CPG Driven Locomotion Control of Quadruped Robot

Transcription

1 Proceedngs of the 2009 IEEE Internatonal Conference on Systems, Man, and Cybernetcs San Antono, TX, USA - October 2009 CPG Drven Locomoton Control of Quadruped Robot Chengju Lu 1 Yfe Chen 1 Jaq Zhang 1 Qjun Chen 1 School of Electroncs and Informaton Engneerng Tongj Unversty Shangha, , Chna 9611luchengju@tongj.edu.cn Abstract Accordng to bologcal evdences, central pattern generators(cpgs) are neural networks responsble for the generaton of rhythmc movements for anmals, such as breathng, heartbeat, and locomoton, even when solated from the bran and sensory nputs. Inspred by ths mechansm, researchers have proposed the CPG drven control method as a new way to generate rhythmc control polces for the locomoton of legged robots. In ths work, we desgn a CPG control constructon for controllng the locomoton of a quadruped robot, whch s capable of realzng the dfferent gats and gat transtons. Frstly, a body CPG network s constructed by mutually coupled phase oscllators, whch can produce multple phase-locked oscllaton patterns that correspond to the four basc quadruped gats. The gat transtons can be realzed by alterng the nternal oscllator parameters. Then, we desgn a robotc platform based on Webots and AIBO, and realze dynamc locomoton wth the desgned CPG network for AIBO. The Smulaton and expermental results demonstrate the proposed CPG network s effectve to generate gat patterns for quadruped robots. Keywords CPG, quadruped robot, gat pattern, gat transton, AIBO, Webots I. INTRODUCTION The locomoton control of legged-robot s a great challenge that has not yet been completely solved. The most popular moton desgn method s the trajectory-based method[1]. The basc dea of ths method s to fnd moton trajectores for every foot and then calculate the movements for the other jonts. These trajectores are usually desgned by tral-and-error or from some optmzaton algorthms[2-4]. There have dsadvantages for ths method: Frstly, we have to possess a perfect knowledge of the robot s dynamcs; Secondly, t s not sut for unknown envronment. Presently, nspred by anmals' rhythmc moton mechansm n nature, researchers have proposed the CPG drven control method as a Ths work s supported by Natonal Natural Scence Foundaton of Chna (No ), and the Natonal Hgh Technology Research and Development Program of Chna (863 Program, No. 2009AA04Z213) new way to generate adaptve control polces for the locomoton of robots. In bology, neurobologsts revealed the evdence that anmals have specalzed neural crcuts, referred to as central pattern generators (CPGs), whch can produce rhythmc movements even when solated from the bran and sensory nputs[5-8]. CPG networks present several nterestng propertes ncludng dstrbuted control, the ablty to deal wth redundances, fast control loops, and allowng modulaton of locomoton by smple nput sgnals[9]. Inspred by bologcal CPGs propertes, researchers found a new way to buldng control blocks for rhythmc movements control n artculated robots. Wth ths method, we do not need to buld knetcs models of the system and can get better adaptve ablty to the envronment. In robotcs, CPGs are often modeled as coupled dynamcal systems, whch can generate complex output waveforms. At present, CPGs are often smulated by neural oscllator model (e.g. Hodgkn-Huxley(H-H) model, Ftzhugh-Nagumo model, ntegrate-and-fre neuron models), and nonlnear oscllators (e.g. Hopf oscllator, Raylegh oscllator and Van der Pol oscllator). The dynamc characterstc analyss of CPG network s usually dffcult because of ts nonlnear and chaotc property. So far, very few methods are useful to modulate the parameters for generatng a perodc sgnal wth a specfc shape. Ths s a certan lmtaton n the development of CPG drven engneerng systems. CPGs have been already employed by researchers n the generaton of gats for robots. Such as, nspred by nsect locomoton, CPGs have been used to control hexapod and octopod robots[10][11]; CPG networks nspred by lamprey have been used for controllng lamprey-lke robots[12][13]. Quadruped locomoton control has been extensvely explored, lke for example by Kmura on quadruped robots Patrush and Tekken[14][15], Ijspeert on salamander robot[16], and Ilg W.[17], Bllard[18], Tsuchya[19][20] n quadruped robots too. CPG drven methods are also ncreasngly used for the control of bped locomoton, often nspred by Taga s work on neuromechancal smulatons[21]. Our work follows the research lne taken by Ijspeert et al. wth ther results n the generaton of gats for the lamprey, but /09/$ IEEE /09/$ IEEE 2442

2 we try to slghtly mprove n several ponts: Frst, we ntroduce a general body CPG archtecture, wth whch we can get several gat patterns and realze gat transtons easly; Second, we use a more complex robot AIBO, whose every leg has three degrees of freedom that must coordnate, and a meanngful control CPG network s constructed; Thrd, we apply CPG control network to the real AIBO robot. The organzaton of ths paper s as follows: In Secton II, by usng smple phase oscllator adapted from Kuramoto model[22], we construct a body CPG network, and by changng nternal parameters, the gat transtons can be realzed easly; In Secton III, based on the prevous work we have done on AIBO, we realze the dynamc locomoton wth CPGs control network for AIBO. By applyng Webots software and real AIBO, we valdate the CPG drven method. Fnally, concludng remarks and future work are gven by secton IV. II. CONSTRUCTION OF THE CPG NETWORK FOR QUADRUPED ROBOTS In ths secton, we wll construct a CPG network by means of coupled oscllators to generate the jont trajectores for the quadruped robots. The CPG model should satsfy several propertes, such as: Has lmt cycle behavor. So the oscllatory patterns are robust aganst transent perturbatons; And, the lmt cycle can be smoothly modulated by some parameters whch offer the possblty to smoothly modulate the gat patterns; The coupled oscllators of CPG must be synchronzed and phase locked. A. CPG model Phase oscllator s probably the smplest type of oscllator, where the radus s completely neglected, only the phase s retaned. In ths paper, we apply an extenson phase oscllator, called ACPO (ampltude controlled phase oscllator), adapted from[22][23], whch oscllatory radus s controlled by a dfferental equaton wth a fxed pont attractor as follows N θ = w + λ sn( θ θ Δφ ) (1) j j j j= 1 r R r r (2) 2 x = r[1+ sn( θ)] (3) Equaton(1) s a modfed Kuramoto model of a populaton of N coupled phase oscllators. θ s the phase of the th oscllator. w s frequency parameter. Each oscllator n (1) tres to run ndependently at ts own frequency, whle the couplng term λ j tends to synchronze t to all the others[22]. Δ φ j denotes the desred phase shft between oscllator and j. Equaton (2) ensures that the ampltude r wllψasymptotcally 2 3 = μ ( ) μ and monotoncally converge to R ths allows us to smoothly modulate the ampltude of oscllatons, and μ s a postve constant. Equaton (3) s the transform of nstantaneous nternal phase to external angle sgnal. Such a CPG model has lmt cycle behavor and the output forms can be adjusted by explct parameters. For example, the ampltude and frequency can be modulated easly as shown Fg. 1. Fg. 1 Change n frequency and ampltude of the oscllator B. CPG Network Archtecture For anmals, the patterns produced by the CPGs varously change to meet the surroundng envronment, such as horses, they select dfferent gat patterns n accordance wth the desred locomotve speed. As n Fg. 2, there are four basc quadrupedal gats: the walk, trot, pace and bound. walk pace Fg. 2 The phase of typcal gats (black: standng phase, whte: swng phase) In the present study, we construct a quadrupedal body locomotor CPG as a network of four coupled phase oscllators. Each oscllator controlled one jont movements of a sngle lmb. By connectng the oscllator of each lmb, oscllators are mutually entraned and oscllate n the same perod and wth a fxed phase dfference. Ths mutual entranment between the oscllators of the lmbs results a gat. And by changng the phase dfference between the oscllators, we can get the four basc gats. In our study, we are only nterested n nterlmb coordnaton,.e., the relatve phases between the lmbs (CPG oscllators) of the quadruped. So we set ampltude parameters R = 2 and frequency parameters w = 10 for all oscllators. Couplng coeffcents λ j set to 4 for all the oscllators, and the phase dfferences between neghbor oscllators are set to postve for the descendng connectons and negatve for the ascendng connectons. Fg. 3 s an example for walkng LF LR RF RR LF LR RF RR trot bound 2443

3 pattern, gat accordng the order Four oscllators are coupled together accordng to a connecton matrx con. walk. The connecton matrxes between the oscllators denote the phase dfference. By desgnng the connecton matrx, we can get the other three basc gats easly as show n Fg. 4. sgnfcant advantage of CPG drven methods for controllng locomoton over other methods (e.g. trajectory-based method). LF RF OSC1 OSC2 con OSC4 OSC3 LR Fg. 3 Walkng network and connecton relaton between the body OSC. RR Fg. 5 Walkng pattern wth perturbaton C. Gat Transtons Quadruped walkng anmals can easly change ther gat patterns to sute the envronment, but shftng locomoton patterns s a dffcult task for legged-robot. Two methods are usually used to realze the gat transtons for CPG drven method: one s changng the drvng sgnal to CPG; another s changng couplng confguraton[15]. In ths secton, we attempt to realze the gat transtons by swtchng the couplng structure,.e. by changng the connecton matrx to realze the smooth gat transton. Fg. 6 shows examples of gat transtons: walk-trot-pace and trot-walk-bound. 0 π π/2 3 π/2 π 0 π/2 π/2 π/2 π/2 0 π π/2 π/2 π 0 walk = (a) wakng pattern 0 π 0 π π 0 π 0 0 π 0 π π 0 π 0 trot = (b) trottng pattern (a) 0 π π 0 π 0 0 π π 0 0 π 0 π π 0 pace = (c) pacng pattern π π π π π π π π bound = (d) boundng pattern Fg. 4 Four basc gat patterns and the connecton matrxes In order to llumnate the robustness aganst perturbaton property, we present the case when the state varable for the left front leg gets fxed for 0.1s and then released agan durng walk. The two vertcal lnes show the tme when the leg s fxed and released agan. As can observed n Fg. 5, after release the fxed term, the leg can catch up wth the other legs to fulfll the requrement of the gat pattern quckly. Ths s a Fg. 6 Examples of gat transtons: (a) walk-trot-pace, (b) trot-walk-bound III. (b) ROBOTIC PLATFORM AIBO ROBOT A. Prevous Work wth AIBO The four legged robot AIBO has 20 degrees of freedom and the coordnaton of all them to obtan a locomoton pattern s very dffcult. Our team has been used AIBO to play soccer n the RoboCup for many years. 2444

4 Prevously, we realzed locomoton control of AIBO based on conventonal trajectory-based methods. We bult the knetc model of robot and then desgned trajectores for every leg. The loc experenced from rectangle, parabola, ellpse, modfed ellpse to 3-D polygon. In ths secton, we take parabola locus wth Lagrange nterpolaton, as Fg. 7 shows, for trajectory plan as example. Fg. 8 shows the angular value plots for jont rules whch are calculated wth nverse knematcs: The frst one s for the shoulder jont whch controls the movng forward; the second one s for the other shoulder jont whch controls the movng sde; the thrd one s for the knee jont. B. CPG Control Network for AIBO In the present work, we evolve a CPG controller for the AIBO to produce the same locomoton trajectores that we have developed for AIBO wth trajectory-based method above, whch s much more meanngful than prevous work to walk n real world. For the locomoton, we only focus on the 12 degrees of freedom on four legs. Fg. 9 shows the structure of whole CPG network. Body oscllators 1, 2, 3 and 4 ndcate the four shoulder jonts controllng to move forward. In the left front leg, oscllator 5 and 6 ndcate the shoulder jont controllng to move sde and knee jont, respectvely. We let two adjacent oscllators are coupled n both drectons, and the oscllators are chaned along the legs. Front Left Leg Front Rght Leg OSC1 OSC2 7 Fg. 7 Locus of walkng gat. Each locus of every leg are generated by applyng Lagrange nterpolaton 11 OSC4 OSC Rear Left Leg Rear Rght Leg Fg. 9 Structure of CPG for AIBO Before usng the outputs of CPG network to control the locomoton of AIBO, we have to do some transformaton, ncludng frequency transformaton, phase relatonshp adjustment and ampltude transformaton. In ths secton, we take the walkng pattern for example. 1) Frequency transformaton To get to know the expected frequency, we do FFT to the three jonts on the left front leg, whch are got n the above secton as Fg. 10. Fg. 8 The control rules to the three jont angles on the left front leg Fg. 10 FFT results of the three jonts of LF leg 2445

5 From the results, we can select the frst term of the Fourer seres for the frst two jonts. By adjustng parameter w n (1), we can get the frequency we want. For the knee jont, we want to select the frst two terms and that wll be closer to the real knee movement, but that wll complcated the CPG network. So n ths work, we only consder the frst term of the Fourer seres for all the jonts. As for the AIBO, we set w = 12.6 for all the oscllators. 2) Phase transformaton From Fg. 11, we can fnd that postve drecton of the jont angles for the rear legs s backwards, whch s opposte to the front legs. For our CPG model, t s easy to change the output waveform n-phase or ant-phase status. As we have mentoned above, by change parameters n (1) and (2), we can change the frequency and the ampltude onlne easly. Thanks to ths property, so we can adjust the frequency and ampltude of the outputs onlne to let the robot adapt the envronment. And because of the lmt cycle behavor, transent perturbatons to the network can be gnored. C. Expermental Results 1) Typcal locomoton gats In our experment, we focus on two basc gat patterns: walkng and trottng. Fg. 13 shows the snapshots of smulated AIBO walkng and trottng gats sequences. And Fg. 14 s the real experment on the real AIBO. From the results we can fnd that the real robot can walk and trot n the same manner as the smulated robot wth some mnor dfference. Fg. 11 The defnton of the jont angles on legs 3) Ampltude transformaton From prevous experment, take left front leg as example, we know that the angles of AIBO n the shoulder jont whch controls the movng forward change (on average) n the range ( , ) and n the shoulder jont whch controls to move sde n the range( , ) and n the knee jont n the range ( , ). To obtan the output control sgnals n above ranges the followng scalng can been done X X X = x = x = x Wth all the above transformaton work, we get the fnal results as Fg. 12. (4) (a) (b) Fg. 13 Smulated AIBO (a) walkng sequence (b) trottng sequence (a) (b) Fg. 14 Real AIBO (a) walkng sequence (b) trottng sequence Fg. 12 The output of the CPG network (LF and LR legs) 2) Control of speed durng walkng As we have mentoned above, by change w n (1), we can change the frequency onlne easly. So f ths parameter could be affected by some feedbacks, robot can adapt to envronment. In our experment, we enlarge parameter w to get faster dynamc walkng speed, but too large w makes dynamc walkng unstable. 3) Gat transton durng walkng 2446

6 By changng the connecton matrx, we can realze the basc gat transtons easly. From our experments, we fnd that the gat transtons can complete wthn one or two gat cycles. In ths paper, we have not consdered the affect of the varaton of the gravty center, so the experments results are not as perfect as we want. What we have done n ths paper s only a part of our whole work. Compared to trajectory-based method, CPG drven approach s more meanngful for AIBO to realze adaptve and dynamc locomoton n the real world. If addng the learnng process, the transformaton work wll be much easer than we have descrbed n the paper because most of the parameters can be acqured by the learnng process. IV. CONCLUSION AND FUTURE WORK The present paper shows how a CPG network can be used to generate gats for a complex quadruped robot wth 12 degree of freedom. The CPG constructed by the couplng oscllators wth locked phase dfference and synchronzaton. The output gat forms can be adjusted on lne by the nternal parameters. We realzed the basc smooth transtons of the four gats, and compared to the other transton methods, t s very easy and effectve. In ths paper, our CPG network does not ntegrate the sensor s feedback, n the future work, we wll construct a CPG network wth a reflex system whch may be helpful n front of unpredcted crcumstances. Many thngs wll be done n future: (1) How to evolve the structure of CPG network to mprove the control effcency; (2) By combnng conventonal methods to compensate the dsadvantages of the CPG drven method; (3) Control the real robot accurately to adapt undetermned envronment. ACKNOWLEDGMENT We would lke to thank the members of the TJArk team of Tongj Unversty for ther efforts n developng the software platform used n ths work. REFERENCES [1] M. Vukobratovc, B. Borovac, D. Surla and D. Stokc, Bped locomoton: dynamcs, Stablty, Control and Applcatons, Sprnger, [2] G. S. Hornby, S. Takamura, T.Yamamoto and M. Fujta, Autonomous Evoluton of Dynamc Gats Wth Two Quadruped Robots, IEEE Transactons on Robotcs, vol. 21, No. 3, [3] N. Kohl, P. Stone, Machne learnng for fast quadrupedal locomoton, In: The Nneteenth Natonal Conference on Artfcal Intellgence, pp , [4] M. S. Km, W. Uther, Automatc gat optmsaton for quadruped robots, n Australasan Conference on Robotcs and Automaton, Brsbane, December [5] CS. Sherrngton, Flexon-reflex of the lmb, crossed extenson reflex and the steppng reflex and standng, J Physol. vol. 40, pp , [6] T. G. Brown, The ntrnsc factors n the act of progresson n the mammal, Proceedngs of the Royal Socety of London, Seres B, vol. 84, No. 572, pp , [7] T. G. Brown, The factors n rhythmc actvty of the nervous system, Proceedngs of the Royal Socety of London, Seres B, vol. 85, No. 579, pp , [8] T. G. Brown, On the nature of the fundamental actvty of the nervous centres; together wth an analyss of the condtonng of rhythmc actvty n progresson, and a theory of the evoluton of functon n the nervous system, J. Physol, vol. 48, pp , [9] M. L. Marlyn, Central pattern generaton of locomoton: A revew of the evdence, Physcal Therapy, vol. 82, No. 1, pp , [10] S. Inagak, H. Yuasa, and T. Ara, CPG model for autonomous decentralzed mult-legged robot system generaton and transton of oscllaton patterns and dynamcs of oscllators, Robotcs and Autonomous Systems, vol. 44, No. 3-4, pp , [11] S. Inagak, H. Yuasa, T. Suzuk, and T. Ara, Wave CPG model for autonomous decentralzed mult-legged robot: Gat generaton and walkng speed control, Robotcs and Autonomous Systems, vol. 54, No. 2, pp , [12] A. J. Ijspeert, A. Cresp, Onlne trajectory generaton n an amphbous snake robot usng a lamprey-lke central pattern generator model, In Proceedngs of the IEEE nternatonal conference on robotcs and automaton, [13] A. J. Ijspeert, A. Cresp, and J. M. Cabelguen, Smulaton and robotcs studes of salamander locomoton: Applyng neurobologcal prncples to the control of locomoton n robots, NeuroInformatcs, vol. 3, No. 3, pp , [14] Y. Fukuoka, H. Kmura, and A. H. Cohen, Adaptve dynamc walkng of a quadruped robot on rregular terran based on bologcal concepts, The Internatonal Journal of Robotcs Research, vol. 22, No. 3-4, pp , [15] H. Kmura, Y. Fukuoka, and A. H. Cohen, Adaptve dynamc walkng of a quadruped robot on natural ground based on bologcal concepts, Internatonal Journal of Robotcs Research, vol. 26, No. 5, pp , [16] L. Rghett, A. J. Ijspeert, Pattern generators wth sensory feedback for the control of quadruped locomoton, IEEE Internatonal Conference on Robotcs and Automaton, pp , [17] W. Ilg, J. Albez, H. jedele, et al, Adaptve perodc movement control for the four legged walkng machne BISAM, IEEE. Robotcs & Automaton, Detrot Mchgan, pp , [18] A. Bllard, A. J. Ijspeert, Bologcally nspred neural controllers for motor control n a quadruped robot, Proceedngs of the Internatonal Jont Conference on Neural Networks, Pscataway, NJ, USA: IEEE, pp , [19] K. Tsujta, K. Tsuchya, and A. Onat, Adaptve gat pattern control of a quadruped locomoton robot, In IEEE nternatonal conference on ntellgent robots an systems, 2001a. [20] K. Tsujta, K. Tsuchya, and A. Onat, Decentralzed autonomous control of a quadruped locomoton robot, Artfcal Lfe and Robotcs, pp , 2001b. [21] G. Taga, Y. Yamagueh, and H. Shmzu, Self-organzed control of bpedal locomoton by neural oscllators n unpredctable envronment, Bol. Cybern., vol. 65, pp , [22] J. A. Acebrón, L. L. Bonlla, and C. J. Pérez, The Kuramoto model: A smple paradgm for synchronzaton phenomena, Revews of Modern Physcs, pp , [23] A. J. Ijspeert, A. Cresp, D. Ryczko, and J. M. Cabelguen, From Swmmng to Walkng wth a Salamander Robot Drven by a Spnal Cord Model, Scence, vol. 315, pp ,