Automatically controlled vibration-driven robotsNikolai N. Bolotnik Sergey F. Jatsun Andrey S. Jatsun Andrey A. CherepanovInstitute for Problems in Kursk State Technical Kursk State Technical Kursk State TechnicalMechanics of the Russian University University UniversityAcademy of Sciences119526 Moscow, 50 let Oktyabrya, 94, 50 let Oktyabrya, 94, 50 let Oktyabry, 94,

Vernadsky ave. 101 b.1, 305040 Kursk, Russia 305040 Kursk, Russia 305040 Kursk, RussiaRussia

bolotnik@ipmnet.ru jatsun@kursknet.ru andj@inbox.ru

Abstract - Mobile robots are widely utilized for variousoperations in environments inaccessible to a human ordangerous for him. They are utilized, for example, forinspection and repair work in nuclear power and chemicalplants, operations in areas of wreckage after earthquakes or __blasts, or dismantling explosive devices [1,2,3,4,5,6]. Most of 1 / vthese robots move by means of wheels or caterpillars, some of \them utilize walking mechanisms. Such robots, however, F,cannot enter narrow slots (for example, during rescueoperations in a zone of wreckage) or move in dense media -F.other than gases or liquids. This justifies looking for new Rconcepts of motion to enable robots to move efficiently in 4 G xenvironments inaccessible to robots with wheel, caterpillar, oand walking propelling systems. This issue is especially /topical for medical robots designed for the motion through /rather narrow channels (e.g., in blood vessels or theintestines) or among muscles to reach an affected organ to Figure 2.perform a diagnostic or surgical operation. Hopping motion of the vibration-driven robot. 1-robot, 2-environment, 3-

supporting surface, 4-traj ectory.I INTRODUCTION

In the present paper, the concept of vibration-driven robots The vibration-driven robot is designed as a mechatronicis developed. Such robots can move in various media system consisting of the mechanical, electrical, andwithout wheels, caterpillars or legs. The propulsion of the electronic (microcomputer) components. The mechanicalrobot is provided due to vibration of internal masses inside vibration is transmitted from the vibration exciter to thethe robot and the interaction of the robot's body with the robot's body, which interacts with the environment withenvironment. The robot can move without separation from some force. The robot is equipped with a feedbackthe supporting surface (Fig. 1) or hop (Fig. 2). microcontroller to maintain an efficient operation mode

and provide prescribed characteristics of motion of theZ end-effector under the action of various disturbances. The

characteristics of the exciter vibration should be tuned to a2 specific task to be executed by the robot. This tuning can

/___ be provided on the basis of parametric optimization inwhich an operating characteristic of the robot (e.g., theaverage velocity of the robot) is used as the objective

l function.

Fzt| \ Xx , tV II MATHEMATICALMODEL AND DESIGN OF A

|~~~~~~x VIBRATION-DRIVEN ROBOT WITH A ONE-77//// X X tv///X X COORDINATE ELECTROMAGNETIC VIBRATION

G EXCITER

Figure 1 .Motion of the vibration-driven robot without separation from thesurface. 1-robot, 2-environment, 3-supporting surface. The motion of the robot can be provided by a one-

coordinate vibration exciter, the working body of whichvibrates along the line of motion of the robot (Figs. 3 and

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N. N. Bolotnik, S. F Jatsun, A. S. Jatsun, A. A. Cherepanov - Automatically Controlled Vibration-driven Robots

4). However, in this case, it is necessary that either the v, ;,characteristic of friction between the robot body and theenvironment or the exciter vibration be asymmetric. Therobot under consideration was designed for cleaningpipelines from solid deposits.

7~715 F1

b)

4 Figure 4. Pipeline-cleaner mnini-robot with an electromagnetic actuatorand two asymmetric friction elements

a) - general view of the cleaner:Figre3.chmaic f virai-dpipenwnithiaceanse liquid 2-e 1-first solid body; 2- electromagnet; 3 - anchor; 4- second solid body;asymmetric friction component. 1-pp 'hacene iud -spherical friction mechanism; 6 - elastic element.

spherical ffiction mechanism,~3- contact element; 4- movableelectromagnet; 5-spring; 6-armature rigidly attached to the contact b)- design schematic of the cleaner;

element.ToXdetermine the parameters of the cleaner robot, we

ml and i2- masses of the robot components; X1 X - generalizedTodetermine the parameters of the cleaner robot, we coordinates of masses; C and jt- spring rate and damping coefficient; C2

developed a mathematical model that describes the j -spring rate and damping coefficient of lifniter; Q -force generated byinteraction of the end-effector with the technological load the electromagnetic exciter; P- force of elastic element; R - force of(due to the resistance of the solid deposits) and the resistance; AX- length of limiter;JA -distance between masses without

electromagnetic vibration actuator. The properties of the reference of spring deformationsolid deposits can be accounted for by the Maxwell-

FirThedynamic of the robot with an electromagnetic

vibration actuator is modeled by the system of Lagrange-Maxwell differential equations

m2 T2 =P2 -R2 + F 2

Din cm c3 i-ob-t M+ I=U(t).Where:

-- - -- fc. ~~~~~~(Xi-X2 C2AX,2AX) if A<AV

There is also

p2 -PI and RI = coVc 4- R

a) 5

1,2

~~~p2Q2

Wher are &-manglesonlntoof the frictionnetsX,X-eerliemendeveope a mtheatial mdelthatdesribs th , lCsurface fatan- apncoefficient offriction; A -fditace beertweenb

interctionof th end-ffectr wit theechnoomasses;a th isecthoagetimgetici;P flux;e of ls thcurreent, W isthreo

electromagnetic ~ ~ ~ ~~~ ~ ~ mgnti energy,o R-uaor ise thprisoterfrne actspivegeectrmaioeisacno.h

solenodSdsquareof the arogapwinsid if electromagnetic

439 to cuao smdld ytessemo arne

ICM 2006 * IEEE 3rd International Conference on Mechatronics

- electromagnetic constant; U(t) is the power supply forces created by the vibration exciters one can control thevoltage, and VI V2. is velocity of masses. motion of the robot.

P(Cd t+Q9To solve the system of nonlinear differential equations y

governing the motion of the robot we utilized the softwarepackage MathCAD Professional. Based on the simulation mresults, we determined the optimal parameters of the (Cdelectromagnetic vibration exciter and analyzed the motionof the robot for various parameters of the technologicalload and various values of the friction coefficient. Theresults of the calculation of the force of friction and theaverage velocity of the robot are illustrated in Figs. 5 and Figure. 7. Dynamic model of the robot moving along a horizontal surface6. Analysis shows that the maj or parameter that affects thevelocity of the cleaner robot is the ratio of the naturalvibration frequency of the robot to the excitation frequency We have investigated the influence of the phase differenceof the electromagnet. on the average velocity of the robot. The differential

equation of motion for the robot under consideration hasthe form

Force of friction40 _ Fx sin(w.t) (mg + Fy sin(It + 0 )) C sign(X) -,u35 m

30 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~whereX-isthedisplacement of the robot (the generalized20 coordinate), 0)-is the exciting frequency, ~ i hs

T il II i *1 h t difference between the vertical and horizontal vibrations of151 1 1 1111 0 l 1001the exciters, f- is the coefficient of friction, m-is the mass10lWT t_ 0 E) E T t 4 T 4 E T tt T 4 l of the r bot, and is the drug coefficient of the

i... 0 tW 40 U E T W W E 4 environment.

0~~~~~~~~~~~~~~~~~~105,,,,,,,,,, 10 1

Figure 5. Time history ofthe force of friction 224 6 8 10 2 1468

-18

-14t

2,50E-01 l zo)

2,00E-01 - ___ - Figure 8. Time history of the displacement of the robot.

1,50E-01 j---__

|1,00E-01 -- ---__ l__

500E-02u- - il

Figure 6. The average velocity of the robot as a function of the relative -.requency o......te v ra on exci.er .or d lect l......feedn ...........

III MATHEMATICAL MODELANDCALCULATIONS FOR A VIBRATION-DRIVEN 5ROBOTWITH TWO INERTIAL VIBRATION l

EXCITERS

Figure 9. The average velocity of the robot as a function of the phasedifference and the coefficient of friction.

Consider a vibration-driven robot with two vibrationexciters to generate the inertial forces both in thehorizontal and vertical directions. This makes it possible to The numerical simulation of the behavior of the robotcontrol the normal component of the force exerted on the shown in Fig. 8 demonstrates high intensity of therobot by the supporting surface. By varying the phase vibration transmitted to the robot body. This vibration candifference between the vertical and horizontal inertial complicate the operation of the equipment of the robot

440

N. N. Bolotnik, S. F Jatsun, A. S. Jatsun, A. A. Cherepanov Automatically Controlled Vibration-driven Robots

(e.g., video cameras or manipulators) or substantiallyreduce the accuracy of measuring devices. To get rid of Figure 11. Time history of the displacement of the robot equipped withthis drawback, we propose to equip the robot with an the platform.additional platform isolated from the robot body by aspritiong-anddaspot vibration absomtherobobdyber.yMlat1 - displacement of the platform, 2 - displacement of the robot body.spring-and-dashpot vibration absorber. Manipulators,video cameras, and other devices should be installed on theplatform. The modified schematic of the robot is shown in IV CONCLUSIONSFig. 10.

Vibration-driven robots with a one-coordinate vibrationexciter can move along a rough surface only if the friction

m2 between the robot body and the supporting surface or/andFy xl ml Athe exciter vibrations have asymmetric characteristics.

\ x2 zI mx2\ M FX M / Robots equipped with a one-coordinate exciter can be

utilized for cleaning pipelines from solid deposits.

Robots equipped with two-coordinate vibration excitersFTp2 FTP 1 can move even in the absence of an asymmetry in the

friction or vibration characteristics. The reverse in theFigure. 10. Schematic of the vibration-driven robot with an additional direction of motion is provided by changing the phase

platform. difference between the vertical and horizontal excitation

m2 is the mass of the robot, x1 is the absolute displacement vibrations.of the platform, x2 is the absolute displacement ofthe robot To reduce the vibration level transmitted to the equipmentbody, Fx and Fy are the forces generated by the vibration of the robot form the exciters it is reasonable to place thisexciters, c and , are the stiffness and damping equipment on a special platform isolated from thecoefficients of the platform suspension. vibration-driven robot body by a spring-dashpot vibration

absorber.

ACKNOWLEDGMENTThe dynamics of the system shown in Fig. 10 is governedby the following set of differential equations This investigation is supported by RBRF project No04-01-

04002, N205-08-33382.

* c.X1-c (X1-X2)-C (X1-X2)-(mlg) f sign(X,) REFERENCES

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[2] Yeh, R.; Hollar, S.; Pister, K.S.J.: Design of low-power siliconFx sin(.-t) - CP X2- P (X2- Xl) - C (X2 - Xl) - (m2g - Fy sin(w. t + ())*f. sign(X2) articulated microrobots. Journal of Micromechatronics, Vol. 1,

m2 Num. 3, 2001, pp. 191-203[3] Gradetsky, V.G.; Knyazkov, M.M.; Kravchuk, L.N.; Solovtsov,

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