SpinybotII: Climbing Har Wall with Compliant Micropine Sangbae KIM, Alan T. ASBECK, Mar R. CUTKOSKY an William R. PROVANCHER Abtract--A new climbing robot ha been evelope that can cale flat, har vertical urface incluing concrete, bric, tucco an maonry without uing uction or aheive. The robot can carry a payloa equal to it own weight an can cling without conuming power. It employ array of miniature pine that catch opportunitically on urface aperitie. The approach i inpire by the mechanim oberve in ome climbing inect an pier. Thi paper cover the analyi an implementation of the approach, focuing on iue of pine/urface interaction an compliant upenion eign. I Inex Term Robotic, Mechanim. I. INTRODUCTION N recent year, there ha been conierable progre in mall, legge robot that can run rapily an tably over rough terrain [1][][3][4]. Climbing an maneuvering on vertical urface preent a more ifficult challenge, which robot are jut beginning to are. For application uch a urveillance or the inpection of har-to-reach location, we woul lie to have mall robot that can climb a variety of har an oft urface unobtruively an cling for extene perio of time without high power conumption. Previouly evelope climbing robot have generally employe uction cup [5][6][7], magnet [8][9] or ticy aheive [10] to cling to mooth vertical urface uch a winow an interior wall. None of thee approache i uitable for porou an typically uty exterior urface uch a bric, concrete, tucco or tone. A recent innovation employing a controlle vortex to create negative aeroynamic lift ha been emontrate on bric an concrete wall [11] with conierable ucce. However, thi approach conume ignificant power (whether the robot i moving or tationary), unavoiably generate noie, an i ifficult to aapt to nonmooth urface uch a winow legean corrugate urface. Still other robot employ han an foot hol in the manner of a human climber [1][13]. When we loo at animal that exhibit canorial (vertical urface) agility, we fin a variety of metho employe [14]. Larger animal uch a cat an raccoon employ trong claw Manucript receive November 8, 004. Thi wor wa upporte in part by the DARPA Bioynotic Program uner Contract No. NC66001-03-C- 8045 an DCI Fellowhip MNA501-030100. S. Kim, A. Abec, M.R. Cutoy an W. Provancher are with the Center for Deign Reearch, Department of Mechanical Engineering, Stanfor Univerity, Stanfor CA, 94305 USA (telephone 650-73-458, email angbae, aabec, cutoy, wil@tanfor.eu ). that penetrate woo an bar urface. Tree frog an many inect employ ticy pa [15][16]. Geco an ome pier employ large number of very fine hair that achieve aheion via van er Waal force on almot any in of urface [17][18][19]. Other inect, arthropo an reptile employ mall pine that catch on fine aperitie [0]. All of thee approache are worthy of examination for bio-inpire climbing robot. However, ry aheive an pine are particularly attractive for har, uty, exterior urface. Several reearcher are currently woring on creating ynthetic verion of the etae foun in geco or the copulae een on pier [1][][3]. The early reult are intriguing but current ynthetic aheive are not able to utain the in of tenile loa neee at the forelimb of a climbing robot. Moreover, they are fragile an lac the elf-cleaning property that allow geco to climb uty wall. II. SPINE AND SURFACE SCALING A. Spine in nature Inect an arthropo that climb well on man-mae an natural urface often ue leg equippe with large number of mall, harp pine. Even geco that frequent roc urface uch a cliff an cave have mall claw on each toe in aition to their ry aheive tructure [4]. Unlie the claw of a cat, the mall pine or claw o not nee to penetrate the urface. Intea, they exploit mall aperitie (bump or pit) on the urface. Several tuie in the biology literature have coniere the problem of pine/urface interaction. Dai et al. [0] preent a planar moel of pine/aperity contact an compute the maximum loa per pine a a function of pine trength, relative ize of the pine tip veru that of an aperity, an coefficient of friction. A expecte, for rough urface the mechanical trength of the pine an aperity become the limiting factor; for moother urface friction i more important an the ability to pull in towar the urface i much reuce. B. Spine caling for a climbing robot Given the oberve relationhip between pine or claw ize an animal ize, we are le to a: For a climbing robot of a given ize, how large houl the pine be? If we conier a robot that weigh approximately 0.5 Kg, we might expect pine or claw imilar to thoe een in quirrel or large climbing lizar. However, thi argument ignore the point that pine mae of harene teel are much tronger an
=5μm =00μm Fig.1 magnifie view of typical haft an tip for pine ue in SpinybotII climbing robot. tiffer than natural pine an can therefore be maller while upporting a comparable loa. Inee, if the trength of the pine/aperity contact were not a contraint, we houl mae the pine a mall a poible. The reaon behin thi argument i that many natural urface, an ome man-mae urface uch a concrete an tucco, have an approximately fractal urface topography [5][6][7] o that characteritic urface feature (aperitie) can be foun over a wie range of length cale. Following the argument of Dai et al. [0] for pine of a certain tip iameter,, we are interete in aperitie of average iameter a to obtain effective interlocing. Given the elf-imilar nature of fractal urface, we can expect the enity of uch aperitie to grow at leat a 1/ a per unit area of the wall. In practice, there i a lower limit to the ueful pine imenion. We have foun that when teel pine catch on aperitie on concrete or tucco, the contact typically fail in one of three way [30]: platic failure of the bae of the pine in bening, exceive elatic rotation of the pine tip cauing it to lip off the aperity, brittle failure of the aperity itelf. In each of thee cae, if we tae a imenion uch a the pine tip iameter,,, a a characteritic length an cale everything uniformly, then the maximum loa of the pine/aperity contact increae a (ee Appenix for etail). For our firt climbing robot, SpinybotI, we employe 4 pine per foot, each with a tip iameter of approximately 40 μm. Thi machine wa able to climb tucco an rough concrete reliably. The pine/aperity contact coul utain loa of everal Newton, uually limite by brittle failure of the aperity rather than of the pine. However, for urface uch a mooth concrete an ree tone, the probability of a pine encountering a ueful aperity uring a vertical troe length of approximately 3 cm wa too low for reliable climbing. SpinybotII employ two row of pine on each foot, each pine having a tip iameter of approximately 5 μm. The maximum force per pine/aperity contact i 1- N, an the probability of fining ueable aperitie per quare centimeter of wall i high. To ummarize the preceing argument, a pine become maller we can acen moother urface becaue the enity of ueable pine/aperity contact increae rapily. However, we nee larger number of pine becaue each contact can utain le force. In orer to mae ue of large number of pine, the firt two eign principle behin climbing with micropine are therefore: enure that a many pine a poible will inepenently fin aperitie to attach to, enure that the total loa i itribute among the pine a uniformly a poible. The eign of feet that emboy thee principle i ecribe in Section III. In aition, a with any climbing robot, it i important to eep the center of gravity a cloe to the wall a poible an to avoi impoing any force or moment at the feet that coul lea to premature etachment. The feature of SpinybotII that achieve thee effect are ecribe in Section IV. Fig. View of upper ection of SpinybotII on concrete wall an etaile view of everal pine inepenently engaging aperitie on the concrete urface.
III. TOE AND FOOT DESIGN: PROMOTING ATTACHMENT AND LOAD SHARING The feet on SpinybotII repreent the ixth generation of a compliant, pine eign. A failing of earlier eign wa that on cloe obervation, only a few pine were carrying mot of the loa. Each foot of SpinybotII contain a et of 10 ientical planar mechanim, or toe. The mechanim are create uing a rapi prototyping proce, Shape Depoition Manufacturing [8] that permit har an oft material to be combine into a ingle tructure. In the preent cae, the white an grey material are har an oft urethane, of 75 Shore-D an 0 Shore-A harne, repectively (Innovative Polymer Inc.). The reulting tructure can be approximate a an elatic multi-lin mechanim, a hown in Fig. 3. The oft urethane flexure provie both elaticity an vico-elatic amping. They permit greater extenion without failure than miniature teel pring (a were ue on ome of the earlier foot eign). For mall eflection, the linear an rotational tiffne of each pine in the (x,y) plane can be moele uing a 3x3 tiffne matrix, K, taen with repect to a coorinate ytem embee in the pine: y 40g 4. x 4. 1. y z ervo elatic ban tip trajectory un-actuate primatic joint Fig. 4. Sie an plan view of one foot containing 10 toe, each lie the toe hown in Fig. 3. The toe can eflect inepenently of each other. In aition, the entire foot can iplace in the ital (y) irection ue to an unactuate primatic joint. The attachment trajectory of the foot conit of an upwar (+y) motion, followe by lift-off motion (-x), touchown (+x), an a ownwar pull (-y). The equence of motion i accomplihe uing an uner-actuate mechanim coniting of a ingle rotary RC ervo motor an an elatic ban that i initially looe an become taut a the leg move upwar. At the en of troe, a har top caue the leg to remain pree againt the wall. y x 3. 5. 1 cm Fig. 3. Photograph an equivalent elatic linage for one toe of the climbing robot. Linage at left how the eflecte poition for a 40g loa, uperimpoe on the uneflecte poition (hown in otte line). Key to label: 1. 00 μm iameter pine (inie otte circle),. tenon for applying loa, 3. oft urethane flexure permitting travel in y irection, 4. bucling flexure with low tiffne in the -x irection uner compreion, higher tiffne uner tenion, 5. primarily rotational flexure for the proximal pine.. 5. 3. xx xy xθ xy yy yθ At initial contact, we require that xx be very mall for iplacement in the -x irection, o that a large number of toe can conform to uneven urface without requiring a ignificant engaging normal force. Thi i accomplihe through the flexure at the en of the toe (labele 4. in Fig. 3), which are eigne to bucle o that they have a very low tiffne for -x eflection. For mall tenile loa on the foot (in the +x irection), ome toe will till be compree from the foot engaging motion. xx houl till be mall in thi cae o thee compree toe o not puh the foot away from the wall. Finally, for large tenile loa, xx houl be large o the toe can iengage from the wall. Thi i alo accomplihe with the flexure at the en of the toe. At the ame time, yy houl be moerate, a it repreent a trae-off. A ofter yy allow each toe to tretch more in the longituinal irection to increae the probability that each one will catch an aperity uring the ownwar troe of the foot; but if yy i too oft, the mechanim will require an exceive troe length to upport a given loa. In eence, thee factor etermine the aperity earch length for the ownwar xθ yθ θθ
TABLE I STIFFNESS AND DAMPING PARAMETERS FOR TOE LINKAGE Location (numbere label, Fig. 3) 1. = 60 N/m c = 0.1 N/m 3. = 60 N/m c = 0.1 N/m t =0.005 Nm Parameter in inematic moel = linear tiffne element c = linear amping element t = rotational tiffne element 4. = 90N/m in tenion = 0.005N/m in compreion c = 0.0 N/m 5. =100 N/m c = 0.001 N/m t = 0.001 Nm troe of the toe. At the ame time, xy houl be mall o that tretching in the y irection oe not caue the pine to retract. The xθ an yθ term houl alo be mall an, preferably, lightly negative o that iplacement in the x or y irection are not accompanie by anticlocwie rotation in the (x, y) plane that woul lea to premature iengagement. The mechanim hown in Fig. 3 wa moele in the Woring Moel oftware (MSC Inc.) an the variou linear an rotational tiffne element were ajute until the moel matche eflection obtaine when applying mall loa an meauring the correponing iplacement in bench-top tet. The reult are ummarize in Table I. The mechanim i eigne o that initial contact at the inner, or proximal, pine actually force the ital pine lightly outwar (+x irection) to increae the probability that it will alo contact an aperity. Once one or both pine have contacte the wall, the toe can apply a force that i mainly vertical, with a mall inwar (+x) component to help the robot climb. Fig. 3 how the effect of a typical 40 gram loa utaine by one toe in climbing. Each toe mechanim can eflect inepenently of it neighbor (a een in the etaile inet in Fig. ) to maximize the probability that many pine on each foot will fin aperitie an hare the total loa. An important obervation of agile canorial animal lie geco i that they employ multi-level conformability (e.g. lamellae, toe, an limb) an reunancy (multiple pa per toe, multiple toe per foot, an multiple feet in contact) for reliable climbing. The ame principle have been foun neceary for SpinybotII. Accoringly, the entire foot mechanim i mounte on a primatic joint with an elatic upenion that allow it to move up to 1 cm in the ital (+y) irection (ee Fig. 4). In aition, the entire foot aembly i pring loae by a econ elatic element behin the pivot, where it i connecte to a rotary RC ervo motor. The reult i an uner-actuate R-R-P erial inematic chain that trace a Ma Max payloa Climbing pee Ditance: COM to wall urface Batterie Proceor Servo motor (7 total) Camera TABLE II SPINYBOTII SPECIFICATIONS 0.4 Kg 0.4 Kg.3 cm/.0 cm lithium polymer total 340 mah, 7.4 volt 40 MHz PIC 0.37 Nm torque 0.0 Kg loop trajectory, a hown in Fig. 4, when the ervo motor rotate bac an forth. After ome experimentation, the bet elatic element were foun to be 6.4mm iameter elatic ban commonly ue for ental brace. IV. BODY DESIGN: PROMOTING LOAD SHARING AND STABILITY Moving from the foot to the boy a a whole, we ee in Fig. 5 that the robot utilize an alternating tripo gait, a foun in climbing inect. At any time, the robot i ieally clinging by three feet. Lie many climbing animal, the robot alo ha a tail which reuce the force require at the front limb to overcome boy pitch-bac from the wall. Thi pitch-bac moment i prouce by gravity acting at the center of ma, which i locate approximately cm outwar from the wall. The weight of the robot, incluing lithium polymer batterie, 58cm 30cm COM camera in tail Fig. 5. Photograph of SpinybotII wall an iagram of climbing mechanim. Each et of three leg i attache to a mechanim that allow the robot to ratchet it way up the wall with an alternating tripo gait. A long tail help to reuce the pitching moment. The center of ma (COM) i alway within the polygon of contact, to minimize yawing rotation in the plane of the wall.
wirele camera, an PIC microproceor i 0.4 Kg. It can carry an aitional payloa of 0.4 Kg while climbing. The climbing pee i currently quite low (.3cm/) but can eaily be improve upon with the aition of tructural amping in the limb an toe upenion. On initial contact of each pine with the wall, the pine an toe upenion ocillate a an unerampe tructure. Such ocillation reuce the probability of engaging ueful aperitie encountere a the pine are troe along the wall. The aition of tructural amping will greatly improve climbing performance (attachment) an permit climbing at greater pee. Higher performance motor may alo be eirable. While the main concern for vertical climbing i to avoi pitching bac from the plane of the wall, it i alo important to maintain rotational tability in the plane of the wall o that momentary lip to not become catatrophic. A een in Fig. 5 the center of ma of SpinybotII lie within a polygon of contact at all time. Alo, a oberve in climbing inect an reptile, the leg have a light inwar pull, towar the centerline of the robot. Thi arrangement reuce the upetting moment (in the plane of the wall) about the center of ma, houl one of the leg momentarily loe it grip. V. CONCLUSIONS AND FUTURE WORK SpinybotII climb reliably on a wie variety of har, outoor urface incluing concrete, tucco, bric, an ree antone with average aperity iameter of greater than 5μm. The main principle behin it ucce have been explaine in Section II-IV. A vieo of SpinybotII climbing variou builing aroun the Stanfor campu an ome cloe hot of it feet an toe engaging aperitie can be foun at http://bml.tanfor.eu/rise/downloa/. Watching the vieo cloely will alo reveal everal intance in which one foot briefly loe it grip. However, there i enough reunancy an compliance that the robot oe not fall. Of coure, if the robot encounter a very mooth patch, it either fail to procee or fall. For greater reliability, we are invetigating miniature accelerometer at the toe that will inicate when contact ha occurre an whether the foot i tationary or lipping. Although the autonomou verion of Spinybot ecribe in thi paper alo lac the ability to move ieway on vertical wall, we have tete variant capable of (very low) lateral locomotion uner raio control. The inwar lateral pull of the leg i eential for thi capability. The main practical limitation of SpinyBotII i that it lac ufficient egree of freeom to negotiate corner an tranition from vertical to horizontal urface (a when climbing over a winow lege. Aing egree of freeom houl be traightforwar, except that the center of ma mut remain cloe to the wall an the aitional egree of freeom mut not interfere with the compliant eign principle of the toe, feet an leg a ecribe in thi paper. Scaling SpinyBotII to larger payloa houl alo be traightforwar; one imply nee more pine. A more challenging problem i to tacle rough or corrugate urface. Either the feet an toe mut have enough upenion travel to accommoate the contour of the urface or they mut have an aitional active egree of freeom, lie the toe of geco or the tenon-actuate taru of inect leg. On uch urface it houl be poible to exploit internal grap force, in a manner imilar to that ue by robot that climb with han-hol an foot-hol [13] [1], for aitional ecurity. The pine an toe on SpinybotII are alo optimize for contact with har urface. For oft material, larger claw that penetrate the urface are more effective [9]. Aing larger, penetrating, claw to the feet of a robot lie SpinybotII i certainly poible. We upect that it will be neceary to mae them retractable (lie the claw of a cat) o that they will not interfere with the function of the micropine on har urface. Another challenging problem i to climb urface, uch a polihe tone or interior wall panel, with much lower roughne than concrete or antone. The caling argument in Section II houl till apply. However, for mooth panel the average aperity iameter may be on the orer of a few micrometer, requiring pine tip iameter of perhap 4 μm. Thee extremely mall pine will be over 100 time weaer than the pine on SpinybotII an a large number of them will be require, unle the overall ma of the robot can be reuce correponingly. Going till maller, we approach the imenion of the hair that are being invetigate for ynthetic ry aheive [19][1][][3]. An intereting quetion i whether ome combination of pine an aheive hair will ultimately prove mot effective for caling a wie variety of har vertical urface. APPENDIX SPINE FAILURE MODES The pine/aperity contact have three primary failure moe. The firt moe of failure i ue to the tenile tre at the bae of the pine [31]. Maximum tre on cylinrical cantilever beam: Mc 3 f l 1 l σ max = = ( if = cont) 4 I π π M = f l, c =, I = 64 f = force exerte on tip of the pine = iameter of cro ection of pine l = pine length The econ moe of failure i exceive tip rotation. Deflection angle at the tip of cantilever beam: θ = f l 3 f l = E π 1 4 EI 4 ( if l = cont)
The thir moe of failure i that the aperity itelf may brea off or fail in hear. Shear tre failure: σ max = f A 4 f = π a 1 ( if a = The etail of the aperity failure will epen on whether the material i brittle an whether crac or efect are preent [30]. However, the trength of the aperity i generally expecte to increae a the quare of aperity iameter. ACKNOWLEDGMENT Thi wor wa upporte in part by the DARPA Bioynotic Program uner Contract NC66001-03-C-8045. Aitional upport wa provie for W. Provancher by the DCI Pooctoral Fellowhip Program uner grant # MNA501-030100 an for A. Abec by a NSF fellowhip. The author than Dr. Michele Lanzetta for hi photograph of pine tip an icuion about pine caling an V. Mattoli for hi evelopment of the PIC proceor program for controlling the RC ervo. Than are alo ue to J. Lee for her help in eigning an fabricating SpinybotI an S. J. Trujillo for hi help with the linage tiffne meaurement an moeling. REFERENCES [1] U. Saranli, M. Buehler an D.E. Koitche. 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