JPH01286002A - Curve interpolating system - Google Patents

Abstract

PURPOSE:To execute a calculation processing at a high speed by selecting suitably in auxiliary vector and using a locus drawn by a point on the vector to move corresponding to the action of a moving point on this vector. CONSTITUTION:A curve interpolation device is composed of a command vector calculating part 20 to prepare a command vector with the coordinates of three points, an auxiliary vector calculating part 21 to prepare an auxiliary vector with a command vector, a moving ratio calculating part 22 to calculate the moving ratio for a sampling period with a sending speed and a command vector, and a moving point coordinate calculating part 23 to calculate and output the coordinates of respective moving points. By using the coordinates of three points A to C given to the command vector calculating part 20, command vectors AB and BC are prepared and an auxiliary vector DC is prepared. Next, the moving ratio calculating part 22 adds for a sampling period with these and a sending speed F and calculates a K value. Thus, the coordinates of the moving point on the curve are calculated and outputted for the said period from these.

Description

[Detailed Description of the Invention] [Industrial Application Field] This invention applies curve interpolation that connects point A and point 0 with a smooth curve using point B as a nearby via point, in addition to the curve interpolation method % formula % in route control, etc. It is related to the method.

[Conventional technology]

When controlling the movement of a robot's hand, etc., it is important to move it quickly and smoothly through a given point! In this case, an interpolation method called path control is used.

As a conventional interpolation method of this kind, for example, "Introduction to rNC Programming" Nozawa, Atsugi (Nikkan Kogyo Shimbunsha, 1985)
Published on November 25, 2015, page 55).

Figure 3 shows this interpolation method. When three points given in space are A% B, C, the center point tangent to the straight line B(1) and straight line BG(2) is R(4 ), a circular arc (3) with a radius of r was obtained, and this circular arc was used as an interpolation curve.

In this case, the movement route is from point A' on the extension of straight line AB to point A
Pass through the arc (3) obtained as an interpolated curve via the point,
It reaches point C' on the extension of song 1aBC, and forms a smooth moving route using point B given by this interpolation curve as a nearby transit point.

(Problem to be solved by the invention) In the conventional interpolation method described above, given three points A
, B%C, and the value of the radius r, it is necessary to find the straight line B and a circle that is tangent to the straight line BG, and to find the coordinates of the moving point on the arc one after another, but in general, these methods in a three-dimensional space Calculations are complex processes involving functional operations,
A controller using a microcomputer or the like requires a considerable amount of time, making it difficult to perform high-speed, detailed real-time control.

The present invention was made to solve the above problems, and an object of the present invention is to provide a curve interpolation method that enables high-speed real-time control with simple calculation processing.

[Means to solve the problem]

The curve interpolation method according to this invention is based on 3
Among points A and B%C, when point B is a nearby via point, define point D in space to create an auxiliary vector ■, and on this auxiliary vector ■, -oc (o≦to≦1 ), and when moving this Q point along the auxiliary vector ■, we sequentially calculate the coordinates of the 'P point on the vector AQ, which is determined by the relation coefficient AP= ＾q, and convert these coordinates into It is a series.

[Effect]

In this invention, by appropriately selecting the auxiliary vector ■, the trajectory drawn by the point P on the vector AP, which moves in response to the movement of the moving point Q on this vector, passes through the point A and touches the straight line AB. , and is a smooth curve that passes through the 0 point and is tangent to the straight line BC. This method eliminates the need for complex calculations including functional operations as in the conventional method, making it simple. This enables real-time control with high-speed calculation processing.

〔Example〕

In FIG. 1, an auxiliary vector (5) is created by taking pects for explaining the present invention in detail and where ■=BC-AB-(1). To this auxiliary vector (5) DQ = K − ■ (0≦≦1) ... (2
) Take a point P.

Here, when the moving point Q moves from the point to the point C on the auxiliary vector ■, the curve (3) drawn by the point P is smooth, touching the straight line B at the point A, and touching the straight line BC at the point C. It becomes a curve.

Also, the above equations (1), (2), (3) and ^Q
= 2 AB + DQ... (4) If the relationship holds true and the value of K is given, three points A, B, C
By substituting the coordinate values of P into equation (4), the coordinates of point P can be easily determined.

Here, the vector is the moving ratio of the moving point Q on the vector ■. Therefore, when taking n division points on the interpolation curve, by sequentially substituting The interpolation point coordinates are given.

Next, a case will be described in which the coordinates of a point moving at a speed F on a curve are calculated every predetermined sampling period T.

If the length of the curve (3) from point A to point 0 is L,
The amount of increase Δ in the movement ratio due to the amount of deviation F-T of the interpolation point during the sampling period T is given by: Therefore, by increasing the value of K by Δ after each sampling period and substituting this value into equation (4) for calculation, the coordinates of the moving point on the curve can be sequentially determined.

Here, the length of vector AB%BC is 8B%B, respectively.
If C, then the length of curve (3) L=AB+BC...
・(7) The movement speed of the moving point in curve (3) obtained by the above processing takes a value close to the command speed when ZABC is large stitching, but as 4ABC becomes smaller, The oscillation velocity is also reduced, and the velocity changes according to the curvature of the curve, achieving the desired result.

FIG. 2 shows an example of the configuration of a device implementing the present invention. In the figure, (20) is a command vector calculation unit that creates a command vector using the coordinates of three points, and (21) is an auxiliary unit that uses the command vector to create a command vector. Auxiliary vector calculation unit that creates a vector (22
) is a movement ratio calculation unit that calculates the movement ratio for each sampling period using the feed rate and command vector, and (23) calculates and outputs the coordinates of each movement point using the command vector, auxiliary vector, and movement ratio. This is a moving point coordinate calculation unit.

The specific operation of this device will be explained below.

First, the command vector calculation unit (20) calculates the given three points A.
, B, and C to create a command vector AB%BC. The auxiliary vector calculation section (21) uses this command vector to create an auxiliary vector (2) according to equation (1).

Next, the movement ratio calculation unit (22) calculates the given feed rate F.
and command vectors AB and BG are added every sampling period to calculate the value of K. Then, the moving point coordinate calculating section (23) calculates and outputs the coordinates of the moving point on the curve (3) for each sampling period using the obtained command vector AB, auxiliary vector (2), and moving ratio K.

Thus, according to this device, curve interpolation is performed in accordance with the principle explanation.

In the above explanation, we have explained the case where the auxiliary vector ■ is given by equation (1), but in general, except for the condition that the curves at points A and 0 are connected smoothly, the starting point of the auxiliary vector ■ is in space. You can choose any position above.

Furthermore, in the above explanation, we have explained the case where the curve is interpolated at each fixed sampling period, but it is also possible to interpolate by dividing the curve into a fixed number of parts using the movement ratio K given by equation (5). It is.

〔Effect of the invention〕

As is clear from the above description, according to the present invention, there is no need for complex calculations including functional calculations as in the conventional method, and high-speed real-time control is possible with simple calculation processing.

[Brief explanation of the drawing]

FIG. 1 is a vector diagram for explaining the invention in detail.
FIG. 2 is a block diagram showing the configuration of an apparatus implementing the present invention, and FIG. 3 is an explanatory diagram for explaining a conventional curve interpolation method. (2G)...Command vector calculation unit, (21)...Auxiliary vector calculation unit, (22)...Movement ratio calculation unit, (23)--Movement point coordinate calculation unit. Note that the same reference numerals in each figure indicate the same or corresponding parts.

Claims (1)

[Claims] In a method of interpolating a curve connecting points A and C with point B as a nearby transit point among three points A, B, and C given in space, point D is determined in space. Create an auxiliary vector ■ and set K to 0
As a coefficient larger than 1, a moving point Q is determined on the auxiliary vector ■ such that ■=K・■, and this moving point Q is set as a coefficient on the auxiliary vector ■.
A curve interpolation method characterized by sequentially calculating the coordinates of points P determined by the relational expression ■=K・■ on the vector ■ when moving along the vector ■, and connecting the coordinates of the P points.