JPS6228872A - Trigonometric function generating processor - Google Patents

Abstract

PURPOSE:To obtain rapidly the value of a trigonometric function without using a large scale memory by providing a switching control part for controlling the selection of a polynomial approximate value calculating part or a difference calculating part. CONSTITUTION:When the number of times of continuously starting the difference calculating part 11 exceeds a prescribed number Nmax as the result of decision of a difference calculation starting frequency deciding part 13, the switching control part 12 starts the calculating part. When angular change DELTAtheta between the current angle theta and the preceding angle theta0 exceeds a prescribed value DELTAthetamax2 as the result of the decision of an angular change deciding part 14, the control part 12 starts the calculating part 10. In other cases, the difference calculating part 11 is started to control the execution of calculation of a trigonometric function. When the angular change is larger than a prescribed value DELTAthetamax1, the angular change DELTAtheta is divided into plural changes less than the DELTAthetamax1 and calculating part 11 is started to calculate the divided changes respectively.

Description

[Detailed Description of the Invention] [Summary] In a trigonometric function generation processing device that sequentially inputs continuously changing angular information and outputs a trigonometric function value corresponding to the angular information, there is provided a means for calculating a trigonometric function by polynomial approximation. 2
and a means for calculating changes in trigonometric functions from changes in angle using the principle of simple harmonic motion, and calculating trigonometric functions by polynomial approximation when the changes in angle are larger than a predetermined value for the first time and when the changes in angle are larger than a predetermined value. In other cases, the present invention discloses a trigonometric function generation processing device that generates trigonometric functions with high precision and at high speed by determining the trigonometric functions based on changes in angle.

[Industrial application field]

The present invention relates to a trigonometric function generation processing device, particularly 1, a trigonometric function s necessary for controlling a link mechanism of a robot, etc.
The present invention relates to a trigonometric function generation processing device that can generate inθ and cosθ at high speed.

[Conventional technology]

FIG. 3 shows a block diagram of the robot control device.

In the figure, 20 is a robot, 21 is a central processing unit that performs overall control according to the work plan, 22 is a numerical processing unit that mainly performs numerical calculations, 23 is a memo IJ, and 24 is a servo control circuit that operates the joints of the robot 20. , 25 is a rotation angle detection circuit for detecting the rotation angle of each joint based on the output of the encoder, and 26 is an interface bus.

The robot 20 is an articulated robot.

In the base coordinate system, in order to cause the robot 20 to perform desired control, it is necessary to perform coordinate transformation based on the current value detected by the two-rotation angle detection circuit 25 and the target value instructed by the central processing unit 21.

Trigonometric function calculations are required for processing such as coordinate transformation.

Generally, when calculating trigonometric functions using a digital processing device, there are two methods for calculating trigonometric functions: polynomial approximation calculations.

A method is used in which all trigonometric function values are stored in a table in memory in advance and referenced using addresses corresponding to angles.

[Problem that the invention seeks to solve]

Calculations of trigonometric functions required to control link mechanisms such as robots need to be performed at high speed in real time. However, when performing general polynomial approximation calculations, it is difficult to increase the speed when trying to obtain high accuracy. Also, to have all the trigonometric function values in a table in memory.

Although it is possible to increase the speed, there is a problem in that a large memory capacity is required to obtain the necessary accuracy.

The present invention aims to solve the above-mentioned problems and provides a means for obtaining trigonometric function values at high speed without requiring a large-scale memory.

[Means for solving problems]

FIG. 1 shows a basic configuration diagram of the present invention.

In the figure, 10 is a polynomial approximation calculation unit that calculates trigonometric functions by polynomial approximation such as the so-called Chebyshev approximation, 11 is a difference calculation unit that calculates trigonometric functions from the change between the previous angle and the angle input this time, and 12 is a difference calculation unit that calculates trigonometric functions from the change between the previous angle and the current input angle. Should the polynomial approximation calculation unit 10 be started?

A switching control unit switches whether or not to start the difference calculation unit 11. Reference numeral 13 is a difference calculation activation count determination unit, which determines the number of consecutive activations of the difference calculation unit 11 to a predetermined value N−.
8 is compared, 14 is an angle change amount determination unit,
Current angle θ and previous angle θ. The amount of change Δθ from Δθ is set to a predetermined value Δθ1. 15, which is compared with
8. Each represents something to be compared with.

The switching control unit 12 switches the polynomial approximation calculation unit 10 when the number of consecutive activations of the difference calculation unit J1 becomes larger than a predetermined value N n s x according to the determination result of the difference calculation activation number determination unit 130. to start.

Also, based on the determination result of the angle change amount determining section 14.

Current angle θ and previous angle θ. The change Δθ from the predetermined value Δθ1. When larger than X2, polynomial approximation calculation section 1
Start 0. In other cases, the difference calculation section 11 is activated and controlled to perform trigonometric function calculations.

This is a case where the calculation unit 11 based on the difference is activated.

When the angle change division determination unit 15 determines that the angle change Δθ is larger than the predetermined value Δθnax+, Δθ is divided into a plurality of changes each not exceeding Δθmmxl, and each of the divided The calculation unit 11 based on the difference is activated for the amount of change.

[Effect]

Given an angle θ, sin θ from this angle θ.

When calculating the value of a trigonometric function such as cos θ, polynomial approximation is generally used. In this case, in order to obtain the required precision, the order must be increased to some extent, so
It takes a lot of calculation time. on the other hand.

Since sin and cos are solutions to a simple harmonic differential equation, using this solution, it is relatively easy to calculate si as quadratic.
n, cosO values can be generated.

What is the solution to the simple harmonic differential equation?

d2x/(dθ)2−− x −−−−(1
), and this solution is .

x=Asin(θ1B) --------
--1--(21).Equation (1) is.

d x / dθ==y, dy/dθ=−x −1
31, so if we express this equation (3) differentially.

X(θ+Δθ)=X(θ)+Δθ・y(θ)y(θ+
Δ θ) = y (θ) −Δ θ ・X (θ
)-(51 therefore.

X(θ) = sinθ, y<θ) = cosθ
- (6) is the trigonometric function sin θ when the angle θ.

From cos θ, using equation (5) above, sin (θ + Δθ) and cos (θ + Δθ) where the angle has changed by Δθ
is found. However, since Equation (4) is equivalent to Equation (3) when Δθ - 0, the larger Δθ is, the greater the error in the values of 5in (θ to Δθ) and cos (θ + Δθ). do. Note that Equation (5) is faster than polynomial approximation calculation because 5in(θ+Δθ) and cos(θ+Δθ) are determined by two multiplications and two additions.

The present invention combines the generation of trigonometric functions using polynomials and the generation of trigonometric functions based on differences using the above-mentioned simple harmonic motion, and uses these functions by switching them using the switching control unit 12. Therefore, the error can be kept within a certain range, and the accuracy can be achieved at high speed and accuracy. Can often generate trigonometric functions.

〔Example〕

The above equation (4) first calculates the known sin θ, cos
A set of θ is required. Therefore, the switching control unit 12 activates the polynomial approximation calculation unit 10 at the first input. Although there are various types of polynomial approximation in the polynomial approximation calculation unit 10, for example, in order to guarantee accuracy up to four decimal places, the following eighth-order Chebyshev approximation is used.

sin θ#-0,0001824θ' + 0.008
301θ5−0.1666θgo+θ cosθ# 0.00002388θ”0.00139
θ6+0.04167θ'-0,50" + 1 -
1 --- (7 squares, -π/2≦θ≦π/2.

Equation (7) can be rewritten as ω=θ×θ.

sin θ# [(-〇, 0001824x ω+0
．． 008301) Xω-0, 16661Xω→-1
]×θ cosQ−[((0,00002388xω−0,00
139) Xω10.04167) Xω−0,5]
Xω −・−(8). Therefore, nine multiplications and six additions and subtractions are required. Now, if we assume that it takes 1 μs for addition and subtraction, and 5 μs for 2 multiplication, one set of sin and cos
It takes 51 μs to calculate.

On the other hand, from equation (5), sin/l? o, cosθ.

is known.

Δθ=θ−θ.

sinθ# sinθ0 +Δθx cosθ0c
osθ# CO3θ0−Δθx sinθ,
---------- 1/4 compared to the formula
It can be calculated in a matter of minutes.

Using the latter difference calculation can speed up the process, but
As the variation Δθ in equation (9) increases, the error increases. Therefore, the amount of change is a predetermined value Δθ.

If it is larger than xl, the calculation is performed twice, dividing Δθ=Δθ and +Δθ2. If polynomial approximation is used, it will take a little less than four times more time, so even if the change is calculated by dividing up to three times, it is more advantageous in terms of time to use calculation based on differences.

Furthermore, polynomial approximation is more advantageous than dividing Δθ four or more times, so if it is larger than Δθmax2,
Calculation is performed using polynomial approximation according to equation (8) without dividing the variation. In this embodiment, Δθ1. X
2-3Δθ□□.

Furthermore, in the differential method using equation (9), errors increase when calculations are repeated. Therefore.

If the number of repetitions exceeds a predetermined value N□8.

Calculation using polynomial approximation is performed again.

The above embodiment of the present invention can be expressed in the form of a flowchart as shown in FIG. The processing numbers described below correspond to processing numbers ① to ① shown in FIG. The initial value of N is
Set it to N□.

■ When the angle θ is input, N is counted up by 1.

■ Compare N and N□8, and if N is large, move to process ■. If N is small, control is transferred to process (2).

■ Perform calculations using polynomial approximation. here.

f(θ)1g(θ) corresponds to equation (8).

■ Set N to O to initialize the count.

■ Calculated results of sinθ, CO5θ and angle θ.

sin θ, respectively. , cos θ. , θ. and output sinθ and cosθ.

■ The current angle θ and the previous angle θ. Δθ
shall be.

(2) Determine whether the absolute value of Δθ is greater than Δθ□0. Δθ1. When it is larger than X2, the following process is executed. If it is not large, move on to the secondary process (2).

(2) Determine whether the absolute value of Δθ is greater than Δθ□□. If it is not larger than Δθ□□, the process moves to the secondary process (■), and if it is larger, the control moves to the process [phase].

■ Execute Equation (9) above and perform calculations based on the difference.

After that, process (2) is executed, the result is output, and the process ends.

[Phase] When the absolute value of Δθ is larger than Δθ□□.

If Δθ is a positive value, process 0 is executed, and if Δθ is a negative value, process @ is executed.

■ Set Δθ11X1 as a new Δθ.

■ Let −Δθ□ be the new Δθ.

0 Perform the calculation using the difference shown in equation (9), and s
Find inθ and cosθ.

[Phase] θ. Add Δθ to the new θ. Let sfnθ be sinθ0. cosθ cos
Let θ0. The difference between θ and θ0 is set as a new Δθ.

Thereafter, return to process (2) and repeat the process in the same manner.

〔Effect of the invention〕

As explained above, according to the two aspects of the present invention, it is possible to suppress errors within a certain range and generate trigonometric functions accurately and at high speed. It is also practical because it does not require a large amount of memory.

[Brief explanation of the drawing]

FIG. 1 is a basic configuration diagram of the present invention, FIG. 2 is a processing explanatory diagram of an embodiment of the present invention, and FIG. 3 is a block diagram showing an example of a robot control device to which the present invention is applied. In the figure, 10 represents a polynomial approximation calculation unit, 11 represents a difference calculation unit, and 12 represents a switching control unit. Patent applicant: Fujitsu Ltd. Representative Patent Attorney Hiroshi Mori (1 other person) Figure 3

Claims (1)

[Claims] A trigonometric function generation processing device that sequentially inputs continuously changing angle information and outputs a trigonometric function value corresponding to the angle information, the trigonometric function value corresponding to the input angle is generated by polynomial approximation. A polynomial approximation calculation unit (10) that calculates, and a difference calculation that calculates a trigonometric function corresponding to the current input angle from the change between the previous angle and the current input angle based on the previously calculated trigonometric function value. part (11), and at least the polynomial approximation calculation part (10) or the difference calculation part based on the number of consecutive activations of the difference calculation part (11) or the change information between the previous angle and the current angle. A trigonometric function generation processing device comprising: a switching control section (12) that performs control to select one of (11).