedback

R^3n×4n은 추후결정될 상수행렬이고 L을 다음의 수학식 46로 분할한다.Where L

R ^{3n × 4n} is a constant matrix to be determined later, and L is divided by the following equation (46).

(43) becomes (47).

Consider the following linear equation

0이므로 모든 정규행렬 H에 대하여 수학식 48의 왼쪽에 행렬이 논싱귤러한 블록 l_ij를 선택할 수 있다. 요소의 동작(row operation)을 적용하여 수학식 48의 왼쪽에 있는 행렬이 서브행렬인 수학식 49가 논싱귤러하다면 가역이라는 것을 보여줄 수 있다.K

Since 0 is a non-singular block l _ij can be selected on the left side of Equation 48 for all regular matrices H. The row operation of the element may be applied to show that the matrix on the left side of Equation 48 is reversible if the sub-matrix Equation 49 is nonsingular.

로 주어진다. 여기에서

는 수학식 47의 평형점이다.As before, if H is regular and L chooses to reversible the square matrix on the left side of (48), {H, L} is an acceptable pair. For a properly given pair {H, L}, the only solution in equation 48 is

Is given by From here

Is the equilibrium point of equation (47).

에 의하여 수학식 44의 출력을 갖는 수학식 43의 시스템은 다음과 같이 쓸 수 있다.

The system of Equation 43 having the output of Equation 44 can be written as follows.

와

이라 정의하면 이 정의를 사용하여 수학식 49와 수학식 43으로부터 다음식을 얻을 수 있다.Suppose you know g (x _1d ) and K exactly

Wow

This equation can be used to obtain the following equations from equations (49) and (43).

이다.here

to be.

0인 미리 결정된 서로 다른 복소수이고 임의의 σ

0를 선택한다. 그러면 Λ={λ₁, λ₂, …, λ_7n}로 표현되는 (A+BLC)의 고유치가 다음의 수학식 54를 만족하는 수학식 46에서 행렬 L이 존재한다.From the above observation, we can summarize the following as in a rigid robot: That is, assuming that the elements of A and B are correctly known in Equations 51 and 52, a regular matrix H is arbitrarily selected. Λ = {λ ₁ , λ ₂ ,... , λ _7n } is i = 1 _,. , Real {λ _i } for 7n

Is a predetermined different complex number of zeros and an arbitrary σ

Select 0. Then Λ = {λ ₁ , λ ₂ ,... , matrix L exists in equation (46) where the eigenvalue of (A + BLC) expressed by λ _7n } satisfies the following expression (54).

0이 충분히 작게 선택하면 {H, L}이 수용가능하며,

를 갖는 원래의 비선형 시스템인 수학식 50은 적어도 부분영역에서 지수함수적으로 안정하게 된다.Moreover if σ

If 0 is chosen small enough, {H, L} is acceptable,

Equation 50, which is the original nonlinear system with, is exponentially stable at least in the partial region.

To prove this, {A, B} and {A, C} given by Equation 52 and Equation 53 by direct assumption are controllable and observable, respectively. Dim (Φ) = 7n, dim (Γ) = 3n, dim () = 5n and dim (Φ) ≦ dim (Γ) + dim (Υ) -1 = 8n-1. Next, the proof that {H, L} is acceptable and the nonlinear system is locally exponentially stable is the same as the proof in a rigid robot.

The linear output control device for position control of a robot according to the present invention can be configured as a control device operating in two modes by combining a control step of coarse motion using a repetitive control method and a new control step for control of fine motion. Rigid robot and flexible joint robot can be converged to the desired position. 5 is a graph showing the output of the robot operated in the two modes in this way.

Hereinafter, the configuration and operation of an embodiment of the linear output control method according to the present invention will be described in detail with reference to the accompanying drawings.

6 is a flowchart illustrating a linear output control method for position control of a robot according to the present invention. As shown here, an operating point and a fine motion reference, which are desired movement positions, are input (S1) and have undergone initial operation. It is set to (S2). It is checked whether the operation mode is fine (S3), and if the result of the check in S3 is not the fine operation mode, the initial control input is set according to the initial position (S4), and the coarse operation mode is controlled so that the robot operates on the set control input signal. Perform (S5). As a result of the control of S5, the robot is operated in the coarse mode and it is checked whether the robot's output is within the approximate area of the operating point determined by the fine motion reference signal input in the step S1 (S7). If the output of the robot has not yet entered the approximate area of the operating point as a result of the check in S7, it is checked in the coarse operation mode whether the output of the robot is stabilized and it is time to correct the control input (S9). If it is not time to modify the control input as a result of the check of S9, wait for the output of the robot to stabilize. If it is time to modify the control input as a result of the check in S9, a new control input is set (S10), and the process returns to the step S5 to repeat the coarse mode control. If the result of the check in S7 is that the robot output is within the approximate area of the operating point, the fine operation mode is set (S8) and the process returns to the step S3. If it is checked in S3 that the micro-operation mode is performed, the micro-movement control is performed to control the robot to approach the reference position exponentially from the current position (S6).

의 식에 의하여 이루어지며 따라서 초기 제어입력은

가 된다. S10의 단계의 제어입력수정도

의 식에 의하여 이루어진다. S5의 단계의 거친동작모드의 제어는 수학식 4로 모델링되는 강성 로봇의 경우 수학식 3의 제어기에 의하여 수행되며, 수학식 2로 모델링되는 유연관절 로봇의 경우 수학식 3의 제어기에 의하여 수행된다. S7의 단계는 동작점과 안정화된 현재로봇위치의 차이와 미세동작기준값을 비교함으로써 이루어진다. S6의 단계의 미세동작모드의 제어는 수학식 4모델링되는 강성 로봇의 경우 수학식 22-26으로 표현되는 제어기에 의하여 수행되며, 수학식 2로 모델링되는 유연관절 로봇의 경우 수학식 43-47으로 표현되는 제어기에 의하여 수행된다.In setting the initial control input in the step S4,

And the initial control input is

Becomes Number of control inputs in step S10

By the ritual The coarse motion control of the step S5 is performed by the controller of Equation 3 for the rigid robot modeled by Equation 4, and by the controller of Equation 3 for the flexible joint robot modeled by Equation 2. . The step S7 is performed by comparing the difference between the operating point and the stabilized current robot position and the micro motion reference value. The control of the micro-operation mode in step S6 is performed by the controller represented by Equation 22-26 in the case of the rigid robot modeled in Equation 4, and in the case of the flexible joint robot modeled by Equation 2 as Equation 43-47. It is performed by the controller represented.

In flexible joint robots containing unknown elements, the only information about these unknown elements is the possible size of their norms. Invented an analytical and practical control device for solving the set point tracking problem of the rigid robot and flexible joint robot. In the present invention, data obtained for the controller are assumed to be only the position of the link in the case of a rigid robot and the position of the rotor in the case of a flexible joint. The controller is basically easy to implement as a time-invariant linear system. First, we realize the real-time control process based on the convergence mapping, drive the robot to the desired approximation area, and the processor starts a new mode where the new output controller operates to exponentially converge to the desired position of the robot. The operation of the controller is based on the convergence mapping and the results, and the proposed controller for the rigid and flexible joint robot models ensures that the time response of the closed-loop system is equally ultimate. Also, the approximate region of the equilibrium point where the trajectory of the system converges can be arbitrarily reduced. In the case of a rigid robot, the convergence ratio by repetition can be arbitrarily fast. In the case of flexible joint robot, the convergence rate by repetition can be arbitrarily fast. In the case of a flexible joint robot, the convergence ratio of the system by repetition may be stored in an appropriate range by the user. However, it cannot be arbitrarily fast as in the case of a rigid robot. As shown above, under certain appropriate conditions the control strategy can be changed in useful ways. In particular, the entire system can be leveled from mode to mode in order to gradually converge to the desired operating point. Thus, in this respect, the first mode causes the coarse motion of the system, ie the controller to move the system from its initial position to a position close enough to the final position. In this process, iterative control is based on convergence mapping and the results. The function of the second motion is related to the micro motion, that is, the controller moves the robot smoothly to its final position. In this process, the controller depends on the stabilization theorem in the first approximation and the resulting system is controlled and observed. Satisfies the geometric conditions.

As described above, the present invention performs two-step control consisting of coarse motion and fine motion in order to move the robot to a desired position, thereby using the position information in the rigid or flexible joint robot system that requires high precision, for unknown parameters. There is an effect that the robot can move to the desired position in a short time.

Claims (2)

In the linear output control apparatus for position control of a robot for controlling a robot having a drive motor and an encoder for detecting the rotation angle as the drive motor rotates to output the current position signal of the robot to the input reference position, First output control means for receiving the current position signal and the control input signal and outputting a signal for controlling the motor of the robot to operate the robot according to the input control input signal; and the current position signal output from the robot is normal. A control input modification request means for outputting a control input modification timing signal for requesting to correct the current control input applied to the first output control means when the current position signal is determined to be in a normal state; Determine and output the initial control input of the first output control means according to the position, and receive the control input modification timing signal. Control input correction means for modifying and outputting the control input according to the current position signal and the reference position input when there is a control input modification request from the control input modification request means, and receiving the current position signal and the reference position signal; A second output control means for controlling the motor of the robot so that the robot exponentially approaches the reference position from the current position, the current position signal, the reference position signal, the control input modification timing signal, and a fine motion reference signal are inputted If the difference between the current position signal and the reference position input is greater than the fine motion reference, the robot is repeatedly controlled by the first output control means, and the difference between the current position signal and the reference position signal is the fine motion reference. And a switching means for switching the robot to be controlled by the second output control means if less than the signal. Constructed by linear output control device for position control of the robot, characterized in that. In the linear output control method for controlling the position of a robot for controlling a robot having a drive motor and an encoder for detecting the rotation angle as the drive motor rotates to output the current position signal of the robot to the input reference position, (1) inputting a reference position to which the robot is to be moved and a reference signal to which the robot is switched to fine motion, determining an initial control input of the robot according to the initial position of the robot, and (2) the current output from the robot Determining whether the position signal is in a normal state and outputting a control input correction timing signal requesting to modify and set the control input when it is in a normal state; and (3) to the control input modification timing signal in the step (2). Modifying and setting a control input based on the current position signal and the reference position input, and the current position signal between (4) and the step of (3) accordingly. Controlling the motor of the robot to operate the robot according to the modified control input signal with respect to the input of the modified control input signal; and (5) the current position signal, the reference position signal, and (3) Comparing the current position signal of the robot with the reference position input of the robot based on the control input modification timing signal of step (1) and the fine motion reference signal of step (1), (6) and (5) If the difference between the present position signal and the reference position input is greater than the micro-movement reference of the step (1), the steps (2) to (4) are repeated, and the present position signal and the reference point are repeated. And controlling the motor of the robot to exponentially approach the current position signal and the reference position signal from the current position to the reference position when the difference between the position signals is smaller than the fine motion reference. Position control method of controlling a linear power characterized in that said robot configuration.

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