The method of calculating the temperament of man and robot

The article provides the author's definitions of the emotions of the robot and the predominant type of temperament. The definition of harmonic emotion is introduced as a particular case of the robot emotion. The derivation of the formula of the predominant type of temperament based on harmonic emotion is given. The ranges of numerical values ​​of temperaments corresponding to the predominant types of temperament of melancholic, phlegmatic, sanguine and choleric are offered. Algorithms for calculating the numerical values ​​of temperament, based on the processing of the amplitude of the sound wave fed to the audio input of a computer-robot through a microphone, are described. A brief description of the program that allows you to calculate the prevailing type of human temperament. The results of verification of the mathematical model of temperament, based on harmonic emotion, are given by field experiments with a person. Experiments have shown the possibility of using a mathematical model of the temperament of a robot to determine the prevailing type of human temperament.

Introduction

Currently, the robotics market is growing rapidly. So according to forecasts, only in Japan in 2016, investments in robotics will amount to $ 10 billion [1]. In this market, humanoid robots with psychological traits inherent in humans will occupy a significant part. Robots are programmable machines, so it is important to describe their “psychological” qualities in the form of formulas and give numerical values ​​to these qualities.

The history of the development of humanlike robots is described in detail in the monograph [2].

In [3, 4], the algorithm of the emotional upbringing of the robot and the correspondence of the emotional upbringing of the robot to the results of its logical thinking is given.

This article is devoted to the construction of a mathematical model of the temperament of a robot, as one of the analogs of human psychological qualities, and to the determination of the numerical characteristics of melancholic, phlegmatic, sanguine and choleric people.

Mathematical model of temperament

We will assume that a robot, like a human, is experiencing emotions. In [5], a mathematical definition of a robot's emotion is given. This definition is given below.

Definition 1 . A robot emotion is a function that satisfies the conditions:

1. Scope , - time.

2 - differentiable by , continuous and unique function on .

3 and .

4. In the domain of definition, there is a single point z , such that: and

The duration of the robot's emotions will be called tact. Let the robot constantly experiences emotions, and each clock has its own sequence number.

We introduce the following definition.

Definition 2 . A harmonic emotion is a function.

, (one)

Where - constant inherent tact; ; , - the beginning and end of the cycle i, respectively.

In the future, the constant We will call the amplitude of the harmonic emotion.

According to definition 1, it is easy to show that the harmonic emotion is the emotion of a robot.

Based on the definition of 1 robot emotion, the temperament of the robot is defined in [2].

Definition 3.

The temperament of the robot satisfies the ratio

, (2)

where . - the number of robots - serial number of the robot, –– The robot's emotion formula for tact.

It is easy to see that temperament is a dimensionless quantity belonging to the [0,1] segment. According to the formula (2) it can be concluded that the larger the value the more temperamental the robot in tact .

It is easy to see that the temperament of an individual robot is determined relative to the group of robots in question.

Based on definitions 1–3, it is easy to get a ratio that determines the temperament of a robot for harmonic emotion:

. (3)

In the works [2, 5] the definition of elementary education of the robot is given. in tact :

.

Obviously, the elementary education of the robot ,, based on harmonic emotion, has the form

, , (four)

Where - duration of tact

Consider the task of calculating the temperament of a robot, when its harmonic emotions depend on the sound signal coming to the robot's audio input through a microphone.

We hypothesize that the elementary education of the robot, defined by the relation (4), with harmonic emotions is equivalent to the integral characteristic of amplitude sound wave input to the robot audio input for each measure .. In this case, the ratio

. (five)

Equating the right sides of relations (4) and (5) to each other, we obtain the equality

from which the formula follows:

. (6)

When taking into account the relation (6), the formula (3) takes the form:

. (7)

Software implementation

The work of the program is based on processing the voice of a person entering the audio input of a personal computer through a microphone.

The temperament of the robot is calculated on the basis of a single tact with duration 5s.

To calculate the integrals of the amplitude of the sound wave in the formula (7) the method of rectangles [6] is used.

The application of this method is due to the fact that in a personal computer a sound wave is represented as a step function [7] with a discretization step equal to the characteristics of a recording device. It is this step that is chosen as the step of numerical integration in the calculation of the integrals in formula (7). According to [6], the error in replacing the amplitude of the sound wave with its numerical integration is equal to .

Thus, the approximate calculation formula for calculating temperament is:

, (eight)

where

We will assume that the robot has four types of temperament [8]: melancholic, phlegmatic, sanguine and choleric. Table 1 shows the types of temperaments of the robot and shows the proposed ranges of values ,, corresponding to these temperaments.

Table 1. Robot temperaments

Verification of the model with field experiments

It is known that a person has a so-called predominant type of temperament, which can be characterized by the main features of his emotional behavior [8].

In order to determine whether the proposed mathematical model of the temperament of the robot corresponds to the predominant type of human temperament, experiments were carried out using the program described above.

As a reference of the aggregate of the prevailing types of human temperaments, a database of voices was used for various emotions, the audio recordings of which are given on our website [9].

Since the calculated value of temperament very much depends on the amplitude of the sound wave arriving at the audio input of a personal computer through a microphone, before conducting experiments, the distance from mouth to microphone was determined as follows: an expert psychologist who knows his dominant type of temperament changes the distance from his mouth and microphone; at the same time, the expert periodically repeats any phrase in a normal voice for 5 seconds; the distance from the microphone to the mouth of a person is considered suitable for experiments if the computer-calculated temperament coincides with the real predominant type of temperament of the expert. After determining the required distance to the microphone, the program is launched. To determine the prevailing type of temperament, the person being studied utters any phrase in a normal voice also for 5 seconds. The program returns the value of the temperament of the subject, according to which Table 1 also determines the prevailing human temperament.

68 people took part in the experiments. Teachers of the Department of General and Clinical Psychology of Perm State National Research University were involved as experts determining the compliance of the prevailing type of human temperament with the temperament computed by the program.

On the basis of computer experiments and expert assessments of specialists, studies have shown that in 84% of the calculated temperament corresponds to the predominant type of temperament of the people studied.

This indicates the adequacy of the mathematical model of the temperament of the robot and the correctness of the choice of ranges of variation of values ​​corresponding to each of the prevailing types of human temperament.

Conclusion

Thus, the proposed article shows the possibility of using harmonic emotion to determine the prevailing type of human temperament, a method for determining the temperament of a robot and the prevailing type of human temperament using the amplitudes of the human voice sound wave transmitted to a computer through a microphone. The good agreement between the experimental results and the mathematical model of temperament confirmed the possibility of using the mathematical model and the proposed intervals of values ​​of the calculated temperaments to describe the robot temperament and the prevailing type of human temperament.

Literature

1. URL: http://www.videolandia.ru/?act=show&id=3535&rasd=video (contact date 02/25/2014)

2. Pensky OG, Chernikov K.V. Fundamentals of the mathematical theory of emotional robots: a monograph. - Perm: Perm.gos.un-t. –2010. –256s.

1. Pensky OG, Chernikov K.V. Mathematical models of psychological installations of robots // Artificial Intelligence and Decision Making - Moscow: Institute of System Analysis of the Russian Academy of Sciences. - 2013, №2. - C.63 - 67.

4. Pensky O., Sharapov Y., Chernikov K. Non-Absolute Memory Matrix Models // Intelligent Control and Automation - Springer. - Vol.4, No.2, May 2013 - P.115 - 121.

1. Chernikov K.V. Mathematical models of robots with non-absolute memory. Thesis for the degree of Candidate of Physical and Mathematical Sciences. - 2013.

6. Kalitkin N.N. Numerical methods.- M .: Science. - 1978. - 512 s.

7. Oppenheim A.V., Shafer R.V. Digital Signal Processing. - M .: Communication, 1979. - 416 p.

8. Ilyin E.P. Psychology of individual differences. - St. Petersburg: Peter. - 2004. - 701 s.

1. Berlin Database of Emotional Speech. URL: http://pascal.kgw.tu-berlin.de/emodb/index-1280.html (accessed: February 19, 2014)