JPS63231285A - Composite function generating method - Google Patents

Abstract

PURPOSE:To generate a function which secures continuity for an input that varies discontinuously and dynamically at random by using a multidimensional normal distribution function as the generating function and performing composition by the linear combination of the generating function. CONSTITUTION:Detected distances of sensors 21-2n are converted into relative position coordinates by a coordinate conversion part 30. A control deviation generating part 31 generates the position error between the target position and current position of a robot and the rotational error. An image conversion part 32 converts the input position coordinates and position deviation into a three-dimensional image of the normal distribution by using a basic function and an image arithmetic part 33 adds respective three-dimensional images after image conversion to generate a potential surface in a virtual space. A conversion part 34 computes an attitude controlled variable from the potential value between calculated virtual spaces. A virtual suctional force generation part 35 generates an induction acceleration force and a virtual turning force generation part 36 generates a turning force to a target rotational angle.

Description

[Detailed description of the invention] 〔table of contents〕 overview Industrial applications Conventional technology (Figures 11 and 12) The problem that the invention aims to solve Means for solving problems (Figure 1) Actions Example (a) Description of one embodiment method (Figures 2 and 3.

(Fig. 4, Fig. 5, Fig. 6, Fig. 7) ('b) Explanation of application examples (Fig. 8, Fig. 9, Fig. 10) (
C) Description of other embodiments Effects of the invention [Summary] Multidimensional normal distribution as a two-generated function in a composite function generation method in which a function is generated in response to an input and one generated function is combined to generate a composite function. By using functions and performing synthesis by taking a linear combination of generated functions, it is possible to generate a function that guarantees continuity for random, discontinuous, and dynamically changing inputs. .

[Industrial application field]

The present invention relates to a composite function generation method for generating a control function from input for state control or the like.

In particular, the present invention relates to a composite function generation method for generating a continuous composite function for random and discontinuous inputs.

In state control, a control function is generated from an input, and a controlled object is controlled using this function.

To obtain such a function, there is a method of synthesizing two generated functions to obtain a composite function.0 In order to generate such a composite function, it is required that the generated composite function has continuity, etc.

[Conventional technology]

For example, consider an example in which the movement of the mobile robot 1 traveling on a two-dimensional plane shown in FIG. 11 (5) is controlled so as not to collide with an unknown obstacle OB.

The robot 1 is provided with a distance sensor (for example, an ultrasonic sensor) 2, and the robot 1 detects the presence of an obstacle OB based on the output (distance information) R of the distance sensor 2.

You will recognize the distance.

To influence the movement of robot 1.

Conventionally, the magnitude of the detected distance was determined through internal processing, and based on the magnitude, it was determined whether the motion (traveling speed, traveling direction) should be changed, and if the motion was to be changed, an appropriate command value ( A control amount) is calculated to avoid a collision with an obstacle OB, take a detour, etc.

In such a conventional adaptive control method, internal processing is also performed in the dimension (one dimension in this example) according to the dimension of the output of the sensor 2.

It is necessary to control the movement state using numerous conditional judgments and complex algorithms.

The present inventors have devised a method that simplifies the internal processing for obtaining control amounts from such sensor information, and also enables one-dimensional processing of a large number of diverse sensor outputs.

Patent application specification No. 150117/1986 (June 1988)
(filed on May 26th).

This method converts the sensor output into a virtual space using an image (function) to obtain a control amount, and will be explained using FIG. 12.

In this proposal, assuming that the robot 10 work space (movement space) is two-dimensional with the X and Y axes as shown in Prisoner 121,
Assume a three-dimensional virtual space in which the P-axis is added to this as shown in FIGS. 12(B) and 12(C).

Then, with respect to the output (distance R) of sensor 2 obtained in the work space of FIG. image (function)
Generate P. That is, the output of the sensor 2 in real space is converted into a three-dimensional image (function) P in virtual space.

In this virtual space, one-dimensional distance information is represented as a multidimensional three-dimensional object as shown in FIG. 12 (Q).

Since the transformed image in the virtual space has a height in the P-axis direction, the state quantity of the field in the P-axis direction due to the three-dimensional image of the obstacle OB at position A in the virtual space corresponding to the robot 1 is used. The control amount can be determined, and the motion of the robot can be adaptively controlled based on this.

In this way, virtual space can be used as a state control field.

This is a method in which the output from the sensor 2 is converted into an image (function), the images (functions) from each sensor are combined in a virtual space, and the state quantities and control quantities are obtained from the nine composite functions.

Conventionally, when such a function is generated and two generated functions are combined to obtain a composite function, the function shape is selected to suit the purpose, and the composite function is obtained by simply composing them. Ta.

[Problem that the invention seeks to solve]

On the other hand, in a system like the one shown in Fig. 11, firstly, since the virtual space is a continuous field, continuity and total differentiability are required for the composite function itself, and secondly, inputs such as those from sensor 2 are random. Since there may be discontinuous cases, it is desirable to dynamically generate a composite function that is continuous in this case as well.

However, in the conventional composition function generation method.

Once these are determined, a method is used in which compensation is performed by setting two various conditions, so there is a problem in that it is extremely difficult to perform all of these compensations for general-purpose functions.

An object of the present invention is to provide a composite function generation method that can dynamically change the shape and generate a composite function that guarantees continuity.

[Failure to solve the problem]

FIG. 1 is a diagram explaining the principle of the present invention.

As shown in Fig. 1 (5), the generation function f(R) of the present invention uses a multidimensional normal distribution function, and this multidimensional normal distribution function is linearly combined as shown in ) to ) in Fig. 1. It is used to synthesize and generate a composite function.

[For production]

In the present invention, a multidimensional normal distribution function is used as a function (referred to as a basis function) generated in response to the power of two people. A multidimensional normal distribution function is fully differentiable and continuous in the entire domain (input range).In other words, the multidimensional normal distribution function/(R) here is 0.

R2=g (xl, x,...xn)
(1) However, 1g is a linear combination of polynomials regarding xl...xfi (n is the dimension).

As.

f (R) = K −e−”” ・・・・・・
・・・・・・・・・・・・・・・Make the mold of (2)! The partial differential of j+X+ is.

It is.

Therefore, equations (2) and (3) are shown as shown in FIG. 1 (3), and both are continuous and differentiable.

Furthermore, if the composition of the basis functions is expressed by a linear combination as shown in Figure 1 (B) - 9, the composite function also has the mathematical properties of the basis functions (
Continuity, total differentiability) can be preserved.

for example.

given that.

The sum of f and f2 in Figure 1 CB) is.

f1+f2=1・exp(−R12/2σ+2
・e x p (-Ra'/2 a"), and the first
The difference in Q, the product of n in Figure 1, and the quotient in Figure 1 (G) are as follows.

fs −f2=to+−exp(−Rn2a′)−to, 5
exp(-R:https://2σ')fi ・fz=Kx ・K
, -exp (-R172a"-R,n2σ2)fl/
f2=Kl/4・exp(−RI/2σ2+Rν2a
2') Therefore, when synthesized by linear combination, one composite function has the form -exp(-R1/2σ2), so the same continuity and total differentiability as the basis functions are guaranteed, and the λ force is constant. A composite function (in the example of Fig. 12, a curved surface on a virtual plane) that has continuity even if it is continuous or random is obtained.

These are not lost even if the shape is changed dynamically.

〔Example〕

(Al 1. Description of Embodiment Method) An example in which the composite function generation method of the present invention is used for adaptive control of the robot shown in FIG. 12 will be described below.

Fig. 2 is a detailed explanatory diagram of the present invention, Fig. 3 is a diagram of the relationship between the real space and virtual space in Fig. 2, and Fig. 4 is an explanatory diagram of function composition in the virtual space in Fig. 2. In the prison, two ultrasonic sensors 21 to 28, each of which is a distance sensor, are installed on the side of a robot 1 that moves in a two-dimensional X, Y real space (work space), as shown in Figure 2 (Q). While grasping the external environment using the sonic sensors 21 to 28, it moves in real space while avoiding obstacles OB1 and OB2 (
An example of translational movement and posture control) is shown.

First, the detection distance rI of the ultrasonic sensors (hereinafter referred to as sensors) 21 to 28 is determined by the coordinates X of the robot (center of gravity origin).
-Represented by Y. Unit vector e = (ext p eyl ) + (i =
1 to 8) and the sensor mounting position set as shown in Figure 2 (q) is the position vector of positions A1 to A. 51 = (8!l
+8. i ) + (i=1 to 8), the obstacle position captured by sensor i is expressed as (Xt, Yt) using the following equation.

(Xt * Yi) = rI * (exi l eyl
) + (8Xl + Sys ) −−15) Therefore,
Detection distance r1 of sensors 21 to 28.

The relative position vector R+=(Xt p Yt ) of the obstacle is obtained from each sensor 21 to 28 of the robot 1.

Next, we expand this using basis functions in a virtual space that is a state field.

As shown in Fig. 3, in the real space R8 and the virtual space Is, the two-dimensional X and Y coordinates of the real space R8 and the two-dimensional X and Y coordinates of the virtual space Is are υ, and the virtual space IS is real space R8
A new orthogonal P axis (potential axis) is added to the X and Y planes of .

Therefore, the position of the two-dimensional real space R8O point A is the virtual space I
It corresponds to the position of the two-dimensional plane X-Y of s.

Using the relative position vector R, based on the detection distance rl of the sensors 21 to 28 described above, a multidimensional normal distribution curved surface (function) that spreads around the position indicated by R on the X-Y plane in the virtual space Is is created. Obstacle OBI.

It is generated as a stereoscopic image P1 of OR3.

This stereoscopic image Pi is a multidimensional (two-dimensional) normal distribution function.

P+) At=KiXexp(-R72σ2) ---
−−−−−−−−−−−−==(6) However, R”=(X
-X, )2+(Y-Y,)2゜A is the sensor installation position.

σ is the standard deviation.

In this virtual space Is, each sensor mounting position A.

Three-dimensional images P1 at (i=1 to 8) are sequentially generated.

The three-dimensional image group (called a potential surface) P, which is a superimposed composite function, is.

P=ΣP+) At...four...
・・・・・・・・・・・・(7)

Therefore, in the example of Fig. 2 (3), the virtual plane is shown in Fig. 2 (3).
As shown in B), at the position of the obstacles OBI and OB2, there is a three-dimensional image pa having a width of 9 in the X and Y directions and a height in the P axis direction,
Pb is generated as a function, and a potential curved surface (composite function) is formed by superposing (synthesizing) these.

That is, as shown in FIG. 4, based on the inputs R, , R2, R3, basis functions Pyu, P2. P, is generated and these are added on the virtual plane Is to form two composite functions F(
8) is obtained.

This composite function F(8) is (6), (Since it has continuity like the force formula and is fully differentiable, as will be described later.

The amount of control for the robot to avoid obstacles is expressed as a composite function F(R
), and the basis functions themselves are continuous and fully differentiable, so even if the input changes dynamically, the composite function F(R)
dynamically changes accordingly, and continuity is not lost.

In this virtual plane Is, as shown in FIG.
The height in the P-axis direction at the position is the height PA in the axial direction of the potential surface (composite function) PSOP due to the stereoscopic images pa and Pb.

In such a potential surface PS, a repulsive force RF is generated that causes the robot 1 to roll along the potential surface P8 toward the lower potential.

Controls the translational displacement and posture of the robot 1 to avoid obstacles.

Next, a method of determining the repulsive force from the potential curved surface generated from the outputs of the sensors 21 to 28 in this manner will be described.

5 and 6 are explanatory diagrams of repulsive force conversion, and FIG. 7 is an F3A diagram of the operation theory in virtual space.

Potential surface P of virtual space Is at point A in Figure 3
When S is enlarged, it becomes as shown in FIG. 5 (5).

θp It is a surface having an inclination in the direction (curved surface slope) -B) A=β.

From this, find the repulsive force that causes the ball to roll along the potential surface PS.

Here, the virtual gravitational acceleration G is set in the negative direction of the P axis as shown in the 51st factor, and the accelerations Xr and Yr are determined as the control amount of the repulsive force in the Y axis and the Y axis direction.

Considering the X-axis direction, since the slope of the potential curved surface PS is α as shown in FIG. 5(B), the acceleration X is.

X, == −G51nα* cosa:= −−Gs
in 2α ・Tokukyokukyokukyoku (8) Tona Jun,
If K==-, G, then equation (8) is.

Xr2@5in2α Curve...Curve...Curved surface (9) is obtained by calculation.

Similarly, the acceleration Y on the Y axis is.

Y, == K・5in2β ・・・・・・
...Curve...obtained as a curved surface (10).

If this is the control amount in the X and Y axis directions, as shown in FIG. 5 (q), assuming that the robot 1 is a sphere, the Y axis.

A rolling force (repulsive force) RF is generated along the potential curved surface PS by the combination of the Y-axis accelerations Xr and Yr.In other words, in the virtual space of FIG. Repulsive force is added in the smaller direction,
Therefore, in real space, robot 1 faces obstacles OBI, OB
2 while avoiding obstacles OBI and OB2.

This principle can be used to control the translational displacement movement of the robot 1 by focusing on the center of gravity O of the robot 10 and setting point A as the position of the center of gravity 0.

In order to use this for posture control of the robot 1, the following procedure may be used.

As shown in Fig. 6 (5) and (B), based on the assumption that the mass point of the entire robot 1 is located at the center of gravity O, the mass point is set at C/21-2.
It is assumed that the installations of No. 8 are distributed at positions A1 to A.

Also, the sum of n (=8) distributed masses (Ms/n) is equal to the virtual mass Ms of the robot 1 in the virtual space.0 The center of gravity of the robot model is the normal mechanical coincides with the center of gravity.

Based on these assumptions, the repulsive force F1 from the virtual space generated from the sensor output acts on the center of the mass points A distributed at the senna mounting position, and the moment at the center of gravity 0 and the virtual suction force 1 rotational force described later. acts.

The moment of inertia) I is the P-axis rotation at one point A (center of gravity 0) with respect to the X-Y axis of translational displacement, as shown in FIG. 6(5). Therefore, in order to determine the moment M for attitude control, first, the control amounts Xrl and Yrl of the repulsive force at the positions A1 to A8 for each senna installation are determined.

That is, first install each senna in position A in the same manner as shown in Figure 5.
, (A1 to A8), find the inclination αi in the X direction and the inclination βi in the Y direction.

And each sensor installation has an acceleration of Xrl at position A.

Transform Yrl into equation (9) and equation (11) to obtain the ninth order: 0 X11= Ka sin 2 dl
Opening song, (11) Yrl = K * 5in2
βl ・・・・・・・・・・・・・・・
......(13Here, each Senna installation receives a repulsive force F at position A.

Fl: (Fzi p Fyi) = mI (Xrl * Yrl) ・
・・・・・・・・・・・・・・・・・・(13. However, ml is the mass of the dispersed mass points.

Therefore, formula (11), type 2, and type α9.

becomes.

Therefore, the moment M of the robot's center of gravity is:

M=ΣS, XF.

=Σ18tl X IFII X5inθi...
.....Gap-(defined in 19).

Therefore, in the Kasumi method, find the repulsive force F from the virtual space machine S at position A for each senna installation of (L'5 formula, (14 formula).

(Sensor position vector S from the center of gravity O by formula 151
The moment M for posture control is determined by i.

Similarly, the translational force F at the double center of gravity O (F = FY) is.

Therefore, each sensor installation determined from the α → formula is at position A.
, the force of translational displacement (the rotation force in Figure 5) is obtained by the repulsive force xl + FA5.

That is, as shown in FIG. 7, from the potential surface (composite function) PS generated by the output of each sensor 21 to 28 in the virtual space l8iC, the robot 1 determines that each sensor is installed at position A,
Obtain the repulsive force F as shown in the figure, obtain the posture control moment (M) from the 9th equation, and the translational displacement force from the αe equation. OB2
(b) Description of application example The above-described attitude control and translational displacement control are executed by calculation from the output of the sensor.

FIG. 8 is a block diagram of such control amount calculation υ.

Each calculation step is shown as a block.

In the figure, the same parts as those shown in FIG.
The detection distance r1%rn of n is determined by equation (5).Sensor 2
The unit vectors e1 to en in the real space of 1 to 2n and the sensor installation convert the position vectors 81 to Sn into Yゎ), and 31 is a control deviation generation unit that calculates the target position of the given robot 1. Position error Rc and rotation error φ between Xr, Yr and the current position. The current acceleration X, Y detected for each axis (X, Y axis) from the internal sensor of the robot 1 is integrated twice by the twice integrating section 31a to obtain the current position. The transformation matrix generation section 31d obtains a transformation matrix using the current rotational angle φ obtained by integrating the current rotational speed H of the robot 1 detected by the gyro provided inside the robot 1 using the integration section 31G, and calculates the above-mentioned current position. A multiplier 31b multiplies this transformation matrix to perform coordinate transformation, a difference part 316 calculates the difference between the target position Xt, Y, and the current position to generate a position error Rc, and a difference part 31f calculates the target rotation angle φ. , and the current rotation angle φ from the integrating section 31C to determine the rotation error φ.

is generated.

Reference numeral 32 denotes an image conversion unit that converts the input position coordinates R1, and specifically uses a multidimensional normal distribution function as a basis function and converts it into a three-dimensional image of normal distribution.

That is, the stereoscopic image Pi is generated by the calculation of equation (6).

Reference numeral 33 denotes an image calculation unit, which adds the transformed three-dimensional images P1 (synthesizes the basis functions) to create a potential surface (composite function) in virtual space. (Value) P is obtained by calculating the (force formula).

Reference numeral 34 denotes a conversion unit, which calculates the curved surface slope αi in the X and Y directions at each sensor mounting position by partial differentiation from the potential value P in the virtual space calculated by the image calculation unit 33 described above.
Determine βi to obtain 2 repulsive force F, combine it with the virtual attraction force described later, combine the translational displacement control amount (velocity y) xr, yr with the virtual rotational force described later, and calculate the attitude control amount. υ, slope calculation mechanism 34a, virtual gravity calculation mechanism 34b
, outer product parts 34C1-b, rotation angle integration part 34f, addition part 34g, translation integration part 34h
have.

The slope calculation mechanism 34a calculates the X and Y values explained in FIG.
The partial differential in the direction is determined at each sensor mounting position Ai to determine the nine curved surface inclinations αI and βl, which are obtained using the 99th equation.

Senna installation vector 8 s-8n, installation is at position A1~
Obtain and find An.

However, +RI'=(Sxt-Xi)"+(Sy+-Y
+)”Furthermore.

are calculated, and the curved surface slopes αi and βl of each mounting position are obtained. Further, the virtual gravity calculation mechanism 34b calculates the accelerations
1 and calculates the repulsive force F using the αth equation.
i and senna installation position vector S! ~Cross product with Sn8. X
F.

The dividing unit 34d converts the virtual rotational force described later into a value of 1/mass m, and the adding unit 348 calculates the sum of the cross products of the cross product parts 34c1 to 34cn.

The two-rotation angular portion 34f calculates the moment M of the 19th formula and adds it to the virtual rotational force from the dividing unit 34d.
mr 1st12) Lte fjt minute * Rotation control amount φ
, which outputs .

The adding unit 34g calculates the sum of the repulsive forces F from the virtual gravity calculation mechanism 34b, and calculates the translational force F(F,) of the αe-th equation.

Fy) and adds virtual attraction forces from a virtual attraction generation unit 35 to be described later, a translational integration unit 34h calculates the combined accelerations Xr and Yr of the addition unit 34g by 1/Msl.

The translational control amounts x, , 'r' are obtained by integrating the equations.

35 is a virtual suction force generation unit that generates an induced acceleration force, which is a suction force in the translational direction from the position deviation Rc to the target position, and converts the position deviation Rc (Xr Proportional part 3 that feeds back as spring force
5a and 2 Differentiate the position deviation Rc to the -order (S is the Laplace operator), obtain the deviation velocity, multiply this by 0 by a proportionality constant to obtain the viscous force, and the spring force of the proportional part 35a and the derivative part 35b. It has a subtraction part 35C which subtracts the viscous force of 35b and generates an induced acceleration force.

36 is a virtual rotational force generating section and has a two-rotation error φ. It is a device that generates a rotational force to the target rotation angle φ.

A proportional section 36a that multiplies the rotational differences φC (φ, -φ) by a proportional constant and feeds it back as a spring force.

Differentiating section 3 that differentiates the rotational error (deviation) φC to obtain the deviation rotational speed, and multiplies this by 0 by a proportionality constant to obtain the viscous force.
6b, and a subtraction section 36C that generates a virtual rotational force by subtracting the spring force of the proportional section 36a and the viscous force of the differential section 36b.

Next, the operation of the embodiment shown in FIG. 8 will be explained using FIGS. 9 and 10.

The outputs of the sensors 21 to 2n of the robot 1 are converted to coordinates by the coordinate transformation unit 3.
The coordinates are transformed at 0, and the relative coordinates from robot 1 are R+ (
Xi P Y+ ). On the other hand, the control deviation generating section 31 generates a position deviation Rc (Xc, Yc) and a rotation error φ. of which Rc is converted into a three-dimensional image P1 by the image conversion unit 32 according to equation (6). At this time K.

If the gain for R1-island is taken as positive, while the gain Kl for Rc is taken as negative, the virtual sky M as shown in FIG.
I S Teha, Ifl [Harmful OB 1, OB 20
Images Pa and Pb have a normal distribution shape with heights in the positive direction of the P axis.

On the other hand, the image of the target position (Xr, Yr), that is, the image Pc due to the positional error, has a normal distribution shape with a height in the negative direction of the P axis. Therefore, when the image calculation unit 33 calculates the sum of these using equation (7), the potential surface (composite function) shown in FIG. 9 is obtained, and in the virtual space Is, at the position where the obstacle exists,
Generate a white part that becomes O.

On the other hand, a concave portion where + < (j) is generated at the target position.

This means that the robot 1 will not roll from the higher side to the lower side along the potential surface in the virtual space IS due to the translational and attitude control amounts described later, and will end up on a movement trajectory that avoids obstacles. A machine M is formed and moves toward a target position along a trajectory RM corresponding to the trajectory IM in real space under translation and attitude control.

For this reason, the conversion unit 34 calculates the two curved surface inclinations αi and βl using the wholesale formula and the US formula, calculates the slope accelerations Xrl and Yrl using the formula (11) and the second formula, and calculates the slope accelerations Xrl and Yrl using the formula (13). Obtain repulsive force Fi.

The adding section 34g calculates the sum of the repulsive forces F1 to obtain the translational control force F, and similarly, the adding section 34e calculates the sum of the cross products of the repulsive forces F and the mounting vector SI.

Attitude control force (moment) M is obtained.

These are created by the repulsive force obtained from the virtual space by the output from the senna to avoid obstacles, and these enable translational movement and posture control to avoid obstacles.

In this example, a virtual suction force and a virtual rotational force are added to such control force.

In this virtual suction force, the control position deviation Rc from the control deviation generation section 31 generates a spring force proportional to the position deviation angle and a viscous force proportional to the deviation speed in the virtual suction force generation section 35, which are then guided. generating force. Then, an adding unit 34h combines the two combined forces with the translational control force from the virtual plane, and an integrating unit 34h integrates the two by 1/M to obtain a speed r, ♀1 as a control amount, which is then used as a translational speed command. is given to the robot 1's server system (not shown).

As a result, the robot 1 moves to the target position (Xr) while avoiding obstacles along the trajectory RM (see FIG. 9).

It will move towards Yr.

Here, a potential surface (image Pc in FIG. 9) corresponding to the two-position deviation is formed also in the virtual space Is, and the guiding force toward the target position is not zero. Therefore.

Robot 1 even if no guidance control amount (virtual attraction force) is generated.
can be said to be guided to the target position.

However, if the two-position deviation is a dog, the force that forces the robot to move toward the target becomes very small, making it difficult to guide the robot.

Therefore, we consider the influence of the image Pc of the target position on the virtual plane IS (9th
If you try to increase the size in Figure 2 and change the shape of the local function (Equation (6)) generated at the target position.

Stable guidance control requires dynamic shape changes depending on the two-position control deviation and robot speed, which complicates the control mode and makes it difficult to set the guidance characteristics to desired characteristics.

Therefore, as shown in FIG. 8, a spring force proportional to one position deviation and a viscous force proportional to the deviation speed are generated.

These two values compensate for positional deviation.

It is designed to compensate for the guidance speed.0 This allows for reliable guidance control while maintaining an appropriate approach speed even if the initial control deviation is large. By adjusting it, the induction characteristics can be changed.

In addition, in the virtual rotational force, the rotational deviation φ from the control deviation generation section 31. However, the rotational deviation φ occurs in the virtual rotational force generating section 36.

A spring force proportional to 9 and a viscous force proportional to the rotational deviation speed are generated, and a virtual rotational force is generated from this. and,
The adding unit 34e combines the resulting one with the attitude control force M, and the integrating unit 34f multiplies the result by m/I and integrates the resultant control amount.
is obtained and similarly given to the servo system of the robot 1 as a rotation speed command. It is possible.

However, posture control only from the virtual space Is.

Because there is a risk of unstable posture control and vibration depending on obstacles, such a target rotation angle
By applying a virtual rotational force based on 1, stable posture control is possible.

In such a system configuration, a dynamic model including a virtual space is formed, and the equation of motion (dynamic constraint conditions) of the robot is as follows.

First, on the translational X axis.

=-cx-drinking
・・・・・・・・・・・・・・・It will be four.

Similarly in the translational Y axis.

MsY+CY1K(Yr-Y)=Fy・・・・・・・・・
・・・・・・・・・(2) On the other hand, in 9-rotation motion.

... d 1, φ=D-(φr-φ)-to(φyo-φ)+M
・・・・・・・・・・・・・・・(c) dt , °, kφ+Dφ10(φr−φ)=M ・・
・・・・・・・・・・・・・・・C4) Here, I=Σmt
l SIl” is the moment of inertia around the P axis passing through the center of gravity.

Based on the above, the robot 1 is constrained by the equations of general quadratic vibration systems such as equations 1, (c), and (l).

It can be seen that when it moves due to external forces Fx, F, , M, its translational motion characteristics are determined by M, , i < , c, and its one-rotation motion characteristics are determined by F, DfC.

Therefore, let us express formula 9 (19, CI!1) more concretely.

Father = Upper (CdCXr-X) - Food (Xr-X) + FX)
・・・・・・・・・・・・・・・(c) M, J
i ■=yo(c -!!-(y,-y) 4αr-y)+F
y) ・・・・・・・・・・・・・・・(a)s
dt... ml d φ=Ding(i(Ddt(φ1-φ)-to(φ1-φ))+
, F 5tXQ+) −−= Penalty* Q+= (
xrt+)'rt) and.

Illusion=fXdt, Y,=fYdt, Small,=fφd
As t.

Xr=, 7((C8(Xr-X)-K(xr-x))+
;mxri) ・・・・・・−・・−・・@Yr=g((
C8(Yr-Y)-K(Yr-Y))"mYri]...
−・・・−・・翰φ、=丙喀代S(φ, −φ)−に(φ
, -φ)) Jubang8tXQt3・・・・・・・・・(7)
However, +Ql=(xrty)'r+)S is not a Laplace operator, and it can be seen that the system constructed by the block diagram of FIG. 8 agrees with the above equation.

By performing such control, the operation as shown in FIG. 10 can be realized.

In this example, a wall is an obstacle, and a self-propelled vehicle (robot) with a four-wheel steering mechanism uses the repulsive force from the virtual space of the senna output to avoid the obstacle.

If the self-centering degree of the rotation of the robot 1 is not taken into account in the virtual space IS and only translation control is performed, the actual stopping position with obstacle avoidance relative to the target stopping position Ps is determined as shown in FIG. 10 (5). The error in Pr is a dog.

On the other hand, attitude control is also performed in the virtual space Is.

When the degree of freedom of rotation is given, the posture is controlled as if it were parallel to the wall, as shown in FIG. 10(B), and almost no error in the stopping position occurs.

In the image transformation process described above, a multidimensional normal distribution function is used for the basis functions generated as shown in equations (2) and (6), so by superimposing them as shown in equation (7), Even if a potential surface (composite function) P is formed on the virtual space Is, the continuity of the nine surfaces can be maintained, and even if it is dynamically changed from time to time by the outputs of the sensors 21 to 2n, etc., the continuity can be maintained. guaranteed, and the stability of the control system can be maintained.

Furthermore, since the continuity of the two surfaces is guaranteed, the continuity of the inclination (curved surface slope) is also guaranteed, and therefore discontinuity in the control amount can be prevented.

Furthermore, in this example, since the position error Rc is also image-transformed into the virtual space Is, the obtained control amount is 1. 1 can be used not only for simple obstacle avoidance, but also for obstacle avoidance in consideration of movement to a target position.

All of these can be realized by calculations by the program of the processor of the robot control device, and although the virtual space Is exists conceptually, in the end, the values shown in equations (6) and (7), that is, one composite function, are in the virtual space. It is not necessary to define the potential surface at Is, it is simply shown by data.

Therefore, the processor coordinately transforms the output of each sensor 21 to 2n, further calculates the position error, executes the fin equation, and X,
Find the slope in the Y direction, and then calculate the slopes of the curved surface α and β using the α-mark formula.
, and perform the following calculations to obtain the translational speed X, .
'f, attitude velocity CI)r should be output to the servo system at each sampling time.

(C) Description of other embodiments In the embodiments described above, nine composite functions are used as potential surfaces in virtual space, and a control system that adaptively controls the robot according to external conditions is explained. It can be used for all systems that require a composition function, and composition of functions is not limited to addition.

Subtraction etc. may be used as necessary.

In the embodiment described above, the control amounts for both translational displacement and posture control are obtained from the repulsive force in the virtual space.

Only the attitude control amount may be determined, and the translational displacement control amount may be determined using another method.

Similarly, the present invention may be applied to posture control of a robot that does not move (translational displacement), and it is not necessary to use virtual suction force or virtual rotational force.

Further, in the above embodiment, an ultrasonic distance sensor is used as the sensor, but other known distance sensors may be used.
Furthermore, although the example of obstacle avoidance of a mobile robot has been explained, the obstacle may be a wall and the movement may be controlled so as not to collide with the wall.Furthermore, it is not limited to mobile robots, and robots having an arm may also be used. It can also be applied to the work of work robots.2 For example, it can be applied to moving a knife to a target position, fitting an object held by a hand to a counterpart object, or performing a tracing motion of an object. However, other appropriate force sensors, temperature sensors, etc. can also be used as sensors depending on these tasks.

Although the present invention has been described above with reference to embodiments, the present invention can be modified in various ways according to the gist of the present invention.

These are not excluded from the present invention.

〔Effect of the invention〕

As explained above, according to the second invention, a multidimensional normal distribution function with continuity and fully differentiability is used as basis functions generated from input, and these are synthesized by linear combination to obtain a composite function. Therefore, it is possible to provide continuity and total differentiability to the nine composite functions, and when used particularly in a control system, stability of the system can be ensured.

Furthermore, continuity can be maintained even if the input is random or discontinuous, and continuity can be guaranteed even if dynamic shape changes occur.

Furthermore, this can be achieved by generating a versatile basis function,
It also has the effect of not requiring any compensation.

Stability of the control system can be easily achieved using such a composite function.

[Brief explanation of drawings]

FIG. 1 is a diagram explaining the principle of the present invention. FIG. 2 is a detailed explanatory diagram of the present invention. FIG. 3 is a diagram showing the relationship between real space and virtual space in FIG. 2. FIG. 4 is an explanatory diagram of function composition in virtual space. FIGS. 5 and 6 are explanatory diagrams of repulsive force conversion in FIG. 2. FIG. 7 is an explanatory diagram of operations in virtual space. FIG. 8 is a block diagram of an embodiment of the present invention. 9 and 10 are operation explanatory diagrams according to FIG. 8. FIG. 11 is an explanatory diagram of the prior art. FIG. 12 is an explanatory diagram of an existing proposal. In the figure, 1... robot. 2...Senna. R8...real space. Is...virtual space. OB...Obstacle. R3 Genealogy of real space and metaphorical space Figure 3 (Sekimaki synthesis explanation of anti-4Ig space 2 Figure 9 (A) (B) Existing embankment wood content explanatory diagram Figure 12

Claims (1)

[Claims] A composite function generation method that generates a function corresponding to an input, and synthesizes the generated functions to generate a composite function, using a multidimensional normal distribution function as the generated function, and A method for generating a composite function, characterized in that a function is generated by taking a linear combination of the generated functions.