Development of Wall Climbing Robot - Nuicone.org

INSTITUTE OF TECHNOLOGY, NIRMA UNIVERSITY, AHMEDABAD – 382 481, 08-10 DECEMBER, 2011 1Development of Wall Climbing RobotA. Chirag R.Vyas, B. J.M.Dave, C. D.J.ShahAbstract-- One of the most promising ways to make arobot climb are vacuum pumps and suction cups. Mostof the mobile robots now days essentially move in 2Dplane without wall climbing capability. Wall climbingrobot is one of the special in mobile robots because itmoves in vertical plane. This paper present a research onthe wall climbing robot with vacuum suction method..AnAnalysis of various aspects in mechanical design, includinglocomotion mechanism, adhesion mechanism are discussed.The generalized equation of wall climbing robot’s to findvelocity and acceleration are derived. Static and Dynamicforces found. Designing two wheeled robot, selection ofcomponents. Developed cost effective ,small size, simple inconstruction wall climbing robot.• Derive kinematic and dynamic equations for robotchassis• Apply Euler-Lagrange formulation for robot chassisEquations for wheel dynamics• Formulate combined chassis and wheel modelequation• Total energy of the system• Apply Euler-Lagrange formulation for the wholesystem for the dynamicsII. INTRODUCTIONn recent time, there have been strong demands that use ofrobots for defense, surveillance, and counter terrorismmissions. Most of the mobile robots now days essentiallymove in 2D plane without wall climbing capability. Wallclimbing robot is one of the special in mobile robots becauseit moves in vertical plane. Wall climbing robot needs not onlyspecial locomotion system but also required adhesion system.One of the most challenging tasks in climbing robot design isto develop a proper adhesion mechanism to ensure that therobot sticks to the wall surfaces without sacrificing mobility.So far many of researchers developed this type of adhesiontechnique, Magnetic Adhesion, Elastomer Adhesion, suctionpadadhesion[5].In this work, mathematical model for wheel velocity, bodyvelocity are obtained by transformation. The torque andacceleration is calculated using Euler-Lagrangian Formulationfor dynamic analysis. The conceptual model is derived formoving on vertical surface and ceiling. Wheeledlocomotion[1] is selected and suction pressure is generated byinstalling impeller which is run by bldc motor. Themathematical equations are formulated for static and dynamicadhesion on wall and suction pressure is calculated.Collecting right components and developed conceptual modelfor wall climbing robot.II. DERIVED MODEL EQUATION FOR TWO WHEELEDWALL CLIMBING ROBOTFor two wheeled robot design[3] the derivation of equationfor position, velocity and angular acceleration for verticalsurfaces.Steps for deriving model equation:• Start from initial conditions to derive the model forrobot chassisFig.1 Coordinates of robot bodyFig.1 shows co-ordinates of robot body. Where, x(t),y(t) are robot position in x and y coordinates and ν(t),ω(t) Robot linear and angular velocity with respect tobody fixed frame.Total kinetic energy of the whole body is the sum ofkinetic energy of the robot chassis and kinetic energyof the wheels is,1 2 1 1 1 1McV + Ic2 2 2 2 2Put the relationship value of the velocities,2⎛ 1 Rw 1 2 1 2 1 ⎞⎜ Ic + McRw + MwRw + Iw ω lRc⎟2⎝ 2 8 2 2 ⎠2⎛ 1 Rw⎜ Ic2⎝ 2 Rc2222ω + MwVl ( ) + MwVr ( ) + Iwω( l)+1 2 1 2 1 ⎞+ McRw + MwRw + Iw⎟ω8 2 2 ⎠( )2( r)2⎛ 1 2 Rw ⎞⎜ McRw _ Ic ω( l) ω( r)Rc⎟2⎝ 4⎠…..(2)Where Mc is robot chassis mass, Mw wheel mass, Rc ischassis radius, Rw is wheel radius, Iw wheel moment ofinertia, Ic chassis moment of inertia.Potential energy of the robot body is Mgy. Apply Euler-Lagrange formulation, total energy becomes,21Iwω( r)2.…(1)++2

2NATIONAL CONFERENCE ON CURRENT TRENDS IN TECHNOLOGY, ‘NUCONE – 2009’⎛ Rw[⎜ Ic⎝ Rc⎛ 1⎜ McRw⎝ 4⎛ Rw[⎜ Ic⎝ Rc2222+2+14Rw_ IcRc14McRw22McRw2⎞+ Iw⎟ & ω(l)+⎠⎞1⎟ & ω(r)− τ ( l)− Mgy ]⎠22+ MwRw+ MwRw⎞+ Iw⎟ & ω(r)+⎠2⎛ 12 Rw ⎞1⎜ McRw _ Ic ( ) − ( ) − ] = [0,0]24⎟ & ω l τ r Mgy⎝Rc ⎠2……(3)Where τ(l), τ(r)torque for left and right wheelLeft wheel acceleration equation is,22 22 22[(4IcRw+ McRw Rc + 4MwRwRc + 4IwRc) τ ( l)+ ( −McRw2Rc222 22(4IcRw+ 2MwRwRc + 2IwRc) Mgy]2 4 2 2 2[(4MwRw Rc + 4IwRc + 4McIcRw8MwIcRw+ 2McIwRw+ 4IcRw4+ 8IcIwRw2RcSimilarly can be derived for ω˙(r)2222) τ ( r)+2+ 8MwIwRw+ 2McMwRw2Rc1 1& & ω + & ω2 2Rw & ω(l)− Rw & ω(r)& ω(t)Rc244Rc+2)]……..(4)Linear acceleration, v( t)= Rw ( l)Rw ( r)..(5)Angular acceleration,= ….(6)These equations are required velocity and acceleration fortwo wheeled vertical moving vehicle.Fig.2 shows the schematic of main components of wallclimbing robot , which includes components like Bldc motor,Drive dc motor, Wheels, Foam sheet body, Plastic cover andinside centrifugal impeller. A special BLDC motor isselected for present application which is assembled withcentrifugal impeller also known as vacuum impeller.III. CONCEPTUAL MODELFig.2 Conceptual modelBLDC motor is rotating at maximum 50,000 rpm. So impellerrotates at this speed and create enough suction pressure toadhere the robot with wall safely. Which matches theanalytical suction pressure requirements, also it is proven byan experiment. Wheels made up of rubber tubes are selectedfor locomotion system. External body material is PVC foamsheet board which is light weight, easy to cut, enough strengthto carry the weight as compare to its size, and best suitable forwall climbing robot.The distance between robot and wall is minimum 0 mm andmaximum 5 mm. Minimum distance is 0 mm because the tailpart of the body is directly connected with wall and upper partwhich is nearer by wheel its distance with wall is 5 mm.Fig.3 Drawing of conceptual modelThe conceptual model of the robot is shown in fig.3.

INSTITUTE OF TECHNOLOGY, NIRMA UNIVERSITY, AHMEDABAD – 382 481, 08-10 DECEMBER, 2011 3IV. STATIC AND DYNAMIC FORCESStatic and dynamic analysis equations for centrifugal impellerbased wall climbing robot are derived by Jun Li, XueshanGao, Ningjun Fan, Kejie Li and Zhihong Jiang[2].It is forcebalancing equation which gives how much static and dynamicforce required to stick the robot with the wall safely.Application of mentioned set of equations is utilized for forceanalysis.(4)inertia force. The first three components shows the justbalancing gravity only when the robots rest on the wall. Theforth component shows drive wheel's dynamic performance,drive wheel must gain sufficient friction to get preconcentrated acceleration. Put the corresponding value of theabove components and get Ff_dmin Drive wheel's minimumdrive friction force which is fundamentally related with staticfriction as shown equation.Fs_d = Ff_d /µd………..(12)When robot's geometrical parameters are fixed, Fs_d isdetermined directly by adhesion force Fa which can beobtained by solving eq.(7-9),Fa_min = 2Fs_d(1 + b1/b2) + G*hg / b2 + Fs_b….(13)This equation provides suction system with necessaryminimum adhesion force index for designing.Fig.4 Force balance diagramStatic analysis:-As shown in fig the balancing horizontal and verticalsurfaces, get,Fa=Fs_b + Fs_eb + Fs_d1 + Fs_d ….(7)G = Ff_d1 + Ff_d2 + Ff_eb ….(8)Where ,G is gravity force, subscript’ s’ for supportingforce, subscript ’f’ for friction force, b for body, eb for edgebody,d1,2 for driving wheel 1,2.Taking moment about center point of axle, torque can befound ,Fa*b1 + G*hg = Fs_eb(b1 + b2) + Fs_b …(9)Consider only sliding friction of wheel balancing gravityforce, neglecting other body force. And solving aboveequation for minimum adhesion force required to stick therobot on wall at rest is,Fa_min = {b1/b2 +1}{G*Kr/µd} + G*hg/b2 + Fs_b …(10)Where b1,b2 is the distance from wheel and center and tailbody and center respectively. Kr is the adhere safety factor,µd is friction between wheel and wall, hg is the distancebetween wall and center of gravity.This equations shows that When G and Kr is constant, tominimized the required necessary adhesion force, For that theratio of b1/b2 small as much as possible, it will cause moredriving forces on drive wheel. To achieve same reduction inhg is also the another option, reduce the distance betweenwall and center of gravity. For the sufficient suction reducesupporting body force(F_sb) as much as possible.Dynamic analysis:-Apply D'alembert's principle on forces, the balancingequation in vertical direction. Take gravity force, accelerationforce, edge body friction force and body friction force.2Ff_d = Fs_b + G + Ff_eb +Ma …..(11)This equation shows the drive wheel's friction force, it dividesin four components, (1)gravity of the system (2)contactbody's sliding friction (3)edge body's sliding frictionV. EXPERIMENTAL WORK AND RESULTWeight of the robot is nearly equal to 1.5 kg(Maximum withpay load). the choosing wheel diameter is 80 mm. The otherdimension of the robot is shown in fig.3. Selected motortorque is 0.5726 N.m. By Using equation 4 and 5 ,get linearacceleration of the robot is 0.0972m/sec 2 ages. And power pis 7 watt(for drive wheel) is found. As per applied forcediagram selected motor is safe and applicable.Force calculation:-Horizontal condition:-When robot rest on ceiling at that time adhesion force is equalto gravity force. Consider robot weight is equal to 1 kg. Forthat required adhesion force is 9.81 N.Vertical condition:-As shown in equation (10) and (13) Adhesion force isdependable on the ratio of b1/b2. Take two case for differentratio of b1/b2.Case 1:b1/b2=0.6875Here,b1=0.55 m, b2= 0.08 m, hg=0.02069 m, G=9.81 N, andµd=0.8 friction coefficient between wall and wheel.Put these values in equation (10), get the required adhesionforce is 23.23 N. neglecting supporting force of body, Takeedge body and body friction force as a whole body frictionforce, Put this value in eq.(11),Ff_d(min) = 9.3681 N is found. Put this value in eq.(12) and using eq.(13), dynamic minimum adhesion force42.058 N is found.Case 2:b1/b2=0.143Where b1=0.01 m, b2=0.08 m for this minimum requiredstatic adhesion force is, 16.32 N. and dynamic adhesion forceis 28.88 N . Analytical result shows that reduce the distancebetween center of the robot and drive wheel’s axle, reduce therequired adhesion force.Experiment work:-Fig.2 shows the conceptual model of the robot and fig.3shows the drawing of the robot. Experiment is done ondifferent surfaces like on ceiling, plywood and glass. Thesnapshot is taken and shown below the working of wallclimbing robot.

4NATIONAL CONFERENCE ON CURRENT TRENDS IN TECHNOLOGY, ‘NUCONE – 2009’source will be beneficial if the robot is to be moved at toomuch height like multistory building. The wheeledlocomotion will be the best suited locomotion system forglass, plywood and vertical surfaces as on wall or as onceiling. It can be run with light weight, low cost dc motors.The suction pressure can be easily generated by impeller withbackward curved vanes. Such impellers are readily availablefrom market with vacuum cleaner supplier and repairer at lowcost. Hence it is concluded that wall climbing robot for civilapplication can be fabricated considering wheeledlocomotion. The suction pressure can be generated byimpeller.Fig 5:-Running on ceilingFig.6:-Running on plywoodFig.7 Running on glassFig.(5),(6) and(7) shows the working of robot on differentsurfaces. Developed robot is small sized, cost effective, lightweight, simple in construction wall climbing robotUnits.VII. FUTURE SCOPE1.It is desirable to make robot autonomous to use it forspecific tasks. Battery powered suction cups are desired .2. A paper by Brockmann Et Al gave inspiration fordeveloping a passive suction cup for Robot. They showed thatwith a pulling mechanism it is very easy to release suctioncups and that pushing them on a surface takes less energythan continuous pumping. This seemed to suit very much, interms of energy consumption and the constructive characterof the system.VIII. REFERENCES[1] R. Siegwart .and Nourbakhsh.” Introduction toAutonomous Mobile Robots”[2] J. Li, X. Gao, N. Fan, K. Li, and Z. Jiang. Bit climber: Acentrifugal impeller based wall climbing robot. InternationalConference on Mechatronics and Automation, china, pages{4605-4609}, 2009.[3] Maple soft a division of Waterloo Maple Inc. Mobilerobot modeling and simulation.[4] Z. Jiang, J. Li, X. Gao, N. Fan, and Wei B. Study onpneumatic wall climbing robot adhesion principle and suctioncontrol. International Conference on Robotics andBiomimetics Bangkok, Thailand, pages {1812-1817}, 2009.[5] Dongmok K. Hojoon Y. Kyouhee L. Kunchan S.Doyoung C. Jongwon K. Hwan, K. A wall climbing robotwith vacuum canterpillar wheel system operated by mechnicalvalve. 9th international conference on climbing and walkingrobots,2006[6] Gecko Inspired Surface Climbing RobotsCarlo Menon, Michael Murphy, and Metin Sitti,Member, IEEE[7] Toward Micro Wall-Climbing Robots UsingBiomimetic Fibrillar AdhesivesMatthias Greuter1, Gaurav Shah2, Gilles Caprari1,Fabien Tâche1, RolandSiegwart1, Metin Sitti2,3VI. CONCLUSIONThe wall climbing robot is designed as per requirement andapplication. The power source required to be decided beforecalculation of actuators. This will facilitate in reducing effortsfor selecting drive motors. It is also concluded that dc power