JPH0522921B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION (Field of the Invention) The present invention relates to a robot control method and device thereof, and particularly to a robot control method and device thereof with improvements in interpolation control.

(Description of Prior Art) When controlling a robot using a playback method or the like, only information on discrete teaching points is stored in the control device, so during playback operations, the positions of these teaching points are It becomes necessary to perform control by interpolating information such as

Examples of such interpolation methods include well-known linear interpolation and circular interpolation. Although these interpolation methods are characterized by relatively simple calculations, they are generally not suitable for trajectories other than those adapted to each interpolation method (for example, in direct interpolation, straight lines or curves with large curvature radii). The disadvantage is that it lacks smoothness.

On the other hand, the inventor of this invention has already proposed a technique in which a shape design algorithm given by Professor Mamoru Hosaka of the University of Tokyo and others is applied to interpolation control of a robot. This technique is described, for example, in Japanese Patent Application Laid-Open No. 56-52408, and Hosaka's algorithm itself is described in, for example, Information Processing, Vol. 17, No. 12, pp. 1120-1127 (1976). December). Therefore, this technique will be explained here within the scope necessary for the following explanation.

This interpolation method, which applies Hosaka's algorithm (hereinafter referred to as "Hosaka's interpolation"), divides one interpolated curve into as many subcurves as there are teaching points (these are called "curve segments"). It is based on the idea that a smoother interpolated curve can be created by treating adjacent curve segments as a set of curve segments and performing a specific averaging operation on adjacent curve segments. In this method, first, as shown in Fig. 1, among the position vectors R→ _i (i=1 to m) of teaching points, a straight line is drawn between adjacent position vectors R→ _i and R→ _i+1. Perform interpolation to create the first stage interpolation curve _C1 . This interpolation curve (broken line) C ₁
Among them, the curved line connecting R→ _i and R→ _i+1 is expressed as D→ _i,1 (u) by the parameter u (0≦u≦1). The subscript i in this symbol D→ _i,1 (u) indicates that it is the i-th curve segment (also called a connected element), and the subscript 1 indicates that it is a curve segment resulting from the first stage of interpolation. (The same applies hereafter). After defining the first stage interpolation curve in this way, the recurrence formula; D→ _i,1 (u)={∫ ^l _u dτ・ω(τ)・D→ _i,k-1 (τ)
＋∫ ^u _p dτ・
ω(τ)・D→ _i-1,k-1 (τ)}÷{∫ ^l _u dτ・ω(τ)
+
∫ ^u ₀・dτ・ω(τ)} (k=1, 2,...)...(1) is repeatedly used to find the nth stage curve segment D→ _i,o (u), and this D→ As a set of _i,1 (u), a desired interpolation curve C _o of the n-th stage is obtained. Here, ω(τ) is a weight function.

The meaning of equation (1) can be understood more clearly by looking at Figure 2. That is, first, the i-th connected element D belonging to the (k-1)th stage interpolation curve C _k-1 shown in FIG. 2 → _i,k-1 (u) and (i+1) connected elements Among D→ _i+1,k-1 (u), the point D→ _i,k-1 (u ₁ ), D corresponding to a specific u (for example, u ₁ )
→ _i
+1,k-1 (u ₁ ) and the boundary point R of these two connected elements
→
Extract the parts L _i and L _i+1 located between ^k-1 _i and k-1 i, respectively. Next, the positions of the respective points on these portions L _i and L _i+1 are weighted averaged using a weight function ω(τ). Then, the pseudo centroid point obtained in this way is set as one point D→ _i,k (u ₁ ) of the curve segment D→ _i,k (u) at the k-th stage. By performing such an operation for each value of the parameter u, the entire D→ _i,k (u) can be obtained.

FIG. 3 is a diagram showing by arrows which connection element each curve segment at each stage is obtained from. However, the symbol (i, n) indicates D→ _i,o (u),
The same is true for others. Among these, for example, arrow AR
From D→ _i,o-1 (u) and D→ _i+1,o-1 (u), D→ _i,o (u)
This shows that it is possible to obtain As you can see from this figure,
D→ _i,o (u) ultimately becomes R→ _i+j (j=0,1,...n
)
Also, since equation (1) is a linear recurrence equation, D→ _i , _o (u) becomes R→ _i+ as follows.
_j
It can be expressed as a linear combination of (j=0, 1,...n).

D→ _i,o (u)= _o 〓 ^j=0 R→ _i+j・f _j,o (u) …(2) D→ _i,0 (u)=R→ _i・f _p,p (u ), f _p,p (u)=1 ...(3) Here, the coefficient f _j,o (u) can be expressed as a polynomial of u by actually calculating equation (1). , details are omitted.

The important point in equation (2) is that each curve segment at the nth stage incorporates information from consecutive (n+1) teaching points R→ _i+j (j=0, 1, 2...n). This means that it is formed in an oval shape. Therefore, for example, when the interpolation curve _C3 obtained in the third stage is used as an interpolation curve in actual control, the interpolation is performed by incorporating position information of four consecutive teaching points.

Therefore, Hosaka's interpolation is an interpolation that takes into account the global geometric properties of the chain of teaching points, and a smoother interpolation curve can be obtained compared to linear interpolation or circular interpolation.

However, Hosaka's interpolation also has some drawbacks. One of them is that the resulting interpolated curve generally does not pass through the teaching point.
Therefore, in order to ensure that the interpolation curve to be obtained passes through all of the teaching points, the calculated teaching point (referred to as the "reference point") P → _i is defined by the following equation (4). .

R→= _o 〓 ^j=0 P→ _i+j・f _j,o (u) (i=1, 2,…) …(4) Then, the reference point P obtained by solving this simultaneous equation → Based on _i , we have to find the interpolation curve mentioned above. The necessity of such a procedure, ie, inverse transformation, increases the number of calculation steps.

Moreover, the parameters in Hosaka's interpolation are spatial parameters introduced for the purpose of displaying parameters for each curve, and their correspondence with actual time is not clear. Therefore, it becomes necessary to add a step of determining a functional form representing the correspondence between u and time for each curve segment.

Furthermore, if an n-th interpolation curve is used for a fairly large n in order to smooth the interpolation curve, it may be possible to avoid trajectories with sudden changes in geometric properties, such as a change from a circle to a straight line. If the robot has been taught, the memory of the trajectory in the time period before that point remains, so the command value for the position to the robot will no longer be able to follow this change. Regarding this problem, for example,
As described in No. 57-125406, there is also a method of disabling the means for Hosaka interpolation at positions where the geometric variation of the trajectory is large. However, if we can obtain an interpolation method that can follow such changes to some extent and ensure sufficient smoothness, we will not need to use this kind of invalidation frequently, and depending on the situation, , it would not require invalidation.

(Objective of the Invention) The object of the present invention is to be able to perform interpolation control that incorporates the global characteristics of a trajectory, although it is relatively simple, and to perform various interpolation controls that are the basis of conventional control devices. The object of the present invention is to provide a robot control method and device that have the advantages of the conventional robot control method.

(Structure of the Invention) A robot control method of the present invention is a robot control method for causing a working point of a robot having a drive mechanism to move through predetermined discrete passing points in a predetermined order, the method comprising: A position interpolation function with a time parameter as a variable and four or more undetermined coefficients is defined, and four consecutive passing points in the above order are defined as Xi-1, Xi, Xi+1,
When Xi + 2, the value of the position undetermined coefficient is determined so as to satisfy both conditions (a) and (b) below, and the passing point is determined by the position interpolation function specified thereby. Determine the interpolation trajectory in the section between Xi and Xi+1.

(a) The magnitude of each velocity vector at the passing point Xi, Xi+1 is
The value shall correspond to each of the speed values prepared for each of the above-mentioned speeds.

(b) The direction of the velocity vector at the passing point Xi is a direction that depends on at least the relative positional relationship of the passing points Xi−1, Xi, and Xi+1, and
The direction of the velocity vector at the passing point Xi+1 is a direction that depends at least on the relative positional relationship of the passing points Xi, Xi+1, and Xi+2.

Furthermore, the robot control device of the present invention includes means for implementing the above method.

However, the term "work point" used in this specification refers to the position where the robot actually performs the work, such as the tip of the robot's tool, the tip of the end effector, or even the focal point of the laser in the case of a laser melting robot. Use as something. Also,
The term "passing point" includes starting points and stopping points.

(Embodiments of the Invention) (1) Overall Configuration and Operation of the Embodiment FIG. 4 is an overall diagram illustrating a robot control device which is an embodiment of the present invention and a robot controlled using this control device. It is a diagram. Although the robot RB shown in FIG. 4 is a rectangular coordinate type laser welding robot, the robot control device of the present invention can also be used for other types of robots, such as various coordinate type and articulated welding robots and assembly robots. It should be pointed out in advance that it can also be used to control such things.

In FIG. 1, this robot RB has a base 1, and this base 1 has a workbench 2 extending in the horizontal direction, that is, the X direction in the figure, and a It is provided with a support stand 3 extending at right angles to the support base 3. A moving table 4 that is movable in the X direction is placed on the work table 2, and this moving table 4 is driven by a motor _M1 (not shown) to perform reciprocating motion in the X direction. Do the following. Two columns 5 are erected approximately parallel to each other on the support base 3.
A beam 6 extending in the Y direction in the figure is installed between the tops of these columns 5. This beam 6
A moving column 7 extending in the vertical direction, that is, the Z direction in the figure, is attached so as to be movable in the Y direction. The motor _M2 is a power source for reciprocating the moving column 7 in the Y direction. The moving column 7 has a motor _M4 attached to its lower end.
A motor _M3 is provided to move the motor up and down in the Z direction. At the bottom of the motor _M4 , an arm 8 extending in the Z direction is attached at a position offset from _the rotation axis of the motor _M4 . Rotate in the direction. Furthermore, a motor _M5 to which a laser torch T is attached is provided on the lower side of the arm 8.
By rotating this motor _M5 , the laser torch T turns in the ψ direction in the figure. Encoders E ₁ to _{E 5 (not shown) are attached to these motors M 1 to M 5 , respectively} , for encoding the rotation angle of each motor.

The laser oscillation device 9 can oscillate a laser beam having enough power for the welding operation, and can provide this laser beam to the laser torch T through the laser guide pipe 10. Control device 1
Reference numeral 1 denotes a robot control device for controlling the robot RB and the laser oscillation device 9, and is an embodiment of the present invention.

FIG. 5 is a block diagram of the control circuit 20 included in the control device 11 described above. This control circuit 20 includes, for example, a microcomputer 21 as a main control circuit. The microcomputer 21 includes a CPU 211, a memory 212, and an I/O port 214 that are connected to each other via a bus 213. The control circuit 20 also includes an interpolation circuit 22 connected to the inside of the microcomputer 21 via an I/O port 214. This interpolation circuit 22 is a circuit for performing interpolation calculations between teaching points, as will be explained in detail later. This interpolation circuit 22
As shown in this figure, the interpolation circuit 22 may be provided as a dedicated circuit, or the interpolation circuit 22 may be omitted by having the microcomputer 21 perform interpolation calculations based on a program. It is.

The I/O port 214 also includes the aforementioned motor.
Servo systems S〓 1 _to S〓 ₅ including M ₁ to M ₅ and encoders E ₁ to _{E 5} , respectively, a teaching box 23,
A teaching switch SW and a laser oscillation device 9 are connected. teaching box 23
The apparatus is equipped with a mode changeover switch for switching between teaching, test, and playback modes, and an input switch for inputting various control conditions (not shown). Also, by pressing the teaching switch SW, the information from the encoders E ₁ to _{E 5} is sent to the microcomputer 21 as teaching information.
be taken into the.

In order to cause the robot RB shown in FIG. 4 to perform a regeneration operation, first, a workpiece (not shown) is fixed on the movable member 4. Thereafter, by operating the teaching box 23, the reproduction mode is set. Then, the CPU 211 sequentially reads the teaching information stored in the memory 212 and provides this information to the interpolation circuit 22 via the bus 213 and I/O port 214. This interpolation circuit 22 has a configuration and operation that will be explained in detail later, and outputs interpolation command values obtained by performing interpolation calculations on input teaching information to motors M ₁ to _{M 6} . do. Motors M ₁ to M ₆ are
The laser torch T rotates based on this interpolation command value, thereby causing the tip of the laser torch T to draw a predetermined trajectory while changing its relative position and relative speed with respect to the workpiece. At the same time, the CPU 211 provides an output control signal to the laser oscillation device 9. Based on this output control signal, the laser oscillation device 9 fixes its laser output to a predetermined output value or changes it as necessary. Through such an operation, the workpiece is irradiated with the laser from the laser torch T, and the workpiece is melted along a desired trajectory.

(2) Principle of interpolation control Here, the principle of interpolation executed in the control circuit 20 described above will be explained using a specific example. For example, in the case of a playback type robot control device, the position information of the teaching point as a discrete passing point, for example, the position vector x→ _i (i=1, 2,..., m: m is (integer) and the magnitude of the passing speed u _i when the work point passes the teaching point. Therefore, the interpolation function for the position interpolating between the chains of x→ _i (1, 2,..., m) is written as x→(t) as a function of time t, and x→
As an example of (t), consider the following interpolation function that holds for each interpolation interval.

x→(t)=u→ _i (T _i −t) ² t/T _i ² +(X→ _i +1−X
→ _i ) (3Ti−2t)・t ² /T _i ³ +u→ _i+1 (t−T _i )・t ² /T _i ² +
X→ _i (i=1,2,...m) ...(5) However, in equation (5), u→ _i has a size u _i as shown in FIG. 6, and the vector x ^{i- 1} x――――→ _i
It is a vector defined as having a _direction intermediate between the _directions of That is, u/→ _i /u _i = (X/→ _i −X/→ _i-1 /‖X/→ _i −X/
→ _i-1 ‖＋X／→ _i+1 −X／→ _i ／‖X／→ _i+1 −X／→ _i
‖)／‖X／→ _i −X／→ _i-1 ／‖X／→ _i −X／→ _i-1 ‖
＋X／→ _i+1 −X／→ _i ／‖X／→ _i+1 −X／→ _i ‖‖…(6
) u/→ _i+1 /u _i+1 = (X/→ _i+1 −X/→ _i /‖X/→ _i+1
−X／→ _i ‖+X／→ _i+2 −X／→ _i+1 ／‖X／→ _i+2 −X
／→ _i+1 ‖)／‖X／→ _i+1 −X／→ _i ／‖X／→ _i+1 −X
／→ _i ‖＋X／→ _i+2 −X／→ _i+1 ／‖X／→ _i+2 −X／→
_i+1 ‖‖…(7). Here, the symbol ‖ ‖ indicates the norm of the vector.

However, at i=1, that is, at the starting point,
Although X→ _i-1 is not defined, X→ _i-1 in this case can be set as an appropriate value. For example, it can be set as X→ _i-1 =X→ _i −(X→ _i+1 −X→ _i )…(8). This equation (8) _is
1 is located on the opposite side of X→ _i+1 with respect to X→ _i . Also, T _i is the working point from x→ to x→ _i+
1 , and is given by T _i =‖x _i+1 −x _i ‖/(u _i +u _i+1 /2) (9). Furthermore, the time t in equation (5) is
The time when the work point passes x→ _i is measured as t=0, so x→ _i (i=1, 2,..., m)
This is the time that is reset to 0 each time the signal passes through each of the points. However, the time throughout the entire trajectory
If you want to express it as t _a , you can replace it with t→t _a − _i-1 〓 ^j=1 T _i …(10).

It can be easily confirmed that x→(t) in equation (5) satisfies the conditions underlying this invention. In fact, in equation (5), if t=0, T _i , x→(0)=x→ _i …(11) x→(T _i )=x→ _i +(x→ _i+1 −x→ _i )=x→ _i+1 ...
(12) becomes. Also, if we set d/dtx→(t)=v→(t), (5)
From the formula, v→(t)=u→ _i (T _i -t) ² /T _i ² +w→ _i (T _i -t)・t/T _i ² +u→ _i+1 t ² /T _i ² ... (13) becomes. However, w→ _i =6/T _i (x→ _i+1 −x→ _i ) −2(u→ _i +u→ _i+1 ) (14). Therefore, if t=0 and T _i , the following equation is obtained.

v→(0)=u→ _i …(15) v→(T _i )=u→ _i+1 …(16) As can be seen from equation (6), u→ _i and u→ _i+1 are x→ _i-1 ~
x → _i+
Since the quantity is determined by the relative relationship of ₂ , the interpolation function given by equation (5) is an example of an interpolation function that satisfies the basic conditions of this invention.

Here, the properties of the interpolation function in equation (5) will be explained in more detail. First, the interpolation function in equation (5) is a cubic equation with respect to time t, so if we rearrange it with respect to t, we get
This means that four coefficients are included. Therefore, if we look at equation (5) from another perspective, 3 for t
The four coefficients included in the following polynomial are used to pass the teaching at both ends of the interpolation interval, and to make the direction of velocity at the teaching points at both ends depend on the relative relationship between the positions of the teaching points. It can also be considered that it is specified based on two conditions.

In this example, the direction of the velocity v→(t) is the vector x _i-1 x――――→ _i at the teaching point x→ _i
Note that the direction is intermediate between the directions of and the vector x _i x ---→ _i+1 . By imposing such conditions, the teaching points x→ _i and x→ _i+
The interpolation function between ₁ and 1 incorporates the positional information of two teaching points x→ _i-1 and x→ _i+2 adjacent to each other outside this section. In other words, the global accuracy of the trajectory along which the work point should move is reflected by a relatively simple function such as equation (5).

Also, since such a condition exists, i=
The overall interpolation function obtained by connecting the interpolation functions of equation (5) obtained for each of 1, 2, 3, ..., m is a smooth function in terms of position and velocity at each teaching point. It is becoming. The fact that the position is a cubic function with respect to time t means that the differential coefficient of x→(t) with respect to t four times or more is always 0→, and continuity exists in these as well.

Furthermore, as can be seen from the general properties of polynomials, the interpolation function of equation (5) can accurately represent both straight and curved sections. Therefore, x→ _i ~x→ _i+3 is smooth in the sense of position and velocity.
If it exists on a straight line, an interpolation function that is very close to linear interpolation is obtained. Furthermore, if x→ _i to x→ _i+3 exist on one circle, an interpolation function extremely close to circular interpolation can be obtained.

The example of the interpolated trajectory obtained in this way is shown in the 13th example.
As shown in the figure. This trajectory F is created using multiple interpolation functions “…, F _i-1 ,
F _i , F _i+1 ,...'' form a smooth chain.

By the way, in the interpolation function of equation (5), u _i =0
The problem is the behavior at the teaching point, that is, the starting point and stopping point. Therefore, by differentiating equation (5) with respect to time t and finding the acceleration α→(t), α→(t)=(-2u→ _i +w→ _i ) +2(u→ _i −w→ _i +u→ _{i +1} ) t/T _i ...(17).

In this equation (17), if t=0 and u _i =0, α→(0)=w→ _i | _ui=0 =6/T(x→ _i+1 −x→ _i )−2u→ _{i+ 1} …(18) becomes. In other words, the direction of acceleration α→(t) is defined even at t = 0, u _i = 0, that is, the starting point, and the interpolation function of equation (5) can also be used for the trajectory including the starting point. It shows. Similarly, at the stop point, the movement up to the stop is completely defined.

In the above explanation, the principle of interpolation used in the present invention has been explained using equation (5) as an example, but it is of course possible to use a function form other than equation (5) as the basis. For example, as x→(t), the conditions necessary for this invention can also be satisfied by a polynomial of degree 4 or higher with respect to t, or by a function of time t that includes at least four coefficients other than a polynomial. can be done. By using a polynomial of degree 4 or higher, it is possible to create an interpolation function that smoothly connects acceleration. In addition, not only the teaching points x→ _i -1 and x→ _{i+2 adjacent} to the interpolation interval x→ i ~ x→ _i+1 of interest, but also
It would also be possible to import information from distant teaching points.

In this way, the interpolation function that meets the conditions of the present invention has advantages comparable to Hosaka's interpolation described above in terms of global characteristics and smoothness. On the other hand, in Hosaka's interpolation, interpolation control can be performed using a simple function form that is not much different from linear interpolation or circular interpolation, without requiring complicated procedures such as determining time correspondences or inverse conversion. That's why it happens. In this sense, an interpolation method that satisfies the conditions of the present invention has the advantages of these conventional interpolation methods.

(3) Implementation of interpolation control Next, implementation of the interpolation control used in the present invention will be described, taking as an example the case where the above-mentioned equation (5) is the basis of interpolation control. In this interpolation control, for example _, inside the control circuit ₂₀ shown in FIG. It is sufficient to output the command values to each motor _M1 to _M5 of the robot. Although this method is of course useful, a method for performing interpolation calculations at higher speed will be introduced below, and control according to the method will be explained. Therefore, first, we rearrange equations (5), (13), and (17) to obtain the following (19) ~
We will reproduce it as equation (21).

x→(t)≡x→=x→ _i +u→ _i・T _i (1−t/T _i ) ²・
(t/T _i )+ (x→ _i+1 −x→ _i )・(3-2t/T _i )・(t/T _i ) ²
+u→ _{i+ 1}・T _i・(t/T _i −1)・(t/T _i ) ² …(19) v→(t)≡v→=dx/→/dt=u→ _i +(−2u → _i
+w→ _i )・(t/T _i ) +(u→ _i −w→ _i +u→ _i+1 )・(t/T _i ) ² …(20) α→(t)≡α→=dv/→ /dt=(-2u→ _i +w→ _i
)・1/T _i +2(u→ _i −w→ _i +u→ _i+1 )・t/T _i ² …(21) Furthermore, the differential β→(t) of acceleration with respect to time t is β→(t )≡β→=dα/→/dt =2(u→ _i −w→ _i +u→ _i+1 )・1/T _i ² (22).

In other words, x→ in equation (19) can be obtained by integrating differential equations (20) to (22) under the following initial conditions.

α→ _ioi =1/T _i (−2u→ _i +w→ _i ) …(23) v→ _ioi =u→ _i …(24) x→ _ioi =x→ _i …(25) By the way, differential equation (20) If ~(22) is solved as is, it will be nothing but calculation of equation (19), which will require many multiplications. Therefore, here, we will attempt to reduce the calculation steps by approximating equations (19) to (22) to be solved by addition. That is, a minute time Δt is introduced and the above differential equation is approximated by the following equation.

x→ _oew =x→ _pld +v→ _pld・Δt …(26) v→ _oew =v→ _pld +α→ _pld・Δt …(27) α→ _oew =α→ _pld +β→ _pld・Δt …(28) β→ _oew =β→ _pld =2(u→ _i −w→ _i +u→ _i+1 )・
1/T _i ² ...(29) In these, the subscript "old" indicates the previous time t
Indicate each value obtained for "new"
indicates each value at time (t+Δt). By performing such transformation, Δt
For example, if we take 2 ^-10 sec,
If the above equations (26) to (28) are added every 2 ^-10 seconds, a new interpolated value can be approximately obtained. In particular, as in this example, Δt=2 ^-N
(N is an integer), the calculation of the second term on the right side of each of equations (26) to (28) can be done by simply shifting v→ _pld , etc. by N bits to the lower side. Differential equations can be solved using only shift operations and addition without the need for . In this way, by solving differential equations using only shift operations and additions, the operation time is shortened, and it becomes easy to have dedicated hardware perform this operation. The repetition of addition in equations (26) to (28) is
The process is repeated [T _i /Δt] times (the symbol [ ] indicates a Gaussian symbol related to integerization), and then the information of the next teaching point is taken in and a new repetition of addition is started. Therefore, the cumulative error is less than 1 decimal in the above example, and the error caused by this approximation does not pose a problem in practice.

(4) Configuration and operation of the interpolation circuit 22 The calculation based on the specific example of the interpolation method described above is
This is performed in the interpolation circuit 22 in the figure. The details of this interpolation circuit 22 are shown as a block diagram in FIG.

This interpolation circuit 22 connects the CPU 211 and the memory 21 via an I/O port 214 and a bus 213.
2, buffers 101 to 104 are provided. Among these, the output of the buffer 101 that buffers the value of the time differential β→ of acceleration is input to the adder 105 that performs addition regarding the acceleration α→. It is given to the buffer 106 which buffers. The output of this buffer 106 is branched into two parts, one of which is given as the other input to the adder 105 mentioned above, and the other one is given to an adder 107 that performs addition regarding the velocity v→. . The output of the adder 107 is given to a buffer 108 that buffers the value of velocity v→, and the output of this buffer 108 is combined with the other input of the adder 107,
It is given as one input of an adder 109 that performs addition for the position x→. The output of this buffer 108 is also connected to the I/O via line 111.
It is also provided to O port 214. Adder 10
The output of 9 is provided to a buffer 110 which buffers the value of position x→. This batshua 110
The output of is branched into two, one of which is provided as the other input of adder 109 and the other is provided to I/O port 214 via line 112.

The above-mentioned adders 105, 107, and 109 respectively shift the inputs obtained as the outputs of the previous stage buffers 101, 106, and 108 to the lower order side by 10 bits among their two inputs, and use the remaining inputs. In other words, the rear buffer 106,
It is configured to add the respective outputs of 108 and 110. Therefore, if the input from the buffer in the previous stage is Q ₁ and the remaining input from the buffer in the latter stage is Q ₂ , then the addition output Q obtained by these adders is Q = Q ₂ + Q ₁ × 2 ^-10 …(30).

The buffers 102 to 104 are acceleration,
It is for initializing speed and position, and its output is a buffer of 10
6, 108 and 110. The clock generation circuit 113 includes buffers 106 and 10.
8 and 110, and receives the clock buffer 114 connected to the I/O port 214, the output of this clock buffer 114, and the output of the timer 116, and outputs the clock signal φ. A counter 115 is provided.

In this interpolation circuit 22, the above-mentioned (26) to
The interpolation calculation based on equation (29) is performed as follows. First, teach box 23 (5th
When the playback mode is entered by operating the (Fig. The initial value β→ _ioi , α→ _ioi ,
v→ _ioi and x→ _ioi (see equations (22) to (25)) are calculated and provided to buffers 101 to 104, respectively. However, since β→ is a constant within one interpolation interval, β→ _ioi =β→=2 (u→ _i −w→ _i +u→ _i+1 )・1/T _i ² …(31 ). Also, in parallel with this, the minute time width Δt
=2 ^-10 sec is provided from memory 212 to clock buffer 114. Further, among the above-mentioned initial values, α→ _ioi , v→ _ioi , and x→ _ioi are transferred to buffers 106, 108, and 110, respectively, and this interpolation circuit 22 is initialized. on the other hand,
The value of Δt is provided to counter 115. Counter 115 receives and counts the timer output from timer 116, and each time the count value exceeds Δt, it outputs a carry signal as clock signal φ.

In the first clock cycle, the buffer 1
Initial value α of acceleration that was buffered to 06 → _ioi
is output to adder 105. This adder 1
05 shifts the initial value β→ _ioi from the buffer 101 by 10 bits to the lower order side and adds it to this α→ _ioi . The output α→ _ioi of the buffer 106 is also given to the adder 107, and the adder 107 shifts this α→ _ioi by 10 bits to the lower side and adds it to the output of the buffer 108, v→ _ioi . .
v → _ioi , which is the output of the buffer 108, is the output of the adder 10
9, and the adder 109 shifts this v→ _ioi to the lower side by 10 bits and adds it to the buffer 11.
Add x → _ioi which is the output of 0. In parallel with these operations, the respective outputs v→ _ioi and x→ _ioi of the buffers 108 and 110 are outputted to the I/O port 214 as a speed command value and a position command value, respectively. Following this, adder 105,
The respective addition outputs of 107 and 109 are given to the next stage buffers 106, 108 and 110, respectively, and the contents of these buffers are updated.

Similarly, in each subsequent cycle of clock φ, adders 105, 107, 109
Respectively, front stage buffers 101, 106, 10
By adding the output of 8 shifted to the lower side and the output of the subsequent buffers 106, 108, 110, the output of the subsequent buffers 106, 108, 11 is added.
Store it in. And Batsuhua 108,110
The respective contents stored in are output as a speed command value and a position command value.

Therefore, if we focus on one clock cycle, the buffers 101, 106, 108, 11
The contents stored in 0 are respectively β→ _pld (=β→
_ioi ), α→ _pld , v→ _pld , and as the addition result,
If the contents to be newly stored in 06, 108, and 110 at the subsequent stages of adders 105, 107, and 109 are expressed as α→ _oew , V→ _oew , and x→ _oew , the following equation holds true.

x→ _oew =x→ _pld +v→ _pld・2 ^-10 …(32) v→ _oew =v→ _pld +α→ _pld・2 ^-10 …(33) α→ _oew =α→ _pld +β→ _pld・2 ^-10 ...(34) β→ _pld =β→ _ioi ...(35) Considering that Δt=2 ^-10 , these equations are none other than the above-mentioned equations (26) to (29). Therefore, the interpolated speed command value and position command value are updated every cycle of the clock φ.

When one interpolation interval is repeated [T _i /Δt] times, the interpolation circuit 22 is reset and then starts interpolation calculation based on a new initial value. This operation is repeated until a reproduction end command is issued, and desired interpolation control is performed.

(5) Modification of control circuit 20 () By the way, in the above-mentioned embodiment, the interpolation calculation is as follows.
This is carried out in the interpolation circuit 22, which is dedicated hardware, and thereby enables a high-speed interpolation calculation circuit. However, this interpolation calculation is also configured to be performed within the CPU 211,
It is also possible to omit the interpolation circuit 22.

Therefore, below, the operation when the CPU 211 performs interpolation calculation will be explained with reference to the flowchart shown in FIG.

First, when the teaching box 23 is operated to set the playback mode, the CPU 211 is transferred to the memory 212.
The integer N is read from (step S1). Next, the number i of the interpolation section is set to 1 ((step S2)), and the teaching information x→ _i-1 ~ x→ _i+2 , u _i , u _i+1 is stored in the memory 21.
Read from step 2 (step S3). Next, u→ _i , u→ _i+1 ,
T _i , [T _i /2 ^-N ], β→ _ioi , α→ _ioi , v→ _ioi and x
→ _ioi is calculated using equations (6), (7), (9), (23) to (25), and (31) (step S4). Set the interpolation repetition count number j to 1 (step S5), define the quantities x→ _pld , v→ _{pld, etc. using the initial values of x→ ioi, v→ ioi , etc.} , and set x→ _pld , respectively. Output as position command value and speed command value (step S6).

Set the internal timer (not shown) of the CPU 211 to t=
It is set to 0 (step S7) and the time t is read in step S8. In the next step S9, if this time t is smaller than j×Δt, the process returns to step S8, but if it is larger than j×Δt, (26) to
Calculate x→ _oew , v→ _oew , etc. using equation (29) (step S10). To multiply Δt by v→ _pld , etc., shift v→ _i+1 , etc. by N bits to the lower side. can be calculated. Thereafter, v→ _oew and x→ _oew are output as a speed command value and a position command value (step S11). It is determined whether j is larger than [T _i /2 ^-N ] (step S12), and J<
In the case of [T _i /2 ^-N ], x→ _pld , v→ _pld, etc. are newly defined by x→ _oew , v→ _oew, etc. (step S13).
Thereafter, the process returns to step S7 with j=j+1.
If J≧[T _i /2 ^-N ], it is determined whether i is the final interpolation interval, that is, whether the interpolation operation has been performed until the final teaching point is reached (step
S14), if i is not the final value, i=i+1
Then, the process returns to step S3. When i reaches the final value, the interpolation operation ends.

(6) Modifications of Control Circuit 20 (2) Incidentally, such interpolation control based on equation (5) can be performed alone, but it can also be combined with other interpolation methods. As such an example, a combination with other interpolation methods that smooths the movement near the starting point and stopping point in teaching will be described here. As mentioned above, the interpolation method based on equation (5) is completely defined at the start and stop points, so it can be used in common with other interpolation methods that aim for smooth starts and stops, that is, soft starts and stops. Although it is not essential to do so, using the combination described below will further refine the control at the time of starting and stopping. Therefore, first, the newly formulated principles of soft starting and soft stopping will be explained, and then other variations of this starting point that are used in common with these principles will be explained.

FIG. 9 is a diagram for explaining the principle of soft starting, in which the work point that was stopped at x→=x→ ₀ at time t=0 changes x→=x→ ₁ to speed u → Indicates the condition of passing with ₁ .

In this soft starting method, the acceleration of the work point α→(t)
is configured to be correlated to a distance from a predetermined position, for example x→ ₁ . Therefore, when a proportional relationship is adopted as this interpolation relationship, the following equation is used as the basis when k is a constant.

α→(t)=dv/→(t)/dt=k ² (−x→+x→ _i ) (36) Here, v→(t) is the speed of the working point. Next (37)
Substituting the relationship in equation (36) into equation (36), regarding t,
Equation (37'), which is a second-order differential equation for the position x→(t), is obtained.

v→(t)=d/dtx→(t) …(37) d ² /dt ² x→(t)+k ² x→(t)=k ² x→ ₁ …(37′) (37′) Formula can be easily solved and the following equations (38) and (39) are obtained.

x→(t)= (x→ ₀ −x→ ₁ ) cos kt+x→ ₁ …(38) v→(t)= −k(x→ ₀ −x→ ₁ ) sin kt …(39) However, u→ _i = -k(x→ ₀ -x→ ₁ )...(40) kT=π/2...(41) where T is the moving time until the work point reaches x→ ₁ . When controlling soft start,
Although it is possible to calculate equations (38) and (39) as they are, here we adopt a method of solving differential equations by repeating addition. Therefore,
Considering equations (37) and (37') as equations for a small time width Δt, the position and velocity of the work point at time t are respectively x→ _pld and v→ _pld , and they are respectively x → pld at time t+Δt. _oew , v → _oew , the following equations (42) and (43) are obtained.

x/→ _oew −x/→ _pld /Δt=v→ _pld …(42) v/→ _oew −v/→ _pld /Δt =k ²・(−x→ _pld +x→ ₁ ) …(43) These equations By rearranging, we get the following formula.

x→ _oew = x→ _pld +v→ _pld・Δt…(44) v→ _oew = v→ _pld +k ²・(−x→ _pld +x→ ₁ )・Δt…(45) However, if we use this formula as it is, ,
Multiplication by k ² becomes necessary on the right side of equation (45). Therefore, if we define the integer k′ and the minute time width Δt′ so that 2 ^k ′・Δt′＝k ²・Δt …(46) Δt＞Δt′＞Δt/2 …(47) holds, then ( The second term on the right side of equation 45) can be rewritten as shown in equation (48) below.

2 ^k ′ (−x→ _pld +x→ ₁ ) Δt′ = 2 _k ′ (−x→ _pld +x→ ₁ )・s・Δt (48) However, s≡Δt′/Δt (49). By performing such transformation, k ²
The multiplication by ^2k ' is replaced by the multiplication by 2k', and furthermore, the multiplication by ^2k ' can be replaced by a shift of only k' bits to the higher order side. However,
Since there is a factor s・Δt, this time s
The problem of multiplication arises. In order to solve this problem, it is sufficient to repeatedly calculate the speed every Δt/s. In other words, for every Δt/ssec, 2 ^k ′(−x→
_pld +x→ ₁ )・Δt is added to v→ _pld , and on average, per Δt, 2 ^k ′(−x/→ _pld +x/→ ₁ )・Δt/(Δt/s) ×
Since the increment of Δt = 2 ^k ′ (−x→ _pld +x→ ₁ )・s・Δt…(50) is added to v→ _pld , the addition equivalent to the first side of equation (48) above is It will be done. Multiplication by Δt is replaced by a shift by taking Δt=2 ^−N (N is an integer). That is,
The following (51) obtained from equations (44) to (50),
The addition of equation (52) is performed using the initial conditions of equation (53),
It is sufficient to repeat the position at a time interval of Δt and the velocity at a time interval of Δt/s.

x→ _oew =x→ _pld +v→ _pld・Δt…(51) v→ _oew =v→ _pld +2 ^k ′(−x→ _pld +x→ ₁ )・Δt…(
52) x→ _ioi =x→ ₀ , v→ _ioi =0→ (53) Next, a method for soft stopping will be explained. The conditions for soft stopping are as shown in Figure 10.
The work point that passed through x→=x→ _-1 at speed u→ _-1 is x→=
x→
This means that it is stopped at ₀ . In this case as well, as in equation (36), the following (54) is used such that the acceleration α→(t) of the work point is proportional to the distance from the passing point x→ _-1 .
can be based on a formula.

α→(t)=dv/→(t)/dt=k ² (−x→+x→ _-1 )…
(54) The meanings of v→(t), k, etc. are the same as before. Since the boundary conditions are different from the soft starting point, the solution to this differential equation is as follows.

x→(t)=(x→ ₀ −x→ ₋₁ ) sin kt+x→ ₋₁ …(55) v→(t)=k(x→ ₀ −x→ ₋₁ ) cos kt …(56) However, u→ _-1 =k(x→ ₀ -x→ _-1 )...(57) kT=π/2...(58).

The calculations of these equations can also be replaced with a method of solving differential equations by repeating addition, similar to the soft starting method, and the above-mentioned (51) ~
The following equations (59) to (61) correspond to equation (53).
The formula is obtained.

x→ _oew =x→ _pld +v→ _pld・Δt …(59) v→ _oew =v→ _pld +2 ^k ′ (−x→ _pld +x→ _-1 )・Δt …(60) x→ _ioi =x→ _-1 , v→ _ioi =u→ _-1 (61) Similarly, the addition of the velocity is repeated every Δt/s.

Next, consider a case where the teaching starts from one teaching point and stops at the next teaching point. In this case, as shown in Figure 11,
After a soft start at the working point x→=x→ ₁ , it becomes necessary to make a soft stop at the next teaching point x→=x→ ₂ . As an example of this case, a method is used in which the acceleration α→(t) of the working point is minimized at an intermediate point between the starting point and the stopping point, and the acceleration α→(t) is increased as the point moves away from the point. Therefore, the basic equation is α→(t)=dv/→(t)/dt=k ² (−x→+x/→ ₁ +x/→ ₂ /2) (62). The solution to this equation is:

x→(t)=x/→ ₁ −x/→ _2/2・cos kt+x/→ ₁ x/→ _2/2 …(63) v→(t)=−kx ₁ −x _2/2・sin kt …(64) As before, the formula for repeated addition is:

x→ _oew =x→ _pld +v→ _pld・Δt…(65) v→ _oew =v→ _pld +2 ^k ′ (−x→ _pld +x/→ ₁ +x/→ ₂ /2) Δt…(66) x→ _ioi =x→ ₁ , v→ _ioi =0→ (67) Again, the repetition of addition in velocity is performed every Δt/s. In this case, the maximum speed is -kx/→ ₁ -x/→ ₂ /2.

FIG. 12 is a diagram showing an interpolation circuit 30 that can perform the above-described soft start and soft stop control in combination with interpolation control using equation (5). This interpolation circuit 30 corresponds to the interpolation circuit 22 shown in FIG. 7, and among the circuit elements included therein, those that are the same as those shown in FIG. 7 are given the same reference numbers. It has been done. Further, among the components of the control device, the parts other than the interpolation circuit 30 are the same as the configuration shown in FIG. 5, and therefore, redundant explanation will be omitted.

The differences between the interpolation circuit 30 in FIG. 12 and the interpolation circuit 22 in FIG. 7 are as follows. First, as a clock generation circuit, a first clock generation circuit 314 generates a clock signal φ ₁ every Δt (=2 ^-10 sec), and a first clock generation circuit 314 generates a clock signal φ 1 every Δt/s (=2 ^-10 /s sec). Second clock generation circuit 3 that generates _φ2
15. First clock generation circuit 3
14 is a first clock buffer 316 that receives and buffers the value of Δt from the memory 212;
and a first counter 317 which receives the respective outputs of the timer 320 and the first clock buffer 316 and outputs a first clock signal φ. In addition, the second clock generation circuit 31
5 also includes a second clock buffer 31 that receives the value of Δt/s from the memory 212 and buffers it.
8, and a second counter 31 which receives the respective outputs of the timer 320 and the second clock buffer 318 and outputs a second clock signal φ ₂ .
9. These clock generation circuits output the carry signals of the first and second counters 317 and 319 as clock signals φ ₁ and φ ₂ at intervals of Δt and Δt/s, respectively. Therefore, the first clock signal φ ₁ is the same as the clock φ of FIG. This first clock signal φ ₁ is applied directly to buffers 106 and 110, but is applied to buffer 108 via multiplexer 321. The second clock signal φ ₂ is given as another input to the multiplexer 321, which receives the switching signal SW ₁ from the CPU 211.
selects one of the clock signals φ ₁ and φ ₂ and applies it to the buffer 108.

The output of buffer 110 is provided as one input of subtracter 323 in addition to adder 109 and I/O port 214. Also, I/O
The output of buffer 322 connected to port 214 is provided as another input of this subtracter 323. The output of the subtracter 323 is the input signal
It is provided as one input of a multiplexer 325 via a shifter 324 which shifts the signal to the higher order side by k' bits and outputs the result. This multiplexer 325 receives the output of the buffer 106 as another input, and receives the switching signal Sw ₂ from the CPU 211.
select one of the two inputs by
This is given to adder 107. The other configuration is similar to the interpolation circuit 22 in FIG. 7.

Using the interpolation circuit 30 in Fig. 12, soft start → (5)
The operation will be described in the case where control is performed in the order of interpolation based on the formula → soft stop. First, in the soft start, the multiplexer 321 selects the input from the second clock generation circuit 315 in response to the switching signal _Sw1 . Then, the second clock signal φ ₂ is input to the buffer 108.
_Moreover , the multiplexer 3
25 selects the input from shifter 324. Therefore, the adder 105, buffer 106, etc.
It becomes unrelated to the operation of this circuit. Initial value of velocity v→ _ioi is 0→, and initial value of position x
→ _i
As _oi , the position of the first teaching point x → ₀ is
The signals are input from the CPU 211 to buffers 103 and 104, respectively (see equation (53)). Batsuhua 32
2, the next teaching point position x → ₁ is CPU2
It is input from 11.

Next, v → _ioi and x → _ioi are each a buffer of 108
，
110. When clock signal φ ₂ is applied, buffer 108 provides v→ _ioi stored therein to adder 107. At the same time,
v _ioi is also given to adder 109. On the other hand, x→ _ioi stored in buffer 110 is supplied to adder 109 and added to a signal obtained by shifting v→ _ioi by 10 bits to the lower side. Therefore, the adder 109 performs the addition of (x→ _ioi +v→ _ioi ×Δt).

x → _ioi , which is the output of the buffer 110, is the subtracter 3
23 is also given. The subtracter 323 calculates this x→ _ioi
is subtracted from x→ ₁ , which is the output of buffer 322, and (−x→ _ioi +x→ ₁ ) is provided to shifter 324.
Shifter 324 shifts this signal upward by k' bits and supplies it to multiplexer 325. Therefore, the other input of the adder 107 is 2 ^k ′×(−x→ _ioi +
x → ₁ ). Adder 107 shifts this input by 10 bits to the lower order side and adds it to the output of buffer 108, v→ _ioi . Therefore, the output of the adder 107 is v→ _ioi +2 ^k ′×(−x→ _ioi +x→
₁ )・
Δt. Buffer 108 buffers the output of adder 107 as v→ _pld in the next cycle of second clock signal φ ₂ . In each cycle of the second clock signal φ ₂ , adder 107 and buffer 108 repeat similar operations. Therefore, if the values stored in the buffers 108 and 110 are respectively v→ _pld and x→ _pld , then the adder 107 performs the calculation of equation (52) and
_oew is obtained and given to the buffer 108. This v→ _oew is treated as v→ _pld in the next cycle. Adder 109 and buffer 110 similarly repeat the operation of equation (51) in accordance with the cycle of first clock signal _φ1 .

Since two signals φ ₁ and φ ₂ are used as clock signals, the calculation cycles of equations (51) and (52) are different from each other. For this reason, for example, when φ ₁ < φ ₂ , the iterations for velocity will be slower than the iterations for position, and the number of additions will be reduced accordingly. However, as already explained in relation to equation (52), In addition, since a large amount of increment is provided for each repetition, the speed command value and position command value actually output from the buffers 108 and 110 are appropriate as command values at that time.

Next, when the soft start control is finished and control is started based on equation (5), the multiplexer 321 selects the first clock generation circuit 314 side by the switching signals Sw ₁ and Sw ₂ , and the multiplexer 325 selects the first clock generation circuit 314 side. The output side of the buffer 106 is set to be selected. Then, the interpolation circuit 30 of FIG. 12 has substantially the same configuration as the interpolation circuit 22 of FIG. 7, and performs interpolation calculation based on equation (5).

When performing a soft stop, the switching signals Sw ₁ and Sw ₂
This causes multiplexers 321 and 325 to be in the same state as the soft start described above. Batsuhua 10
The initial values given to 3 and 104 are u→ _-1 and
x→ _-1 , and x→ _-1 is given to the buffer 322 (see equations (59) to (61)). The subsequent operation is the same as in the case of soft start.

Furthermore, if you want to perform soft starting and soft stopping in succession, give the values of equation (67) as initial values to buffers 103 and 104, respectively.
2 should be given x/→ ₁ +x/→ ₂ /2. In this case, the operation of this circuit is also similar to that described above.

Each of the embodiments and modifications explained above is mainly based on (5)
Although the control is based on equation (5), it was previously pointed out that equation (5) is only the basis for one preferred embodiment of the invention and that other interpolation functions can be used. In addition, by not calculating the interpolation function as it is, but by basing it on a differential equation whose solution is this interpolation function, it becomes possible to perform repeated calculations, and high-speed calculation control using addition is possible. It is also within the scope of the present invention to calculate using the method described below. Further repeat time is 2 ^-N (N is an integer)
By taking sec, the above differential equation can be solved with only shift operations and addition, and even faster calculation control can be obtained, but the interpolation control of this invention requires the introduction of such a repetition time. It's not a thing. In this invention, the interpolation method that is the basis of this invention may be used alone, and any other arbitrary interpolation method such as soft start/soft stop as described above, linear interpolation, circular interpolation, Hosaka interpolation, etc. It also includes being used in common with.

Further, the control method and control device of the present invention can be used not only for controlling playback type robots but also for controlling other types of robots such as numerically controlled robots. Selection of the direction of velocity at a position such as a teaching point where a work point should pass is not limited to the direction exemplified in the above embodiment; for example, at a teaching point x→ _i , x _i-1 x――――→ _i
The direction may be a direction obtained by giving different weights to the direction of x _i x ---→ _i+1 and averaging them. This selection is also effective in cases where the curvature of the trajectory to be drawn at the work point monotonically increases or decreases from the starting point to the stopping point (for example, a spiral). It is.

(Effects of the Invention) As described above, according to the present invention, although it is relatively simple, it is possible to perform interpolation control that incorporates the global characteristics of the trajectory, and it has become the basis of conventional control devices. Therefore, it is possible to obtain a robot control method and apparatus that have the advantages of the interpolation method. In particular, since the present invention does not prohibit acceleration/deceleration on the interpolated trajectory, smooth acceleration/deceleration can be performed along the interpolated trajectory even when high-speed changes are required between adjacent passing points. Therefore, the robot is not subjected to sudden movements, and there is less burden on the mechanical parts of the robot.

[Brief explanation of the drawing]

1 to 3 are diagrams for explaining Hosaka's interpolation. FIG. 4 is an overall diagram of a system using a robot control device according to an embodiment of the present invention. FIG. 5 is a diagram showing the overall configuration of a control circuit included in the robot control device of FIG. 4. 6th
The figure is a diagram for explaining the principle of the interpolation method used in the embodiment of the present invention. FIG. 7 is a block diagram showing an example of an interpolation circuit included in an embodiment of the present invention. FIG. 8 is a flow diagram for explaining a modification of the present invention. FIGS. 9 to 11 show soft starting points commonly used in other modifications of the present invention.
It is a figure for explaining the method of a soft stop. 12th
The figure is a block diagram showing an interpolation circuit included in another modification of the present invention used in combination with the soft start/soft stop method, and FIG. 13 shows the interpolation trajectory obtained by the embodiment of the present invention. It is an explanatory diagram to illustrate. 11...control device, 20...control circuit, 21...
... Microcomputer, 22, 30 ... Interpolation circuit, 101 to 104, 106, 108, 110,
322...Batsuhua, 105, 107, 109...
... Adder, 321, 325 ... Multiplexer,
323...Subtractor, 324...Shifter.

Claims (1)

[Scope of Claims] 1. A robot control method for causing a working point of a robot having a drive mechanism to move through predetermined discrete passing points in a predetermined order, comprising the steps of: preparing position data representing a position and speed data representing a magnitude of speed that the work point should have at each of the passing points; the step of obtaining interpolation data that has a value for each time interval and that interpolates the movement of the work point at the passing point; and the step of driving the drive mechanism based on the interpolation data, and the step of driving the drive mechanism based on the interpolation data. The step of calculating is the step of defining a position interpolation function that uses the time parameter as a variable and includes four or more undetermined coefficients, and the step of defining four consecutive passing points in the above order as Xi
-1, Xi, Xi+1, Xi+2, (a) The magnitude of each velocity vector at the passing point Xi, Xi+1 is the corresponding passing point Xi, Xi+1
(b) the direction of the velocity vector at the passing point Xi depends on at least the relative positional relationship of the passing points Xi−1, Xi, and Xi+1; Along with the direction,
The value of the undetermined coefficient is determined so as to satisfy both the condition that the direction of the velocity vector at the passing point Xi+1 is at least dependent on the relative positional relationship of the passing points Xi, Xi+1, and Xi+2, and the following conditions. , a step of determining an interpolation trajectory in the section between passing points Xi and Xi+1 using the position interpolation function specified thereby. 2. The robot control method according to claim 1, wherein the position interpolation function is expressed as a polynomial of degree 3 or higher regarding a time parameter. 3. The robot control method according to claim 2, wherein the position interpolation function expressed by the polynomial satisfies a differential equation regarding a time parameter, and the interpolation data is determined based on the differential equation. . 4 The predetermined time interval is when N is an integer.
2 ^-N seconds, the differential equation is approximated by an iterative expression whose value is updated at each predetermined time interval, and the iterative expression is including multiplication with a number and addition of the multiplication result of the multiplication and the augend,
and the robot control according to claim 3, wherein the calculation of the iterative calculation formula is achieved by a calculation of shifting the multiplicand by only N bits to the lower side and adding it to the augend. Method. 5 If the value of the speed data for at least one of the two adjacent passing points along the predetermined order is 0, the interpolation data for interpolating between the two adjacent passing points is A robot control method according to any one of claims 1 to 4, wherein the acceleration of a point is calculated so as to change in correlation with the distance from a predetermined position. 6. The interpolation data for interpolating between the two adjacent passing points is calculated based on a differential equation that describes the correlation, and the differential equation that describes the correlation is based on the predetermined time interval and the predetermined time interval. and another time interval different from the time interval of , and the iterative operation is achieved by a shift operation and an addition. The robot control method described. 7. A robot control device for causing a working point of a robot having a drive mechanism to move through predetermined discrete passing points in a predetermined order, comprising position data representing the position of each of the passing points. and a storage means for storing speed data representing the magnitude of the speed that the work point should have at each of the passing points; and a reading means for reading out the position data and the speed data from the storage means. and interpolation for inputting the position data and the speed data read from the reading means, having values for each predetermined time interval, and interpolating the movement of the work point between the passing points. interpolation data generation means for generating data; and output means for outputting the interpolation data generated by the interpolation data generation means to the drive mechanism to drive the drive mechanism, and the interpolation data generation means: Means for holding a position interpolation function with parameters as variables and including four or more undetermined coefficients;
-1, Xi, Xi+1, Xi+2, (a) The magnitude of each velocity vector at the passing point Xi, Xi+1 is the corresponding passing point Xi, Xi+1
(b) the direction of the velocity vector at the passing point Xi depends on at least the relative positional relationship of the passing points Xi−1, Xi, and Xi+1; Along with the direction,
The value of the undetermined coefficient is determined so as to satisfy both the condition that the direction of the velocity vector at the passing point Xi+1 is at least dependent on the relative positional relationship of the passing points Xi, Xi+1, and Xi+2, and the following conditions. , means for determining an interpolation trajectory in the section between passing points Xi and Xi+1 using the position interpolation function specified thereby. 8. The robot control device according to claim 7, wherein the position interpolation function is expressed as a third-order or higher-order polynomial regarding a time parameter. 9. The position interpolation function expressed by the polynomial satisfies a differential equation regarding a time parameter, and the interpolation data calculation means includes a differential equation calculation means for calculating the interpolation data based on the differential equation. A robot control device according to claim 8. 10 The predetermined time interval is 2 ^-N seconds, where N is an integer, and the differential equation calculation means includes iterative calculation means whose output value is updated at every predetermined time interval, The means includes multiplication and addition means for multiplying the predetermined time interval by the multiplicand and adding the result of the multiplication and the augend, and the multiplication and addition means multiplies the multiplicand by N. 10. The robot control device according to claim 9, wherein the arithmetic means shifts the augend by bits to the lower side. 11 The interpolation data generation means further comprises, when the value of the speed data for at least one of the two adjacent passing points along the predetermined order is 0, the interpolation data generating means Any one of claims 7 to 10, comprising a second interpolation data calculation means for calculating interpolation data to be interpolated so that the acceleration of the work point changes in correlation with the distance from a predetermined position. The robot control device described in . 12 The second interpolated data calculation means includes a second differential equation calculation means that performs calculations based on a differential equation describing the correlation, and the second differential equation calculation means is configured to perform calculations based on the predetermined time interval and , further comprising intertemporal iterative operation means for performing a combination of respective iterative operations at other time intervals different from the predetermined time interval, and the intertemporal iterative operation means performs a shift operation and an addition. A robot control device according to claim 11, comprising: