JPS5930690A - Method of controlling multiple articulated type robot having redundancy - Google Patents

Abstract

(57) [Summary] This bulletin contains application data before electronic filing, so abstract data is not recorded.

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a method for controlling an articulated robot with redundancy.

There are two conventional methods of controlling this type of robot: one is to specify elements as many as the number of degrees of freedom and perform strict numerical analysis, and the other is to control by solving approximate equations based on measurement of current values. . That is, in general, a rigid body has six degrees of freedom. For example, since the articulated robot mechanism shown in FIG. 1 has six degrees of freedom and the hand H is a rigid body, it is necessary to specify six elements to determine its position and orientation. - For example, point P of the hand. (X.

Y, Z) coordinates, and the posture of the hand is expressed by three angles (1, m.

rL) can be expressed as ``3-''.

Therefore, we obtain the following relationship.

This is a matrix determined from the shape, and although it is very complicated, the unknowns (θ, θ1, . . . , θ6) can be solved from this equation.

This leads to the first method of the prior art, that is, the method of specifying as many elements as there are degrees of freedom.

That is, by specifying the above CX, Y, Z, l, rn, rL), the above equation is solved based on this.

(θ1.θ1....θ,) is determined, and this is used to control an articulated robot with six degrees of freedom. Although this is very complicated, it is accurate because it is an exact formula.

On the other hand, it is the $2 method and it is an approximate formula.

There is a much easier way than this. The above formula is written as follows.

Here, use the relational expression between total differential and partial differential, and here
θl = a, ' t...To summarize, in this equation, the left side is expressed as ΔX, the first term on the right side is expressed as [J], and the second term is expressed as Δ.

Δ input = [J) + 1 Δ It can be written as

By solving this equation Δω=(J)−’ ΔX That is, Be careful.

The element C) is wound by (θ1.θ,...θ,). This is the current value at that point, so it is only necessary to input it as a measurement value using a potentiometer, etc. If this element is considered as a constant, the above equation becomes 6 elements 1
Using simple calculations such as solving the following simultaneous equations, (ΔX,
If ΔY, ... ΔFL) is specified, (Δθ1.Δθ2
..., Δθ, ) can be controlled by determining 1,
This is the second prior art. Although this is much easier than the first prior art, it is an approximate equation.

These conventional techniques have the following common drawbacks. , FIGS. 3(1) to 3(5) show typical examples of changes in Φ with respect to time. First, the drawbacks of the prior art will be explained with reference to these. As mentioned earlier, if you have six degrees of freedom, you only have the minimum necessary degrees of freedom when performing a certain task.

Changes in each angle (θ1, θ2...θ6) are uniquely determined.

For this reason, it is good if the angle changes smoothly like θ1 shown in Figure 5 (1), but tl of θ in Figure 6 (2)
When the angle changes rapidly, as in the interval from to t,
A sudden load is applied only to the drive shaft of that shaft. For this reason,
It is conceivable that the tracking may be delayed or even stop (in some cases). Also, even if the change is not rapid, as in θ in Figure 3 (6), if the speed changes constantly and changes to positive or negative degrees, a large load will be placed on that axis as well. . Even if the load is small, the operating angle limit (allowable range is shown in the figure) as shown in 04 in Figure 3 (4).

It is also undesirable for safety to constantly move just within the range of .

The above runner-up points can also be pointed out from an energy perspective.

Figure 4 (α) shows the change in energy consumed by the drive unit of each axis over time. The part indicated by El is the energy consumption of the first axis, and these are added below. , the top curve shows the change in total energy over time.

At t, the total energy is at its peak, and at t, the total energy is not so great.

This is a point that shows Elka peak. In this way, from the standpoint of energy, t-o and t = ten in Figure 4 (α)
d and E, = o, and the area enclosed by the top curve indicates the energy consumed in °C. It is important to suppress such total energy consumption, and on the other hand, it is also important to reduce the time required for operation. However, the fact that the total energy becomes a cylinder like tl means that if a motor is used, a large current will suddenly flow there, and t,
In this case, a large current flows through the first axis, which is not good.

This large change in energy consumption at each moment is also a major drawback.

The present invention overcomes the above-mentioned drawbacks of the prior art.

It is possible to control a multi-degree-of-freedom articulated robot without forcing it into an unreasonable posture or taking large accelerations, and as a result, without overloading each axis or the entire body. The purpose is to provide a method.

The present invention achieves the above-mentioned object by using a relational expression for the Jacobian matrix described above and by increasing the degrees of freedom to more than six. That is, in the present invention, in addition to the six elements that regulate one position and orientation, an element that regulates redundancy is also specified. This element is called a redundant degree of freedom. This element (redundant degrees of freedom)′? If : is also specified, effective robot control can be achieved using the relational expression expressed by the Jacobian matrix described above. redundant degree of freedom p
is shown as below.

Here, q = 6 + P t P : Redundant degree of freedom q : Me Yurin By the way, in non-invention, as shown in Figure 4<b), at the same time as reducing the change in total energy, we can reduce the change in energy in each state. I also want to reduce I would also like to reduce the energy required to reach f'it 7Ld.

From these points of view, we have come up with a first-order Kotoriko firing point.

ff1J This is because the degree of redundancy is p in Chigami Niji's equation.

Free reaction (factor q = 6 + p.Therefore, there are q caps to be controlled.On the other hand, the number of elements that can be rounded as in the conventional method is 6.According to the conventional method, these 6
You can specify the temperature, position and posture of the hand using the purple key7).
However, since the redundancy is p in the other method, it is necessary to make one specification of some kind. Here, the following relational expression is used.

Lo-Σ (Epot + Ekin) E: Energy Epot: Potential energy E to Ln: Kinetic energy, or in a rotating system, EkL 0Σ7IθRI: yj Performance rate This is also known as the basic formula I2. Therefore, it is conceivable that one of this formula, i:i, and i/i, is considered to be one of the above-mentioned elements. , using the first British inertia Z) means that
Energy control 1' is closely related to the locus, so if you use the Jacobian instead of the Pubike, which suits the purpose of the present invention, you will benefit from the intermediate pressure θ and θ term of the Jacobian element.

This has the advantage of not requiring a velocity or acceleration detector, and for this reason, two types of inertia hL rates I can be effectively used as embodiments of the present invention.

Here, using FIG. 5, we will describe the method of making koji with a rate of inertia I. When the object is planar as shown in FIG. 5(α), the inertia factor I with respect to the axis AVc perpendicular to the plane and passing through the center of gravity of the object can be easily calculated.

This is called IG. Also, as shown in Fig. 5(b), the inertia factor I with respect to axis B, which is similar to Fig. 5(α) but is parallel to the above axis A and has a distance of r, is 1 = 16 + rnr'' (here m is the mass of the object, ).Next, in the case of a solid as shown in Fig. 5(c), under similar conditions, the same form of equation 1 = Ia + mr'' is obtained.

However, Ia and r are the functions already described here. In addition, as a method for selecting one type of I, it is necessary to select one with the greatest influence.

I around the first axis, that is, I I or tI around the second axis I of the P-th axis, that is, pl There are two types.

An embodiment of the present invention will be described below.

As an example of this method, when P-2 (redundant degree of freedom is 2) is used, the result is as shown in Figure 6. If we choose the inertia factor I as in the method explained above.

First, the first I (=, I) becomes as shown in FIG. 7, and the second I (=21) becomes as shown in FIG.

The details of which variables each Ia or r include are as follows.

11=IGII+rn1r2+10. , (θ, )
Ten meters! rI”! (θ, )−1−IG,, (
θ6. θ,) 10m, f,% (θ7.θ,)+IG
,, (θ7.θ8.θ4 * ”' +θ,) 10m, r
:, (θ,, θ3.θ7 + ”' +08) −11(
θ1. θ1. ..., θ,) 11 = lG22 -1- m, r:
.

+IQ, 8Cθm) + m, r! (4,)
10Ic,,Cθ3. θ4)+rn4? −2(θ,,θ4
)+IO,,C03,θl+”' *θs) +m8r
:, Cθl + G4 ”' tθ, )=, I(θ3.
θ4. ..., G8) To summarize the above, each term will be abbreviated and expressed as follows in the same way as described above.

Δ = [7) @Δω Here, if I is used as the element regulating redundancy as described above, each element of [J] is composed of only ω, and Φ and Φ are not included. About this.

This means that it is only necessary to detect the angle of each joint of the robot at the necessary time, and there is no need to detect angular velocity and angular acceleration. Therefore, control 1 by equation 1 ΔΦ = C/)-'・ΔX
- The power quantity ΔO is determined. for example.

Here Δ, I=0. Δ, specifying l=0 is 1.ノ and
It is possible to control I to be constant. In addition to this, it is possible to perform control in response to many requests within a certain range.

As mentioned above, with the conventional method of control using six degrees of freedom, when performing a certain movement, the robot may be forced to take an unreasonable posture, or some axes or the entire robot may be momentarily overloaded. However, according to this method, the overall movement becomes smoother, and it is possible to reduce excessive overload on a particular axis and the occurrence of unnatural postures.

Note that the above embodiment uses a relational expression expressed by a Jacobian row example and achieves control by subtraction similar to the conventional method. In addition, in this embodiment, since the inertia factor is used as the element regulating redundancy, there is an advantage that all that is required is the position of each joint of the robot, and there is no need to detect velocity or acceleration. Furthermore, in this example, the change in inertia rate selected as an element regulating redundancy,
By always setting zero to maintain the inertia factor, the drive w
This has the effect of avoiding sudden changes in load at one source.

However, although the Kinio side has a specific effect as described above, the present invention is of course not limited to this example.

[Brief explanation of drawings]

Figure 1 shows the base coordinates and joint angles of a conventional 6-degree articulated robot, f, Figure 2 shows the hand posture, and an example of the three parameters. It shows the disadvantages of technology divided into various elements, and the fifth [!
! I(11 to (5) represent the time changes of θ1 to θ4 and θ6, respectively)'f6 (Note that θ5 is not shown because it is unnecessary,
The contents have also been omitted. ] m4 diagram (a, + +1! 11 is a diagram showing the time change of energy, (α) is a conventional explanatory diagram, (hl is a corresponding good state 'f), Figure 5 is the inertia factor I This is a diagram showing the calculation method of fd1~+c
+ indicates each state of the object.7) Figure 6 is for explaining one embodiment of control according to the method of the present invention, and the redundancy is 2. Figure 7 shows the base coordinates and each joint angle in an articulated robot in the case of 8 degrees of freedom (that is, 8 degrees of freedom). This is an illustration. FIG. 8 illustrates various elements constituting I in the same manner as FIG. m7. p...The degree of freedom that regulates redundancy (redundant degree of freedom) I...
Inertia rate Jl...Hand agent Patent attorney Usui 1) Toshiyuki 1 Figure Hi Shu 2 Figure 3 Figure 4 Figure 4 (c,,) 1-1・-(5) θ6 te shoulder 6th P , Touno! '7ri! J + 1- (IGII 10m+l"'I+')+(
15,, + l') 12 f-J) 10, , ,,,
, (b, , (158f-J) 2nd Ii21

Claims (1)

[Claims] t. A control method for determining the amount of each joint angle to be used in a multi-joint robot with redundancy, which includes six elements that regulate position and posture, and further regulates redundancy. The feature is that the amount of each joint angle to be driven is determined by also specifying the element to be driven. A control method for an articulated robot with redundancy. Z The angle amount is determined by using a relational expression expressed by a Jacobian matrix to determine the amount of each joint angle,
A method for controlling an articulated robot having redundancy as set forth in claim 1. 6. A method for controlling an articulated robot with redundancy as claimed in claim 1 or 2, characterized in that the inertia rate is used as the element regulating redundancy. 4. It is characterized by a configuration that avoids sudden changes in the load applied to the drive source by keeping the inertia factor constant by setting the change proof of the inertia factor selected as an element regulating redundancy to zero at all times. do. A method for controlling an articulated robot having redundancy according to claim 6.