Recent Advances in Mechatronics - Ryszard Jabonski et al (Eds) Episode 1 Part 3 pptx

Mathematical model of snake robot is realized in Matlab/Simulink gram and is based on designed construction Fig.. 3: Model of independent snake robot segment with position control system

The SIMULINK part of the framework consists of Stateflow charts, each

concerning one of the following behaviors: turn left, turn right, obstacle avoidance, right wall following and so on Every chart (behavior) obtains

the following types of information The first is a distance between the bot and obstacles coming from eleven infrared sensors The second one is the information from three axes of the accelerometer about the orientation

ro-of the robot There is also available data (a few features ro-of the image puted by the recognizing subsystem) from a camera mounted on the front

com-of the robot Furthermore, the charts are provided with information about the current intensity of the motors, level of the battery charge and, the most important, the planned tasks

Basing on the mentioned information each chart generates information about the linear velocity of point S and the turning radius R for its behav-ior This information serves as input for a kinematical model of the robot

It enables to compute a turning angle and angular velocity of every wheel

of the robot

2.3 Kinematics of the robot

Below presented is a conception which allows determining the kinematical rules for the movement of the robot Basing on the geometry of the robot there was assumed that the robot consists of the main body of 200x200

[mm] (LxB) dimensions and four driving units Each driving unit is an sembly of a motor and driving wheel of radius R w=30 [mm] Of course, it

as-is a quite big simplification – main body and driving units consas-ist of many other parts

Each driving unit has two degrees of freedom The motor drives the ing wheel Furthermore, every driving unit can rotate round axes (passing through points A,B,C,D) perpendicular to axes of the wheels The wheel

driv-base is l=160 [mm] and wheel track is b=160 [mm]

The base for the next considerations is an assumption that the robot is

con-trolled by two parameters: the linear velocity of the point S and the turning radius R

It was proposed that the robot moves in the following manner When it goes straight every motor rotates with the same speed but with inverse di-rection with respect to the side it is mounted on Rotary planes of the wheels have to be parallel to each other Turning radius goes to infinity

When the robot turns on the radius R the rotation axis of every wheel is

coincident in O point which is the instantaneous turning point of the ing robot Rotating speed of every point of the robot is ω equal to

in in out

out s

R

V R

V R

2/)

(

b R

l arctg

in out

The instantaneous radius of the circle covered by points A and D (B and C) is

2 2

) (

When the robot turns on the radius R with the linear speed V s of the point S

(centre of robot area) then the linear speed V in of points B and C and linear

speed V out of points A and D equal to

R

R V

R

V

=

4 Conclusions and future work

For this time the framework allows manually controlling (using joystick, game pad) the virtual robot Thanks to the MSC.visualNastran 4D soft-ware, there can be obtained the information about the kinematics (also dynamics) of the robot – positions, orientations, linear/angular veloci-ties/accelerations of any part of the robot or any point placed on it The second advantage of this approach is that the behavior of the robot can be assessed visually

The main disadvantage of the proposed solution is a time-consuming eration It results from the complexity of computing the contact joints be-tween the wheels of the robot and the ducts

op-6 Behavior-based control system

Since Stateflow enables to model and simulate event-driven systems and also to generate C code implementation in the future the authors are going

to further develop the behavior-based control system of the mobile robot

This research will start with the simulation of simple behaviors, e.g ing left where the robot moves to the corner, stops, turns the driving units,

turn-moves on the assumed radius to the assumed point, turns back the driving units and goes straight The others simple behaviors will be trained and then joined together When the simulation results are promising the code will be implemented into the control system of the real robot

References

[1] Adamczyk M.: “Mechanical carrier of a mobile robot for inspecting ventilation ducts” In the current proceedings of the 7th International Con-ference “MECHATRONICS 2007”

[2] Adamczyk M., Bzymek A., Przystał ka P, Timofiejczuk A.: ment detection and recognition system of a mobile robot for inspecting ventilation ducts.” In the current proceedings of the 7th International Con-ference “MECHATRONICS 2007”

“Environ-[3] A D’Amico, Ippoliti G., Longhi S.: “A Multiple Models Approach for Adaptation and Learning in Mobile Robots Control” Journal of Intelligent and Robotic Systems, Vol 47, pp 3 – 31, (September 2006)

[4] Arkin, R C 1989 Neuroscience in motion: the application of schema theory to mobile robotics In Visuomotor coordination: amphibians, com-parisons, models and robots (ed J.-P Ewert & M A Arbib), pp 649-671 New York: Plenum

[5] Brooks, R A., “A Robust Layered Control System for a Mobile bot.” IEEE Journal of Robotics and Automation, Vol RA-2, No 1, 1986,

Ro-pp 14-23

[6] Carreras M., Yuh J., Batlle J., Pere Ridao: “A behavior-based scheme using reinforcement learning for autonomous underwater vehicles.” Oce-anic Engineering, IEEE Journal, April 2005, Vol 30, pp 416- 427 [7] Moczulski W., Adamczyk M., Przystałka P., Timofiejczuk A.: „Mobile robot for inspecting ventilation ducts” In the current proceedings of the 7th International Conference “MECHATRONICS 2007”

[8] Rusu P., Petriu E.M., Whalen T.E., Cornell A.: Spoelder, H.J.W.: havior-based neuro-fuzzy controller for mobile robot navigation” Instru-mentation and Measurement, IEEE Transactions on Vol 52, Aug 2003 pp.1335 1340

“Be-[9] Scheutz M., Andronache V.: “Architectural mechanisms for dynamic changes of behavior selection strategies in behavior-based systems” Sys-tems, Man and Cybernetics, Part B, Dec 2004, Vol 34, pp 2377- 2395

Simulation and Realization of Combined Snake Robot

V Racek, J Sitar, D Maga

(a) Alexander Dubcek University in Trencin, Studentska 2,

Trencin, 911 50, Slovakia

Abstract

The paper is deals with verification of mechanical construction design by simulation of combined snake robot This robot can be used for various applications Universality of the solution is assigned by special construc-tion of snake robot This construction is consisting of independent seg-ments design Each of designed segments can realize not only linear movement but curving movements too Verification of designed structure

is realized in program Matlab/Simulink Obtained results are presented in video and picture format Designed and simulated model can be realized from lightweight materials mainly from duralumin, bronze and from nylon

1 Modeling and simulation of snaking system

Fig 1: Model of combined snake robot construction Model is consisting of four

independent segments

Mathematical model of snake robot is realized in Matlab/Simulink gram and is based on designed construction (Fig 1) Complete model is

pro-consisting of subsystems These subsystems are described all prismatic and rotary bonds, movement definitions for different environments types and different controls system As is mentioned before all robot movements are based on prismatic and rotary bonds These bonds are arranged in lines as

is shown in Fig 2 All this lines models are connected to the central agonal part In the final solution only two basic type of arm mechanisms are used (Fig 2) First one type is substitution of cogged dovetail guide way Each end is finished with rotary joints Rotation angle of these joints

hex-is 25º Model hex-is conshex-isting of two rotating and one prhex-ismatic bond as hex-is shown in Fig 2a) Movement and angle displacement is defined by drive control (joint sensor and joint actuator) Joint sensor is used for measure-ment of actual bond position and the joint actuator is used for bonds movement control Rotary bonds are substituted by universal bonds With universal bonds is possible create revolution in three axis of Cartesian co-ordination system Second mechanism type is substitution for central con-nection part This part is used to stabilization of mutual position between two independent segments This model part is without drive unites (joint actuators) and is consisting of two simple prismatic bonds which are con-nected by rotary bond (universal rotary bond) In Fig 2 b) the internal structure of central connection part with kinematics block diagram is pre-sented

Fig 2: Internal structure of individual

mechanisms and arms of snake robot

sys-tem (prismatic and rotary bonds): a)

cog-ged dovetail guide way structure b)

struc-ture of central connection part

Fig 3: Model of independent snake robot segment with position control system together with his kinemat- ics block diagram

From both of these interconnections are created simple subsystems PosM and Os In subsystem PosM are described all connections and bonds in cogged dovetail guide way In Os subsystem is defined structure of central

connection part After connection of three PosM subsystems and one Os subsystem to the one central item described in Body block with name Disk1 the model of one independent snake robot segment can be created The output block diagram is presented in Fig 3 together with control sys-tem and alternative kinematics block diagram Final mathematic model of combined snake robot is realized by four independent robot segments Segments are connected together as is shown in Fig 3 Internal structure connection of snake robot mechanism is shown in Fig 4 Complete movement is realized in block machine environment and is set into the kinematics calculation Snake robot movement is possible thanks to the prismatic and weld bonds which are connected with machine environment With assistance of these bonds is possible realized rotational and transla-tional movement in Cartesian coordinate system

B F

Wel d

Env

Ma ch ine

Environ me nt Gro und

axe of the disc 3 input Disc 3.1 input Disc 3.2 input Disc 3.3 input Disc 5

Dics 4 m ov em ent Disc 3.1 input Disc 3.2 input Disc 3.3 input axe of the disc 3 input

out disc 4.1 out disc 4.2 out disc 4.3 axe of the disc

Di sc 4

Disc 3 m ov em ent Disc 3.1 input Disc 3.2 input Disc 3.3 input axe of the disc 3 input

out disc 4.1 out disc 4.2 out disc 4.3 axe of the disc Disc 3

Disc 2 m ov em ent Disc 2.1 input Disc 2.2 input Disc 2.3 input axe of the disc 2 input

out disc 3.1 out disc 2.2 out disc 2.3 axe of the disc

Fig 4: Model of internal structure of

combined snake robot assembly

Fig 5: Complete model of bined snake robot with control sys-

com-tem

In Fig 5 the final model of snake robot mechanism is shown and is consist

of presented subsystems Control system for complete set is realized by generating of input control signals

har-is presented maximal length of snake robot In thhar-is case all prhar-ismatic bonds are protuberant to the maximum possible expanse state

6 Simulation and realization of combined snake robot

Fig 6: Simulation of snake robot activity

(caterpillar movement), primary position –

minimal length of snake robot is turned

into the final position – maximal length of

snake robot

Fig 7: Simulation of four ment snake robot (orientation angle between two segments is maximally 30º)

seg-Changes in angular position between snake robot segments can be seen in Fig 7 and is realized by motion control of individual prismatic bonds In reality these prismatic bounds are created from cogged dovetail guide ways and servomotors with cogwheel Gear drive in servomotor is equili-brating actual prismatic position

Realization of snake robot

For verification process two independent segments are created (Fig 8) Connection between segments is realized by guideways with servomotor (distance changes) and ball joints (rotation in all directions)

Fig 8: The experimental set of snake robot (set is consist of two segments)

The maximal possible angle between these two segments is 35º and is ited with central connection joint Distance between segments is from 12cm to 20cm Verified model have instabilities in ball joints (rotation) For this reason the ball joints are displaced by cardan universal joints

Fig 9: Design of cardan universal joint without axis rotation

Conclusion

The paper is focused on construction design verification, basic motion type simulation of combined snake robot Model is simulated by Mat-lab/Simulink program for several types of movement (caterpillar move-ment, side waving, worm’s movement and harmonic movement) These movements’ types pertain to the different robot activities These combined snake robots can be use for many applications as inspection and service activities of unavailable equipment, for pipes inspection, for explore of underground and thin passages

Acknowledgement

Combined snake robot is the result from support of Research Grant Agency VEGA, project number: 1/3144/06: Research of Intelligent Mechatronics Motion Systems Properties with Personal Focus on Mobile Robotic Systems Including Walking Robots

References

[1] Matlab, Simulink - Simulink Modeling Tutorial - Train System

[2] K Williams, „Amphibionics Build Your Own Biologically Inspired Reptilian Robot“

[3] Copyright © 2003 by the McGraw-Hill Companies, Inc

0-07-142921-2

[3] L Karnik, R Knoflicek, J Novak Marcincin, „Mobilni roboty“, Marfy Slezsko 2000

[4] http://www.fzi.de/divisions/ipt/WMC/walking_machines_katalog/walk ing_machines_katalog.html

1 Simulation and realization of combined snake robot

Design of Combined Snake Robot

V Racek, J Sitar, D Maga

(a) Alexander Dubcek University in Trencin, Studentska 2,

Trencin, 911 50, Slovakia

Abstract

The paper is deals with mechanical construction design and simulation of designed structure of combined snake robot This robot can be used for various applications Universality of the solution is assigned by special construction of snake robot This construction is consisting of independent segments design Each of designed segments can realize not only linear movement but curving movements too Obtained results are presented in video and picture format Designed and simulated model can be realized from lightweight materials mainly from duralumin, bronze and from nylon

1 Introduction

Basis inspiration for construction of snake robots are life forms – snakes, who populating in large territory on Earth To move used variously meth-ods of movement that are depended from medium in which are (sand, wa-ter, rigid surface et al.) They can move in slick surface or slippery surface, climb on barrier and so negotiate it Snake robots architecture in conjunc-tion with large numbers degree of freedom makes is possible to three-dimensional motion Snake robots are defined slender elongated structures that consist of in the same types of segment that are together coupled The mode of moves flowing from two basic motion models of the animals – snake and earthworm The bodies of these animals are possible think it an open kinematics chain with a large number of segments that are coupled

by joints It is making possible between this segments actual rotation around two at each other vertical axis The advantage of this design is high ability at copied broken terrain The snake robots are used in compliance with choices construction and movement in terrain with large surfaces bumps, different types of surfaces etc The main disadvantage is low speed

and energy title that directly relate with type and number of used engines The snake robots with large number of segments are used for inspection and service activity within hardly accessible conveniences, pipes in under-ground and narrow spaces At the present time is began implement also in fire department and automobile industry Additional zone usable snake robots are by motion in a very broken terrain that is unsuitable for wheeled

or walking robots In this case is construction of the snake robots it tures small number of segments with rigid structure at which is able to outmatch barriers that are superior to half-length

fea-TABLE I: Advantages of the snake robots

Mobility in

terrain

Makes it possible to movement through rough, soft or viscous terrain, climb to barrier

Tractive force Reptiles can used all the long of body

Dimension Low diameter hull

Multiplicity The snake robots consist of number of similar parts

Defection some of mechanism part can be compensated all the others

TABLE II: Disadvantages of the snake robots

Actual load Complicated transportation of materials

2 Basic movement possibilities of snake

As previous was say the snake robots may move in multiple environs Then at design is strong to analyses environs and method move of the snake robots In our design we try to combine multiple types of movement and so achieved more universality and taking advantage of the snake ro-bots Types of elementary motion are:

• Serpentine motion

• Concertina motion

• Side winding motion

• Slide shifting motion

• Caterpillar rather motion

 Design of combined snake robot

• Worm motion

In an analysis we are focus on creating combined type the snake robot that was demonstrated no fewer than three types of motion (worm motion, cat-erpillar and serpentine) In snake robots are not realized on basis of wheels but as by shrinking and tension of individual parts, rolling, wave motion etc These forms of motion are request used special type’s drives In most

of examples are use dc electric motors or servomotors with low energy severity The exiguousness drive units allow also reduction general robot dimensions In the design is important make provision for also friction be-tween surface and external robot cover In some types are requires that the using special structure of surface which emulates function real snakes skin (e.g bigger friction in reverse motion and less in direct motion) The ex-ternal cover has to conformation motion robot body and is flexible or not allowed to leak water yet

3 Design structure of the snake robot

Fig 3: Model of independent snake robot segment (construction with four

ser-vomotors, gear drive system, three prismatic systems)

The snake robots are realized in several realizations so that is minimizing number of drives and actual is achieved maximum effectiveness, moment

and force The important parameter in design structure is its locomotion

At the present time is beginning to use special modified joins so called gearless design, angular bevel, double angular bevel and orientation pre-serving bevel

In our design try combine several types of snake motion (caterpillar, pentine, worm motion and concertina), that is requested great requirement

ser-on degree freedom It is demser-onstrative mainly ser-on number of drive units in final realization of the snake robot In Fig 3 is presented model for one element of the snake robot Consist of the master hexagons on which are attachments all the moving parts (movable and rotary joins) Cross connec-tion between parts is created by toothed dovetail groove On of both back-ends are rotary joints modified in the master hexagon

The motion is realized by four DC servomotors with performance 35-45 Ncm Three servomotors are used for drive toothed dovetail grooves In this manner achieve disengagement and swiveling part of the snake robot Total length of the dovetail groove is 110 mm and its maximum extension

is 190 mm That means single part is possible extension about 80 mm that present 88 % lengths of one parts As was firstly mentioned is possible realized not only protraction but twirling of the individual segments to-wards themselves Movement realization is based on optimal control algo-rithms selection This algorithm is dependent mainly on surrounding envi-ronment, obstructions and on selected movement type Maximal rotation angle of one segment is from 25º to 35º

Fig 4: Model of combined snake robot construction Model is consisting of four

independent segments

Rotational angle is dependent mainly from quality of rotational joints With designed construction is obtained high flexibility of snake robot Fourth servomotor is used to increasing and decreasing of segment dimen-

 Design of combined snake robot

sion With gear drive assistance the moment from servomotor is delegated

on prismatic bonds These prismatic bonds are located in three arms nected to the central hexagon Servomotor is located in position where don’t hobble the next three servomotors in their work Diameter of one segment is 160mm and can be resized to 220mm Construction is created from lightweight materials as nylon, duralumin, bronze and aluminum With this materials can be reached the lover weight of snake robot This is proving on power and dimensions of used servomotors

con-Conclusion

The paper is focused on construction design and basic motion of combined snake robot Basic construction of snake robot is designed for various en-vironments which are presented by various robot movements Model is realized in construction program for several types of movement (caterpillar movement, side waving, worm’s movement and harmonic movement) These movements’ types pertain to the different robot activities These combined snake robots can be use for many applications as inspection and service activities of unavailable equipment, for pipes inspection, for ex-plore of underground and thin passages

Acknowledgement

Combined snake robot is the result from support of Research Grant Agency VEGA, project number: 1/3144/06: Research of Intelligent Mechatronics Motion Systems Properties with Personal Focus on Mobile Robotic Systems Including Walking Robots

References

[1] Matlab, Simulink - Simulink Modeling Tutorial - Train System

[2] K Williams, „Amphibionics Build Your Own Biologically Inspired Reptilian Robot“ Copyright © 2003 by the McGraw-Hill Companies, Inc 0-07-142921-2

[3] L Karnik, R Knoflicek, J Novak Marcincin, „Mobilni roboty“, Marfy Slezsko 2000

[4] http://www.fzi.de/divisions/ipt/WMC/walking_machines_katalog/walk ing_machines_katalog.html

Design of small-outline robot - simulator of gait

of an amphibian

M Bodnicki (a) *, M Sęklewski (b)

(a) Institute of Micromechanics and Photonics, Warsaw University

of Technology, 8 Św A Boboli Str 02-525 Warsaw, Poland

(a) Graduate of Institute of Micromechanics and Photonics, Warsaw University of Technology, 8 Św A Boboli Str 02-525 Warsaw, Poland

Abstract

A subject of presented work ware design and construction of a prototype

of robot, which can move, like an amphibian, for example salamander A lot of issues were considered in this work connected to quadrupeds, par-ticularly amphibians Robot, which has been built, generates both types of gait: walking gait and swimming gait Modular structure is one of its fea-tures, and constructed modules are fully interchangeable This feature makes that construction easy to reconstruction and makes it multitasking Considered device is a great base for a further development of animals-like robots and is a very valuable tool for didactic purposes It is a typical ex-ample of mechatronic device structure, which combines mechanical and electronic parts with software

1 Introduction – four legs microrobots inspired

by biology

A walk or a swim are typical form of the number of animals Some of them connect both forms of the movement A movement of them is study-ing by biologists, biomechanics and now – specialists in robotics There is popular tendency in microrobotics to design objects inspired by mechani-cal solutions of the Nature There are analyzed a walk structures [1] as well as maintained amphibious ones [2,3,4] The directly inspiration for authors were works of Ijspeert at team [3,4], especially presented algo-rithms of the motion and analysis of the walk/swim phases

2 General characteristics of the robot build in IMiF

The works realized in Institute of Micromechanics and Photonics, Warsaw University of Technology had following stages: design of electromechani-cal components, adaptation of control algorithms and implementation of them on PC and test of work of prototype The modular structure of the robot was assumed (its block diagram is presented on Fig 1) There are used two kinds of modules:

• A – type – basic element of the body, with characteristic details: metric design, coupling element, rotary servodrive (with gear) – for re-alisation rotating movement between module and the following one

sym-• B – type – the leg module built on A – type and equipped with tional two leg units; each leg unit is driven by next two servodrives with gears

Fig 1 The scheme of the lizard-robot

A – basic module of a body (head, thorax, tail), B – legs module; C – controller

The fundamental stage of the design process was analysis of the ics of the legs and – in effect – assumption of the structure of the B module first, and then – a control algorithm

kinemat-As the actuators systems of 18 servodrives (hobby-type) with SK18 troller are used Transmission from PC “master unit” is realised via RS232

con-in typical transmission protocol Servodrives are control by PWM signals The structure of the modules possible the battery supply, but prototype is supplied from outside source (6V)

3 Analysis of a joint structure of legs

The possibility and quality (realism) of the walk depends on the degrees of freedom in joints of the legs The structure apply in the robot consist from

two joints and two-segment legs (a tight and a shinbone, without a feet) A scheme of the leg is shown on Fig 2 and the general view on robot – on Fig 3

ϕ ϕϕ ϕ

ϕ ϕϕ ϕ ϕϕϕϕ

Aϕϕϕϕ1 angle (in shoulder joint) - this degree of freedom establishes length

of the step of quadruped From point of view of realization of a translation changes of this angle is the most important The range of the ϕ1 angle is usually about π, but could measure to 2π In robots is possible to generate the movement using only this degree of freedom – with legs sliding on a surface (but there is necessary blocking mechanism for support phase), e.g

by change of a friction coefficient according to move direction like “seal skin” for skiing

A ϕϕϕϕ2 angle (in the shoulder joint) - this degree of freedom establishes rise

of the leg in carriage phase, and is very important during the movement The ϕ2 angle gives the change of leg position in carriage phase – which enables avoiding of obstacles as well as to distinguish legs in support phase The range of the ϕ2 angle is usually about 1/4π, but value to 2/3π

is better for bigger obstacles

A ϕϕϕϕ3 angle (in the elbow joint) - during the walk of the quadruped this

angle makes possible change of the trajectory – movement by the line, curve or sideways (than the length depends on ϕ3 and ϕ1 is an equivalent

of ϕ3) The end of the leg can be located in the selected point in the space (according to kinematic of the mechanism) The range of the ϕ2 angle is usually about 1/4π, and for folding of the legs this angle has to measure to

π It means that the realization both swim /walk phases and realistic turn depends on this angle

 Design of small-outline robot - simulator of gait of an amphibian

4 Control algorithms and software

The control software is an integrated part of the robot In presented phase

of the works operator of PC microcomputer realizes all control options The block diagrams of the main algorithms is presented on Fig 4

Initiation of primitive variables

START

Generation of the move?

End of programme?

Calculation of current walk parameters

Generating of walk/swimm Calculation of current position

of the servodrives (angle ⇒⇒⇒ PWM)

Generation of the transient move

Choice of the move

Visualisation Sending data to controller

Yes No

Change of the move type phase?

Drawing of control parameters

Procedures of the walk Procedures of the swim

by main window is realized via buttons (fields) no 6 The 7 button izes the move For a change of the variant walk/swim the button 8 is used Initialization of the button 8 starts the special procedure, which begins change of the legs position after full cycle of the move The amplitude of the bow of the body is automatically and fluently minimized to zero and than returns to nominal value

[4] M A Ashley-Ross Miriam, Journal Exp Biol v 193 (1994) pp

255-283

1 Design of small-outline robot - simulator of gait of an amphibian

The necessary condition for information

usefulness in signal parameter estimation

Grzegorz Smołalski

Department of Biomedical Engineering and Instrumentation,

Faculty of Fundamental Problems of Technology, Wrocław University

of Technology, WybrzeŜe Wyspiańskiego 27, 50-370 Wrocław, Poland

Abstract

The entire knowledge available of the investigated signal has been sented as a set of specific constraints imposed in the signal space The no-tion of the subsets' cluster was introduced and used for formulating the necessary condition for both direct and indirect usefulness of the given information item in estimating the needed parameter of the signal Since the checking procedure for the presented necessary condition is quite sim-ple, it seems to be a practical tool for elimination of useless information items

repre-1 Introduction

A one-dimensional signal is a typical object of measurement and the value

of certain parameter of such a signal is a typical measurement purpose

Here, the parameter of interest E is referred to as the estimated parameter

and the maximum, acceptable value of this parameter uncertainty, which is

usually given or tacitly assumed, will be denoted as E∆

The procedure of the parameter estimation is always performed in stances of a preliminary knowledge of the investigated signal (see, e.g., [1-6]) This knowledge is usually composed of the set of individual informa-tion items A signal investigation consists in the measurement of the value

circum-of certain parameter M or the whole set circum-of them The estimation circum-of the value of the required parameter E is finally performed thanks to all the ac-

quired knowledge of the signal A crucial point in the procedure is then the verification of an information item usefulness in the reduction of the esti-mated parameter uncertainty

2 Information item as a restriction in the signal space

If an adequate mathematical model of the investigated signal u(t) is

neces-sary for the time interval of the finite length only, the generalized Fourier series may be used:

(

n n

n b t c t

investiga-(1) truncation to the first N terms This way, the finite-dimensional

nu-merical representation { }N

n n

c =1 is obtained for the signal Any signal ment investigated in practice may then be mapped into the N-dimensional

seg-vector space which will be referred to as the signal space

The entire available knowledge of the investigated signal is usually posed of a number of individual information items:

com-J

II II

These items may refer not only to various signal properties but also to various signal components originated from various physical phenomena [3,7] All individual information items are, in turn, connected by the ap-propriate logical functions which determine the logical structure of the available knowledge The most typical relation, which is often tacitly as-sumed, is the logical conjunction

Each information item II imposes a specific constraint in the signal i

space, of the form:

0)

,

,( 1 2 N >=<