WALKING QUADRUPED WITH SUPPORT/STEERING WHEELS

Transcription

1 AKING QUADRUPED IH SUPPOR/SEERING HEES Ahwin Mudigonda Dept. of Eletrial Engineering, Ohio Univerity, 9, Stoker enter, Athen, OH-457,USA Robert. illiam II Dept. of Mehanial Engineering, Ohio Univerity 59, Stoker enter Athen, OH-457,USA Abtrat- hi paper preent a new deign for a walking quadruped. It inorporate a upport/teering axle with two wheel alway in ontat with the ground to enure the quadruped an tably lift two leg during gait. Abilitie inlude following omplex traetorie. Kinemati, forward-poe gait, and imulation example are preented in thi paper. I. INRODUION alking and running mahine are laified into two ategorie baed on the tability of their motion: paively table and dynamially table. For a paively table ytem, the vertial proetion of the enter of ma alway remain within the loed region formed by the ontat point of the feet on the ground. hi region i alled the upport polygon. hey typially have four or ix leg but may be biped with large feet urfae area. In ontrat, dynamially table ytem utilize dynami fore and feedbak to maintain balane. Dynamially table mahine have been built with one, two, and four leg. Beaue dynamially table ytem are more diffiult to deign, ontrol and analyze, the early legged robot were motly tatially table mahine. Robert MGhee of Ohio State Univerity built a Hexapod in 977 by uing eletri drill motor (Buket 977; MGhee 98). A eond hexapod from OSU, the Adaptive Supenion Vehile, wa a three-ton vehile with a human driver but automati poitioning of the leg (Song and aldron 989). Many deign have been propoed to implify both mehanial onideration and the load on the proeor for maintaining balane. For example, Shigeo Hiroe 98 PV II quadruped inorporated a pantograph leg mehanim that allowed atuator independently to ontrol eah degree of freedom in arteian pae, oniderably implifying the kinemati poe equation (Hiroe and Umetani 98). he Ambler, a thirty-foot-tall, hexapod planetary explorer built at arnegie Mellon Univerity, ued an orthogonal leg deign to implify the kinemati equation (Simmon et al. 99). Another robot built at MU, Dante, ued et of leg mounted on liding frame. In 994, Dante II uefully deended into an ative volano in Alaka and analyzed high temperature gae he Quadruped, built by MI during wa ued to explore running on four leg. It wa programmed to trot, pae, bound, and do everal tranition between gait. It wa found that priniple for one-legged hopping ould be generalized to fourlegged running, with the addition of a low-level leg oordination mehanim. he Quadruped generated different type of gait like trotting (diagonal leg a pair), paing (lateral pair), and bounding (front pair and rear pair). Quadruped deigned to date either have to be tethered from above or need to have a low learane. Dynami ytem need to have bulky ontrol atuator and alo have to arry along onboard miroontroller to ontrol them. hi leave little pae for payload. A wheeled mehanim provide fat and effiient loomotion on flat terrain, while legged loomotion i apable of adapting to a hotile terrain. Marrying wheel and leg, alled heg (Quinn, R. D. Nelon et al., ) i a new onept under development. "alk'n Roll", built by the Mehanial Engineering aboratory of AIS, Japan i a prototype of the new mehanim that ombine leg and wheel. alk'n Roll ha four leg, with a wheel attahed at the end of eah leg. he front leg have three oint, and a paive wheel i attahed at the end of eah. he rear leg have one oint and a relatively large ative wheel attahed at the end. he robot exhibit three loomotion mode: wheel mode, hybrid mode, and tep mode. In the wheel mode, all the four wheel are ued for loomotion. he leg motion an be ued for teering. In the hybrid mode, the front two leg are ued to walk. he tep mode i ued to limb or deend a large tep. he rear wheel i moved from the rear ide to the front ide through the air by leg motion. Another key fator i the inability to ue one limb due to eletromehanial failure. hi would render the robot inapaitated. imping i a biologial phenomenon and would inreae the performane of a quadruped in harh and untrutured environment. he Birod program (Biomorphi Robot with Ditributed Power) ha been built at the Univerity of Arizona (Ramohalli, 999) to make pae exploration more dependable. he urrent paper preent our deign for a quadruped with a frontal upport/teering wheeled mehanim, followed by kinemati analyi, forward-poe-baed gait, and walking imulation.

2 II. SYSEM DESRIPION Figure how the arrangement of our quadruped with a upport/teering wheel attahment. he robot onit of four idential leg (the right-ide leg are ymmetri to the left-ide leg), eah having two revolute oint (J, J) and one primati oint (J). he firt revolute oint wing the entire leg forward and aft at the body; the eond revolute oint lift the leg up and down (in a irle) at the houlder; the primati oint lengthen and horten the leg to meet the ground. he upport/teering wheel are on a teerable axle at the end of a fixed rod. hi rod i attahed to the body at the midpoint of it width. It i added to the Quadruped body for added tability, allowing two leg to move at a time and till maintain tati tability. Eah leg ha a law to inreae tability of the ytem when any two leg are off the ground. he upport/teering wheel would have the apability to rotate and maintain a ommanded teering/heading angle. In onuntion with the leg, the teering angle ontrol the orientation of the robot. he upport ytem an be modified to arry an appropriate tool and if uitably modified, ould alo work a a SARA. Figure. Kinemati Diagram of One (Right-Side) eg ABE I DH PARAMEERS FOR RIGH-SIDE EG i α i- a i- d i i 9 9 he left-ide leg DH parameter are the ame a able I, negating the eond two α i- angle. he variable for eah -dof leg are,, and. Note the index indiate the four leg,,,,4 ; i a fixed length hared by all four leg. For alulating the enter of gravity, we aumed mae for different etion of the robot. he body and leg were given a ma of 5; the haft wa given a ma of.5 and the teering ytem along with the wheel,. III. POSE KINEMAIS MODEING Figure. AD model of Quadruped with Support/Steering heel Figure how the kinemati model of one (right-ide) leg. he Denavit-Hartenberg (DH, raig (989)) parameter for thi leg are ummarized in able I below. Poe kinemati relate the arteian poition and orientation (poe) of eah leg to the referene frame. Further, the poe of robot body enter frame an be related to the arteian world the robot i walking in. Invere poe kinemati i required for ahieving general deired robot traetorie (i.e. plaing eah foot independently in D pae). Forward poe kinemati i required for imulation and real-time enor-baed ontrol. In thi paper, however, emphai i given to the forward poe kinemati problem (i.e. alulate the XYZ oordinate of eah foot and the upport/teering wheel poe given the three leg oint variable for eah of the four leg, plu the teering angle). Our urrent gait are baed on ymmetri forward-poe motion. he invere poe kinemati olution i given for ompletene and future gait development.

3 A. Forward Poe Kinemati he forward poe kinemati (FPK) problem i tated: Given the eight ative oint angle and, and the length of the four ative primati oint ( 4,,, ), alulate the arteian poe of the eah of the four robot leg, expreed by [ ]. hi poe an then be interpreted and ued for robot gait imulation. Note that firt variable ubript i the oint index (,, or ) and,,,4 i the leg index. he hemati top view with frame aignment for eg i hown in Figure. e take the geometri enter of the quadruped body a the moving referene {} frame. Initially, the {} frame oinide with the orld frame {}. All leg and upport/teering wheel oordinate tranformation are derived with repet to the moving {} frame. hen the robot body hange poition, we hange the {} frame with repet to the {} frame with appropriate tranformation. Figure. Shemati op view of the robot howing the frame alloation. he primary ative homogeneou tranformation for the right-ide leg are hown in (), giving the poe of the th foot with repet to the th {} frame at the body. Note that and are ued to abbreviate ine and oine, repetively. () he ymmetri tranformation for the left-ide leg are in (): () he following tranformation equation expree the poe of the th foot with repet to the body enter frame {} frame. () where are ontant homogeneou tranformation matrie giving the fixed poe of the th leg bae frame {} with repet to the ommon {} frame. Now, the tranformation relating the poe of eah th foot frame with repet to the world frame {} are given below. (4) where i the tranformation ued to repreent the poe of moving robot body referene {} with repet to the fixed {} frame. It initially i et to a 4 x 4 identity matrix and i modified orrepondingly a the robot hange it poition during walking. he tranformation matrix for the frame {S} at the midpoint of the teering ytem to the {} frame i given by: S E y (5) where E y i the ditane along the Y-axi from the {} frame to the point where the teering haft begin. hen the teering wheel i et to an angle φ, the tranformation matrix i modified to δ δ (6) where δ i the inremental diplaement (.6 for thi imulation) in the forward diretion. B. Invere Poe Kinemati he invere poe kinemati problem for one leg i tated: Given the deired foot poe [ ], alulate the three ative th leg oint variable,, and. e extrat the arteian oordinate of the poition vetor from the given tranformation matrix [ ] a {x y z}. e obtain oupled tranendental equation, the olution of whih are given below for one of the right-ide leg. z z x a y x y x o, o in tan tan ± (7)

4 here are two olution for and one olution and for eah; therefore, there are two overall IPK olution et for eah leg. he IPK olution for the left ide leg will be imilar: he ymmetry of the robot allow u to ue the ame angle with oppoite ign for the left ide leg. In the urrent paper we ue FPK imulation to ontrut our gait, enforing ymmetry on diagonally oppoite leg. Hene, the invere poe kinemati ha not yet been ued in our gait. e will extend our gait to more general IPK-baed method in the future. hu, we will fou more on the multiple olution and ingularitie in future work. For impliity, we have omitted the wheel in the imulation. e aume, without lo of generality, that the enter of ma of the wheel ytem lie at the midpoint of the line oining the enter of the wheel. IV. GAI DESIGN he gait employed for thi robot reemble a reptilian trot. Due to the inherent tati tability of our ytem (thank to the upport/teering wheel), two leg an be lifted off the ground at any time, during normal gait. Diagonally oppoite leg are linked together ymmetrially to imulate a virtual biped gait. he oint variable ommanded to the three oint i the ame for both leg. ike a human bipedal gait, the robot fall forward (via puhing from the two grounded leg) after the firt pair i off the ground. he preene of the upport/teering wheel prevent the robot from toppling over. A. alking in a Straight-ine Path hi etion preent the equene of event leading to traight-line forward motion of the robot, a demontrated in the imulation of Figure. Firt, leg and are lifted off the ground (ee Figure 4b). hey are then moved to their maximum oint limit on both revolute oint on eah leg. hen the primati oint i extended to reah the ground. At thi point of time, two event happen in parallel. eg and traighten themelve, uing the fritional fore to puh the body frame forward. At the ame time, leg and 4 lift off the ground. hi entire yle repeat again with leg and 4. hi drive the body forward a demontrated in the erie of diagram. he teering heading angle i maintained at nominal (zero angle) o the paive wheel are rolling traight ahead. Figure 4d Figure 4e Figure 4f Figure 4g Figure 4h Figure 4. Gait Simulation for Straight-ine raetory he enter of gravity of the ytem i plotted at eah intant to verify that tati tability ontraint are atified. Snaphot of the tati tability polygon for poition 4b, 4 and 4d are hown in Figure 5. Z X Y Figure 5a. Stati Stability Polygon for Figure 4b Figure 5b. Stati Stability Polygon for Figure Figure 4a Figure 4b Figure 4 Figure 5. Stati Stability Polygon for Figure 4d

5 Figure 5. Plot howing the enter of gravity of the ytem he O mark on the diagram in Figure 5 i the enter of gravity of ut the quadruped with leg but without the upport/teering wheel. he X mark on the diagram i the enter of gravity of the entire ytem. It an be een that the enter of gravity of the entire ytem doen t i loe to the quadruped enter of gravity; thi i true for all motion. i hown in Figure 7 (a)-(). eg repeat the ame. hi i hown in Figure 7 (d)-(e). It i obviou that thi partiular equene i unique to the failure of eg. Hene, the on-board proeor ha to orretly determine whih leg i at fault and run the orreponding limping routine. hi add a deign ontraint in that eah leg hould be powerful enough to drag the entire body frame forward. B. alking along a urved Path hen the teering wheel i ontrolled to deired angle, the robot walk along a urved path. he leg power the body forward and the teering mehanim et the traetory. Intuitively, the body will follow where the teering mehanim goe. If the teering angle i ontant and non-zero, the urve will be a irle. he appropriate tranformation give the next et of arteian oordinate and alo the orientation of the robot. In our imulation, we et the robot on an infinite loop to move by degree to the left every tep (traing a irle). wo naphot of the robot at different poition along the traetory are hown in Figure 6 below. Figure 7a Figure 7b Figure 6a Figure 7 Figure 6b Figure 6. Gait Simulation for a urvilinear raetory. imping in the ae of Failure hi i a unique feature that our preliminary invetigation ha given u. e have deigned the robot o that when one of the leg wa diabled and the gait orrepondingly modified, the robot ould till arry on forward motion. hi i a firt tep (pun intended!) toward one-failure-afe operation. Figure 7d e imulated eg to be handiapped. e then modified the gait in the following fahion: eg lift up, balaning the body on eg, eg 4 and the upport wheel. hen eg move forward, ome down and advane the body frame forward. hi

6 make an amphibiou biomimeti robot apable of travering hotile terrain. REFERENES Boone, Gary, and Hodgin, Jeia. "alking and Running Mahine". he MI Enylopedia of the ognitive Siene, MI Pre, 998 Figure 7e Buket, J. R. (977). Deign of an On-board Eletroni Joint Sytem for a Hexapod Vehile. Mater thei, Ohio State Univerity raig, J.J (989), Introdution to Roboti: Mehani and ontrol, Addion eley Publihing o., Reading, MA. Hiroe, S., and Y. Umetani. (98), he bai motion regulation ytem for a quadruped walking mahine., Amerian Soiety of Mehanial Engineer Paper 8-DE-4. Figure 7f Figure 7. Gait during imping V. ONUSION hi paper preent a new deign olution addreing tati tability iue for a walking quadruped robot. e preented our onept, followed by forward and invere poe kinemati. e then preented example for linear, urvilinear and limping gait and oberved the poition of the enter of ma at every intane (it mut remain within the grounded foot polygon to enure tati tability). o date we have ued imple, ymmetri FPK-baed gait. e will develop general IPK-baed gait method to omplement thi imple approah. IPK-baed method will be developed at two level:. at the leg level, to allow general plaement of eah foot relative to the body; and. at the world level, i.e. ontrolling the walking of the robot in the global arteian frame. hu far we have foued on planar motion but we will oon onider general D walking motion and gait. he reult obtained were enouraging and we plan to build a model of the ytem. e are working on ommanding the robot to follow ompliated urve. Due to the relatively mall hardware requirement on board, we plan to inorporate a imple arm to enable pik and plae operation. e ultimately plan to Hiroe, Shiego, Kato, Keiuke Soure (), Study on Quadruped walking robot in okyo Intitute of ehnology pat, preent and future. IEEE International onferene on Roboti and Automation, v, p MGhee, R. B. (98), Vehiular legged loomotion. In G. N. Saridi, Ed., Advane in Automation and Roboti. JAI Pre. Quinn, R. D. Nelon, G.M., Bahmann, R.J., Kingley, D.A., Offi, J. and Ritzmann, R. E. (). Inet Deign for Improved Robot Mobility. In Pro. of limbing and alking Robot onferene (AAR), Profeional Engineering Publiation, edited by Bern and Dillmann, Karlruhe, Germany, pp Simmon, R., E. Krotkov,. hittaker, and B. Albreht. (99). Progre toward roboti exploration of extreme terrain., Applied Intelligene: he International Journal of Artifiial Intelligene, Neural Network and omplex Problem-Solving ehnologie (): 6 8. Song, S. M., and K. J. aldron. (989). Mahine hat alk. ambridge, MA: MI Pre.