KR20160040027A - Muti-degree of freedom(dof) system having parallel structure and method for deriving optimum solution thereof, parallel type manipulator using the same - Google Patents

Abstract

Provided are a multi-degree of freedom system having a parallel structure, and a method for deriving an optimum solution thereof. The multi-degree of freedom system having a parallel structure is designed to allow a manipulator to move based on two shafts to enable spare driving by removing a degree of freedom, which is mechanically unnecessary, from the manipulator having multi-degrees of freedom; thereby satisfying real-time control and rapid response by deriving an optimum solution to minimize a moving time for moving the manipulator to a target position. The method for deriving an optimum solution of the multi-degree of freedom system having a parallel structure comprises: a step of setting a target point of a parallel manipulator; a step of moving the parallel manipulator to the target point; a step of calculating a change in length of a multi-link of the parallel manipulator; and a step of calculating an optimum solution which the change in length of the multi-link is minimized.

Description

TECHNICAL FIELD [0001] The present invention relates to a parallel-type multi-degree-of-freedom (" DOF ") system,

Embodiments of the present invention relate to a parallel structured manipulator and a multi-degree-of-freedom system, an optimal solution derivation method thereof, and a parallel manipulator used therefor, which is a type of manipulator used in various fields such as automobile industry and aviation simulator.

In general, a parallel structured manipulator has the advantages of high rigidity and precision, so it carries out tasks such as automobile, airborne simulator, interceptor system, and medical surgical robot that need to keep horizontal in all moving means moving on uneven terrain or water surface And the like.

However, in recent years, research has been conducted to eliminate unnecessary degrees of freedom from six degrees of freedom in terms of development and cost. Three-degree-of-freedom parallel type manipulators have been studied in consideration of basic safety and operability. In particular, a structure has been developed in which the base and the platform are connected directly to the spherical joint-link-spherical joint.

In order to perform such a parallel structured manipulator on a desired task, an inverse kinematic solution for obtaining the length of the link at a target angle is required. Generally, it is known that it is rather easier to solve the parallel structure than the serial type.

However, even if the platform exists at the same position according to the characteristics of the work, the conventional kinematic solution method is not a method of deriving the optimal solution. In other words, the conventional inverse kinematics solution has been formulated as a mechanism that can not find the optimum solution required in a system requiring fast response because the link length is obtained using only the parameters corresponding to three degrees of freedom.

Korean Patent Laid-Open Publication No. 10-2001-0035973 (Three-degree-of-freedom system with two axes, disclosed on Jan. 1, 2003)

One embodiment of the present invention is a parallel structure that derives an optimal solution satisfying real-time control and quick response by designing the mechanism to move based on two axes that can be freely driven by eliminating kinematically unnecessary degrees of freedom in multiple degrees of freedom A multi-degree-of-freedom system and a manipulator, and a method of deriving an optimal solution using the system.

The problems to be solved by the present invention are not limited to the above-mentioned problems, and other matters not mentioned can be clearly understood by those skilled in the art from the following description.

A method of deriving an optimal solution in a parallel-structured multi-degree-of-freedom system according to an embodiment of the present invention includes: setting a target point to which a parallel manipulator moves; Moving the moving plate to a position of the target point using the multiple links of the parallel manipulator, and moving the moving plate about two axes; Calculating a variation in length of the multi-link of the parallel manipulator according to an angle change of the moving plate rotated so as to follow the target point in the three-dimensional orthogonal space in which the moving plate moved; And calculating an optimal solution that minimizes the amount of change in length of the multi-link.

In this case, the condition that the length change amount of the link becomes minimum in the method of deriving the optimal solution is to minimize the value of the maximum length change amount of the multilink so that the moving time of the parallel manipulator is minimized do.

The step of moving the moving plate of the parallel manipulator with respect to the two axes may include shifting the reference point of the moving plate to the position coordinates of the target to be moved based on the pan and tilt driving with reference to the Y axis and Z axis .

The step of calculating the change amount of the length of the multi-link may be calculated using the following Equation 1 based on the geometric approach.

[Equation 1]

는 i번째 링크의 길이 변화량,

는 i번째 링크의 길이임)(Where? Is the rotation angle of the moving plate,

The length variation of the i-th link,

Is the length of the ith link)

Meanwhile, a parallel-type multi-degree-of-freedom system according to an embodiment of the present invention includes a parallel-type manipulator in which a moving plate connected to a base plate and a multi-link is rotated in a three-dimensional orthogonal space with multiple degrees of freedom; And a parallel manipulator for setting a target point to which the parallel manipulator moves, and moving the moving plate of the parallel manipulator with respect to two axes so as to follow the set target point, and rotating the moving plate in a three- And a control device for calculating an optimal solution that minimizes a change in length of the multi-link by calculating a variation in length of the multi-link of the parallel manipulator in accordance with a change in angle caused by the change in angle.

According to another aspect of the present invention, there is provided a parallel manipulator including: a base plate; A moving plate disposed above the base plate; A multi-link connecting the base plate and the moving plate, the moving plate supporting the moving plate rotatably with respect to the base plate and being adjustable in length; And a center zone having both ends fixed to the center of the base plate and the moving plate and having a constant length.

The multi-link may include an expandable actuator; And a spherical joint provided at both ends of the actuator and coupled to the base plate and the moving plate, respectively.

The center zone may include a first support having one end fixed to the base plate; A second support having one end fixed to the moving plate; And a spherical joint connecting the other end of the first support and the other end of the second support, wherein the second support is rotatably connected to the first support.

The details of other embodiments are included in the detailed description and the accompanying drawings.

According to an embodiment of the present invention, when a method of deriving an optimal solution using the geometric algebra of the present invention is applied to a military defense system or various other applications, real-time control and quick response can be satisfied. As a result, Thereby providing an effect of improving the performance.

1 is a configuration diagram of a parallel-structured multi-degree-of-freedom system according to an embodiment of the present invention.
2 and 3 are a perspective view and a side view showing a structure of a parallel structure manipulator according to an embodiment of the present invention.
FIG. 4 is a flowchart illustrating a method for deriving an optimal solution satisfying fast responsiveness in a parallel-architecture multi-degree-of-freedom system according to an embodiment of the present invention.
FIG. 5 is a diagram illustrating parameters required in the optimization process for a parallel manipulator according to an exemplary embodiment of the present invention. Referring to FIG.
6 is a view for explaining a state in which a parallel manipulator is moved to a target point by two-axis driving according to an embodiment of the present invention.
7 and 8 are diagrams for explaining a method for deriving an optimal solution candidate according to an embodiment of the present invention.
9 is a diagram illustrating an optimal solution candidate point according to an embodiment of the present invention.

BRIEF DESCRIPTION OF THE DRAWINGS The advantages and / or features of the present invention, and how to accomplish them, will become apparent with reference to the embodiments described in detail below with reference to the accompanying drawings. It should be understood, however, that the invention is not limited to the disclosed embodiments, but is capable of many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, To fully disclose the scope of the invention to those skilled in the art, and the invention is only defined by the scope of the claims. Like reference numerals refer to like elements throughout the specification.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings.

1 is a configuration diagram of a parallel-structured multi-degree-of-freedom system according to an embodiment of the present invention.

According to the embodiment of the present invention, the parallel structure multi-degree of freedom system can be implemented by a robot manipulator 10 of a parallel structure and a control device 20 for controlling the operation thereof.

The robot manipulator 10 (hereinafter referred to as a manipulator) has a base plate and an upper moving plate connected by a multi-link to have degrees of freedom (DOF) in a three-dimensional rectangular coordinate system, Plate can be rotated.

The structure of such a manipulator 10 is shown in the accompanying drawings, but it is not limited thereto. The specific structure of the manipulator 10 will be described in detail with reference to FIG. 2 and FIG.

The control device 20 inputs the setting of the target point to which the manipulator 10 is moved and moves the moving plate of the manipulator 10 based on the two-axis degrees of freedom so as to follow the set target point. At this time, the angle for moving to the target point is infinite because of the kinematic allowance of the manipulator 10, and the controller 20 derives the optimal solution through a geometric approach to minimize the moving time to the target point .

2 and 3 are a perspective view and a side view showing a structure of a parallel structure manipulator according to an embodiment of the present invention.

2 and 3, a manipulator 10 according to an embodiment of the present invention includes a base frame 12, a moving frame 11 disposed above the base plate 12, A multi-link 13 connecting them, a base plate 12 fixed to the center of the moving plate 11, and a center belt 14 fixed to the center of the moving plate 11.

The multiple link 13 includes a prismatic actuator 13b and a spherical joint 13a provided at both ends of the actuator 13b and coupled to the base plate 12 and the moving plate 11, . The moving plate 11 supports the moving plate 11 so as to be rotatable with respect to the base plate 12 by the engagement of the spherical joint 13a and adjusts the length of the link 13 through the actuator 13b, Thereby making it possible to freely move the moving plate 11 in the space.

The multiple link 13 may be abbreviated as SPS in the structure of a spherical joint 13a, an actuator (prismatic actuator) 13b, and a spherical joint 13a.

The center zone 14 is composed of a first support 14a and a second support 14b and a spherical joint 14c connecting them. One end of the first support 14a is fixed to the base plate 12 and one end of the second support 14b is fixed to the moving plate 11. The spherical joint 14c is fixed to the first support 14a, And the other end of the second support frame 14b to make the second support frame 14b rotatable with respect to the first support frame 14a.

The center zone 14 has a constant length and restricts movement so that the moving plate 11, which can freely move on the orthogonal space, can only rotate. Also, And serves to disperse the load concentrated on the joint 14a.

At this time, the spherical joint 14a of the center zone 14 is applied as the origin in the geometric analysis described below.

Therefore, the manipulator 10 according to the above structure can be free-running even by two-axis driving by the Y-axis and Z-axis. Therefore, it is possible to implement a system that eliminates the unnecessary degrees of freedom, that is, the driving of the X-axis and satisfies the quick response by the two-axis driving.

Hereinafter, a process for deriving an optimal solution to satisfy a quick response will be described in detail based on the configuration of the multi-degree of freedom system and the manipulator 10 shown in Figs. 1 to 3.

4 is a flowchart for explaining a method of deriving an optimal solution in this regard.

First, in a first step S10, the control device 20 sets a target point at which the parallel manipulator 10 moves. At this time, the target point can be set by the user's operation through the input unit. The position to be moved can be designated by the touch input, or the position value can be set by numeric input. The target point can be represented as a vector value according to the position coordinates.

In step S20, the controller 20 removes the unnecessary degree of freedom and moves the moving plate to the target point on the basis of the two axes.

Thereafter, in step S30, the target is followed by rotating the moving plate with respect to the axis having the degree of freedom of freedom at the position moved by the control device 20. [

In step S20, the two axes are based on the pan-tilt driving based on the Y-axis and the Z-axis.

For example, as shown in FIG. 5, it is assumed that the position vector Pt = [xt, yt, zt] T of the output coordinate system from the base coordinate system to the origin B0 of the output coordinate system. Then, the kinematic constraint for the position vector Pt is as follows, since it is only possible to rotate by the center zone located at the center of the manipulator.

The attitude of the output coordinate system represented by ZYZ Euler angles is expressed logarithmically as Rotor Rt 'as follows.

At this time, in the embodiment of the present invention, a parallel structure having redundant driving as described above is proposed. Since the biaxial pan / tilt requires only the rotation to the yaw and pitch, define the angle ψ of the output coordinate system in the ZYZ Euler angle set (Euler angle set) as the free freedom. The total output vector u consists of only two of the six parameters in the Cartesian space.

Therefore, given the output vector u, the posture Rt of the output coordinate system can be expressed as a function of angle ψ as shown in the following equation. (See Fig. 6)

는 아래 수학식과 같이 등가 함수에 의해 표현된다. Due to the kinematic margin of freedom, the self-motion becomes possible according to the change of the angle ψ with respect to the axis ZB (Z 'axis in FIG. 6). Position from the base coordinate system to the i-th spherical joint of the moving plate

Is expressed by an equivalent function as shown in the following equation.

Therefore, the joint variable li is calculated as follows.

이 3차원이고, 작업 공간 상에서 출력벡터

가 2차원이므로 다음과 정의된다. The kinematic relational expression of the mechanism proposed in the present invention is a joint vector

Is three-dimensional, and the output vector

Is two-dimensional, it is defined as follows.

Robots with free degrees of freedom have the advantage of being able to perform various forms of motion, so that the inverse kinematics can be interpreted to meet the operator's desired working purpose.

Then, in step S40 of FIG. 4, the control device 20 calculates the amount of change of the length of the multiple link of the manipulator in accordance with the angle change of the angle? Caused by the rotation of the moving plate.

Then, in step S50, the controller 20 calculates an optimal solution that minimizes the amount of change in length of the multiple link. At this time, the condition that the length change of the multiple link becomes minimum includes minimizing the function represented by the maximum length change amount of the link. This is because when the link having the longest change is fast, that is, minimized, it is possible to minimize the movement time to the target point.

For example, in an embodiment of the present invention, the cost function can be defined as follows with respect to the amount of change in the length of the link in order to find a solution that minimizes the travel time of the travel plate.

는 이동판의 회전각도에 따른 비용함수,

는 i번째 링크의 길이 변화량,

이동판의 회전 각도에 따른 관절변수,

는 i번째 링크의 길이임)(Where? Is the rotation angle of the moving plate,

Is a cost function according to the rotation angle of the moving plate,

The length variation of the i-th link,

Joint variables according to the rotation angle of the moving plate,

Is the length of the ith link)

In this equation, the moving time of the moving plate can be reduced by minimizing the cost function represented by the maximum length variation of the link. For example, when the target posture (φ = 40 °, θ = 30 °) moves from the initial position of the moving plate (φ = 0 °, θ = 0 °), the maximum value of the displacement fcost of the proposed mechanism 0.1914 m, and the minimum value is 0.0997 m. This can reduce the travel distance of up to 10cm by eliminating the unnecessary degrees of freedom in the existing mechanism and allowing free freedom. Also, the proposed mechanism can move the actuator to the target point by moving the actuator at least 1 cm compared to the 2-axis pan / tilt structure, which means that the inverse kinematics solution can have more advantages than the existing system.

와 가장 가까운 이동플랫폼 상의 하나 이상의 점이 최적해일 가능성 높으므로, 이를 CGA(Conformal Geometric Algebra)를 이용하여 기하학적으로 찾는다.Current i-th link length

And one or more points on the nearest mobile platform are likely to be optimal, and are geometrically searched using CGA (Conformal Geometric Algebra).

는 하기 식과 같이 반경이 현재의 링크 길이

이고, 원점이 Ai인 구라 가정한다.As an example, referring to FIG. 7

Is the radius of the current link length

And the origin is Ai.

는 하기 식과 같이 세 점Bi가 속하는 원이라 가정한다. 원

은 이동 플랫폼 상의 점 Bi가 존재 가능한 점의 집합으로 볼 수 있다.

Is a circle to which the three points Bi belong, as shown in the following equation. won

Can be seen as a set of points on which points Bi on the mobile platform can exist.

과 가장 가까운 이동 플랫폼 상의 하나 이상의 점

은 하기 식과 같이 두 기하학적요소의 외적으로 인해 원

와 구

가 교차하여 생성된다.At this time, as shown in FIG. 7,

And one or more points on the nearest mobile platform

Is due to the externals of the two geometric elements

And

Are generated.

와 구

가 교차하지 않는 경우 가장 가까운 이동플랫폼 상의 하나 이상의 점 PPi는 원 과 평면

이 교차하여 생성된다.However, as shown in Fig. 8,

And

0.0 > PPi < / RTI > on the nearest mobile platform, And flat

.

는 기저좌표계의 원점, 원

의 중심

, 구

의 원점

가 속하는 평면으로, 아래의 식과 같이 정의할 수 있다.here

Is the origin of the base coordinate system,

The center of

, Sphere

The origin of

And can be defined as the following equation.

The parallel robots have no guarantee that the length variation of other links will be minimal even if one link length variation is minimized because the three multilinks depend on each other when the target position of the moving plate is given. Therefore, we calculate the other link length geometrically as shown in the following equation, and then select the most appropriate optimal solution.

는 Point pair로 두 점 간의 외적으로 정의된다. Point pair

는 다음과 같이 각각의 점

(j=1,2)으로 분해할 수 있다.One or more points where the length variation of the multiple links is minimized

Is a point pair defined externally between two points. Point pair

Is the value of each point

(j = 1, 2).

상의 한 점

외에 나머지 두 점

와

는 항상

와 구

가 교차하여 생성된다.Also, in the i-th link,

A point of consultation

The remaining two points

Wow

Always

And

Are generated.

If all the candidate point pairs are found for approximately 3 multiple links, all 6 candidate points can be generated as in the example shown in FIG.

를 원점이 점

이고 반경이

인 구라 가정하면 다음과 같은 수학식으로 정의할 수 있다.after,

The origin is point

And the radius

Assuming an in-plane, the following equation can be defined.

는 Point Pair

가 분해된 한 점이고,

는 점

와

간의 거리이다.Here,

Point Pair

Is a decomposition point,

Point

Wow

.

,

는 원

과 구

가 교차하는 두 점

이다.On the other hand, the position of another spherical joint on the moving plate

,

The circle

Section

Two points that intersect

to be.

는 각각 한 점

,

로 분리할 수 있다.Therefore,

Respectively,

,

. ≪ / RTI >

는 다음과 같이 산출된다.At this time, since all the position of the ball joint in the state where the moving plate is not driven is known,

Is calculated as follows.

After calculating all the length variations of the optimal solution candidates by the above method, the candidate with the smallest maximum length variation is selected as the optimal solution.

Meanwhile, the performance of the optimal solution obtained by using the geometric method proposed in the embodiment of the present invention is compared with the numerical solution.

The numerical solution is a combination of the golden partition search method and the quadratic interpolation method, which are often used in nonlinear optimization problems. The golden partition search method has high computational complexity but high reliability, and the second interpolation method has low reliability but low computational complexity. By combining these two methods, the advantages can be emphasized and the weak points can be offset, which is suitable for comparison.

In order to compare the performance between the proposed geometric approach and the numerical solution, we consider the computation time and the accuracy of the optimal solution.

Comparisons of computation times were confirmed through 1000 repeated measurements in the same computing environment. Table 1 below compares the computation time between the two solutions. The proposed geometric solution consumes significantly less computation time than the numerical solution, so that it has an effect of improving real - time control and response.

Numerical Method Geometric Method Average calculation time 2.6880 msec 0.6355 msec Relative time 4.23 1.00

While the invention has been shown and described with reference to certain preferred embodiments thereof, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention. Therefore, the scope of the present invention should not be limited to the described embodiments, but should be determined by the scope of the appended claims and equivalents thereof.

10: parallel type manipulator 11: moving plate
12: base plate 13: multiple links
13a: Old joint 13b: Actuator
14: center zone 14a: spherical joint

Claims (8)

Setting a target point to which the parallel manipulator moves;
Moving the moving plate to a position of the target point using the multiple links of the parallel manipulator, and moving the moving plate about two axes;
Calculating a variation in length of the multi-link of the parallel manipulator according to an angle change of the moving plate rotated so as to follow the target point in the three-dimensional orthogonal space in which the moving plate moved; And
Calculating an optimal solution that minimizes a change in length of the multi-link
A method for deriving an optimal solution in a parallel multi-degree-of-freedom system. The method according to claim 1,
The condition that the variation of the length of the multiple link becomes minimum is
Wherein a value of the maximum variation of the length of the multi-link is minimized so that the moving time of the parallel manipulator is minimized. The method according to claim 1,
Wherein the step of moving the moving plate of the parallel manipulator with respect to two axes comprises:
Wherein the reference point of the moving plate is moved to a position coordinate of a target point to be moved based on the pan-tilt driving based on the Y-axis and the Z-axis. The method according to claim 1,
The step of calculating the length change amount of the multi-
Wherein the computation is performed using Equation (1) based on a geometric approach.
[Equation 1]

(Where? Is the rotation angle of the moving plate,

Is a cost function according to the rotation angle of the moving plate,

The length variation of the i-th link,

Joint variables according to the rotation angle of the moving plate,

Is the length of the ith link) A parallel manipulator in which a moving plate connected by a base plate and a multiple link rotates in a three dimensional orthogonal space with multiple degrees of freedom; And
Wherein the parallel manipulator moves a moving plate of the parallel manipulator with respect to two axes so as to set a target point to which the parallel manipulator moves and follows the set target point, A control device for calculating an optimal variation in which the length variation of the multi-link is minimized by calculating a variation in length of the multi-
/ RTI > A multi-degree-of-freedom system. Base plate;
A moving plate disposed above the base plate;
A multi-link connecting the base plate and the moving plate, the moving plate supporting the moving plate rotatably with respect to the base plate and being adjustable in length; And
And both ends are fixed to the center of the base plate and the moving plate,
And a parallel type manipulator. The method according to claim 6,
The multi-
A stretchable actuator; And
And a spherical joint provided at both ends of the actuator and coupled to the base plate and the moving plate, respectively. The method according to claim 6,
The center-
A first support having one end fixedly installed on the base plate;
A second support having one end fixed to the moving plate; And
And a sphere joint connecting the other end of the first support and the other end of the second support, wherein the second support is rotatably connected to the first support.

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