Adaptive Gait Pattern Generation of Biped Robot based on Human s Gait Pattern Analysis

Transcription

1 Adaptve Gat Pattern Generaton of Bped Robot based on Human s Gat Pattern Analyss Seungsuk Ha, Youngjoon Han, and Hernsoo Hahn Abstract Ths paper proposes a method of adaptvely generatng a gat pattern of bped robot. The gat synthess s based on human s gat pattern analyss. The proposed method can easly be appled to generate the natural and stable gat pattern of any bped robot. To analyze the human s gat pattern, sequental mages of the human s gat on the sagttal plane are acqured from whch the gat control values are extracted. The gat pattern of bped robot on the sagttal plane s adaptvely generated by a genetc algorthm usng the human s gat control values. However, gat trajectores of the bped robot on the sagttal plane are not enough to construct the complete gat pattern because the bped robot moves on 3-dmenson space. Therefore, the gat pattern on the frontal plane, generated from Zero Moment Pont (), s added to the gat one acqured on the sagttal plane. Consequently, the natural and stable walkng pattern for the bped robot s obtaned. Keywords Bped robot, Gat pattern, Genetc Algorthm. I. INTRODUCTION UMANOID robots are expected to assst human actvtes H n daly lfe. Therefore, humanod robots are asked to walk natural to provde ntmacy to human. The human gat s a complex dynamc actvty. The complcated human model that has 3D deformable frame, hgh DOF, and complex mechancal structure cannot be appled drectly to smplfed bped robots. To overcome these problems, many researches have assumed that the human gat s optmzed n the vew of the gat energy, and they have defned the natural gat of the bped robot as the movement that mnmzes ts gat energy. Therefore, many researches about the gat pattern generaton of the bped robot focus on mnmzng the gat energy of them[,2,3,4]. Snce a lot of the parameter values cannot be obtaned only from mnmzng the gat energy of the bped robot, adaptve technques such as Genetc Algorthm and Neural Network Algorthm have been studed. Cap[5] proposed a gat synthess method of bped robots usng GA. The gat synthess durng walkng s analyzed from the mnmum consume energy (MCE) and mnmum torque change (MTC). The stablty of the robot Manuscrpt receved June 30, F. SeungSuk Ha s wth the Electrcal Engneerng Department, Unversty of Soongsl, Sando-dong, Dongjak-ku, Seoul , Korea (e-mal: ssu004@ssu.ac.kr). S. Youngjoon Han s wth the Electrcal Engneerng Department, Unversty of Soongsl, Sando-dong, Dongjak-ku, Seoul , Korea (e-mal: young@ssu.ac.kr). T. Hernsoo Hahn s wth the Electrcal Engneerng Department, Unversty of Soongsl, Sando-dong, Dongjak-ku, Seoul , Korea (e-mal: hahn@ssu.ac.kr). gat s verfed by of the bped robot. Zhe Tang[6] analyzed dynamc elements of the sagttal, frontal and transverse plane and combned the dynamc elements on every planes usng Pareto Optmal Soluton and GA. Although these works have acheved the mnmum energy and stablty of the gat pattern usng MCE and adaptve technque, the gat pattern of the bped robot s stll not natural lke human because t was consdered only n the vewpont of robot s structure In order to acheve the natural gat of bped robot lke human, human s gat has to be modeled accurately. However, snce the human s gat s composed of dynamc motons on the sagttal, frontal and transverse plane, the complete gat of the bped robot can be acheved only f the gat s analyzed on two more planes. Ths paper proposes adaptve gat pattern generaton method usng GA. Snce the smplfed structure of bped robot s not enough to model human s complex body structure, to accurately analyze the human s gat pattern, sequental mages of the human s gat on the sagttal plane are acqured, and then human s gat control values are extracted from the mage sequences. The extracted gat control values are appled to the bped robot model, and the dynamc elements on two more planes have to be consdered to obtan 3-Dmensonal gat patterns. For ths purpose, ths paper analyzes dynamc elements on the sagttal and transverse planes, and then generates the adaptve gat pattern usng GA. The human s sagttal plane analyss drves the bped robot gat pattern smlar to the human natural gat pattern. And then dynamcs elements on the transverse plane generate the gat pattern of the bped robot on the frontal plane. That s, the gat pattern of the bped robot on the frontal plane s generated so that the calculated of the bped robot converges nto the desred. Ths paper s organzed as follows. Secton II explans the analyss method of human s gat pattern. Secton III descrbes the walkng dynamcs. Secton IV presents the gat plannng method of the bped robot. Experments of gat generatons and smulatons about the bped robot are executed n Secton V. Conclusons are gven fnally. II. HUMAN S GAIT PATTERN ANALYSIS It s dffcult for the human s gat pattern to be appled to the bped robot model because t has the complcated mechancal structure. Therefore, the human model for the gat analyss PWASET VOLUME 23 AUGUST 2007 ISSN WASET.ORG

2 needs to be as possble as smple. From ths pont of vew, physologsts make t show that the most walkng dynamcs take place on the sagttal plane [7], or the plane bsectng the human body as shown n Fg. (a). Hence, ths paper uses a 5-lnk bped locomoton model to approxmate the human s complex mechancal structure n the mage sequences. The helpful walkng devce as shown n Fg. (b) s used so that the human s walkng movement s lmted to sagttal plane. That s, the human s walkng pattern s lmted to X-Y plane. ( xb, y b) : the coordnate of the tp of the swng lmb τ : control torque of lnk III. WALKING DYNAMICS Ths paper analyzes Sngle Support Phase(SSP) and Double Support Phase (DSP) usng the dynamc model of Lagrangan equaton of the 5-lnk bped robot [8]. A. Sngle Support Phase (SSP) dynamcs The SSP s a state that one leg of the bped robot swngs and the other leg s n contact wth the ground. The dynamcs of the 5-lnk bped on the SSP can be derved from Lagrangan equaton as shown n Eq. () D( θ) θ + H( θ, θ) θ + G( θ) = T () (a) sagttal plane (b) the helpful walkng devce Fg. sagttal plane and the helpful walkng devce The 5-lnk bped model s constructed as shown n Fg. 2. The bped robot model conssts of fve lnks: a torso and two legs. It also has two pelvses at the hp, two knees between the thghs and the shanks, and two ankles at the tps of the two lmbs. All of the jonts can only rotate on the sagttal plane and have no frcton. Feet are not consdered n ths bped model. Ths fve lnk bped model parameters are represented as follows. M : mass of lnk L : length of lnk d : dstance from jont to the COM of lnk I : moment of nerta of lnk θ : angle of lnk ( x, y ) : the coordnate of the supportng pont e e where D( θ ) s the 5 5 postve defnte and symmetrc nerta matrx, H ( θ, θ ) s the 5 5 Centrfugal and Corols matrx, G ( θ ) s the 5 matrx of gravty terms, θ, θ, θ,t are the 5 vectors of generalzed coordnates, veloctes, acceleratons and torques, respectvely. B. Double Support Phase (DSP) Dynamcs On the DSP, both of the feet are n contact wth the ground. Snce contact postons of tps of two lmbs on the ground are known durng DSP, a set of holonomc constrants s gven as Eq. (2): f x x L Φ = = = e b ( θ ) 0 f y y 2 e b where L s the dstance between tps of two lmbs. In order to be appled to the dynamc dervaton, t s dfferentated twce wth respect to tme as gven n Eq. (3). (2) Φ ( θ) = J ( θ) θ = 0 (3) Φ ( θ) = J( θ) θ + J( θ) θ = 0 where J ( θ ) s the jacoban matrx n Eq. (4). J( θ ) = l cosθ l cosθ 0 l cosθ l cos θ l snθ l snθ 0 l snθ l snθ (4) The vector equaton of the dynamcs on DSP s gven n Eq. (5). T D( θ) θ + H( θ, θ) θ + G( θ) = J ( θ) λ + T (5) where λ s a 2 vector of Lagrange multplers. Fg. 2 5-lnk bped model IV. GAIT PATTERN GENERATION Moton components of the complete gat for the bped robot PWASET VOLUME 23 AUGUST 2007 ISSN WASET.ORG

3 are dvded nto three planes: sagttal, frontal, and transverse plane. Therefore bped robot must have gat patterns on two more planes. Ths paper consders two gat patterns on the sagttal and transverse plane to analyze the dynamcs of the bped robot. The gat pattern on sagttal plane can be generated usng human s gat control values. And the gat pattern on frontal plane s generated usng the desred trajectory on transverse plane. A. Gat Phases The gat of the human s a perodc moton whch alternates between the DSP and the SSP. On the DSP, both of the humanod robot feet are n contact wth the ground. On the other hand, one leg swngs and the other leg s n contact wth the ground on the SSP. The constrant values of the bped robot can be extracted from the human gat. The humanod moton on the frontal plane ams to move the of the bped robot from one foot to the other. One leg of the robot has two DOFs, one at the hp jont and the other at the ankle jont, to control the robot gat on the frontal plane. To smplfy the gat plannng, t s assumed that the bped robot always keep two legs parallel. So the angles of four DOFs have the same value θ frontal as shown n Fg. 3. Moreover, t s assumed that the bped robot s feet are parallel wth ground. walkng. The gat pattern on the sagttal plane can be adaptvely generated by the skewness and kurtoss value. For unvarate data Y, Y,, Y, formulas for skewness and kurtoss are gven 2 N n Eq. (6) and Eq. (7) respectvely. Skewness > 0 Skewness = 0 Skewness < 0 Kurtoss > 3 Kurtoss = 3 Kurtoss < 3 Fg. 4 Skewness and Kurtoss Skewness= Kurtoss= N = ( Y Y ) ( N ) s N = ( Y Y ) ( N ) s where Y s the mean, s s the standard devaton, and N s the number of data ponts. C. Zero Moment Pont () In ths paper, the whch determnes the stable pose of the bped robot s used to generate the gat pattern of t. It follows that the moton of a bped robot would be always stable only f the s located nsde the supported area where the feet of the bped robot are confned as the contactng boundary [9]. The s the pont where the total nerta force of the bped robot equals zero. The can be gven n Eq. (8) (6) (7) Fg. 3 Walkng patterns on the sagttal and frontal plane B. Gat Control Values on the Sagttal Plane In order to obtan features of the gat torques durng gat, the skewness and kurtoss value of the gat torques are calculated. The skewness and kurtoss, fundamental values n statstcal analyses, characterze the varablty of the dstrbuton of a data set. The skewness s used as a symmetrcal measure of the data dstrbuton. If the skewness of a data set s zero, the dstrbuton of a data set s symmetrc. The kurtoss s a measure of whether the data dstrbuton s sharp or flat relatve to a normal dstrbuton. That s, the dstrbuton wth hgh kurtoss tends to have a dstnct peak at the mean, declne rather rapdly, and have heavy tals as shown n Fg. 4. Therefore, the gat torque of the bped robot can be compared wth the gat torque of human bped robot durng x y = n n n m ( z + g) x m x z I Ω y y = = = n = = m ( z + g) = n n n m ( z + g) y m y z I Ω x x = = = n m ( z + g) where m s the mass of lnk, I x and I are the nertal y component, Ω and Ω are absolute angular acceleraton x y components, g s the gravtatonal acceleraton, ( x, y, z ) s the coordnate of the mass center of lnk n an absolute Cartesan coordnate system. Usng the Eq. (8), the of the bped robot can be desgned on the transverse plane as shown n Fg. 5. (8) PWASET VOLUME 23 AUGUST 2007 ISSN WASET.ORG

4 After obtanng the gat pattern on the sagttal plane, the GA s executed to generate the gat pattern on the pattern frontal plane. The ftness functon of the GA for the gat pattern on the frontal plane s defned as Eq. (0). Fg. 5 Desred D. Adaptve Gat Pattern Generator The schematc dagram of the proposed algorthm s summarzed n Fg. 6. T c J = E dt mn 2 (0) 0 where E s the absolute error value between the desred robot and calculated gven n Eq. (8). V. EXPERIMENTS Fg. 6 Adaptve walkng pattern generator The algorthm begns to acqure the sequental mages of the human s gat to fnd control values of the human s gat n the mages. The control values generate the gat pattern of the bped robot on sagttal plane. In the second stage, Genetc Algorthm (GA) s executed as shown n Fg. 7. A. Human Gat Analyss Four makers are attached to head, hp, leg, and ankle for analyzng the gat pattern of the human such as shown n Fg.8. Two gat helpful frameworks are also set at two legs so that the human s gat s lmted to the sagttal plane. Then sequental mages are acqured through CCD dgtal camera (IPX-VGA 20). The human s gat control parameters are obtaned from Extract Human Walkng Parameter (EHWP) program. And human s gat pattern s conssted of total 80 frames durng one perod. Fg. 8 Extracton Human Walkng Parameter Fg. 7 Genetc Algorthm The angles, veloctes, and acceleratons of the jonts of the human are shown n Fg. 9. The GA s used to fnd a true or approxmated soluton wth respect to optmzaton problem. The GA s categorzed as global search heurstcs and nspred by evolutonary bology such as mutaton, selecton, and crossover. Ths paper defnes ftness functon of the GA for sagttal plane gat as followng Eq. (9). T c J = ( ) mn E + E dt (9) skewness kurtoss 0 (a) Angle where T s the walkng cycle, E s the absolute error value c skewness between the human skewness and robot skewness, and E kurtoss s the absolute error value between the human kurtoss and robot kurtoss. PWASET VOLUME 23 AUGUST 2007 ISSN WASET.ORG

5 Lnk TABLE II ROBOT PARAMETER M (kg) L (m) d (m) I (m) (b) Velocty TABLE III GENETIC ALGORITHM PARAMETER GA parameter Maxmum Generat 300 Populaton sze Crossover Probabl 0.6 Mutaton Probablt 0.05 (c) Acceleraton Fg. 9 Human gat control values Lnk M (kg) TABLE I HUMAN SEGMENT PARAMETER L (m) d (m) I ( 2 kg m ) Fg. Robot torque of ntal populaton Fg. show jont torques of the bped robot before applyng the adaptve gat pattern generator. The human s segment parameters are gven as Table I [0] and the human s segment torques are obtaned from Lagrangan equatons (Eq.() and Eq.(2)) as shown n Fg. 0. (a) Robot angle after optmzaton Fg. 0 Human Torque B. Gat Pattern Generaton on the Sagttal Plane Intal populatons of GA and segment parameters of the bped robot must be prevously determned to generate the gat pattern of the bped robot usng the human s gat torques. Intal populatons are gven from a cubc splne nterpolaton method. The segment parameters of the bped robot are gven n Table II, and the GA parameters are gven n Table III. (b) Robot torques after optmzaton Fg. 2 Control parameter after optmzaton The natural gat pattern lke human s obtaned after applyng the adaptve gat pattern generator. The Fg. 2 shows the jont torques of the bped robot after the optmzaton. PWASET VOLUME 23 AUGUST 2007 ISSN WASET.ORG

6 TABLE IV SKEWNESS AND KURTOSIS Human Robot(before) Robot(after) Skewness Kurtoss Table IV shows the human s skewness and kurtoss, and ones of the bped robot before and after optmzaton. It s showed that results of the bped robot after optmzaton become smlar to the predefned ones of the human. C. Gat Pattern Generaton on the Frontal Plane In order to verfy the effectveness of the gat patterns after optmzaton, they were smulated usng 3D bped robot model whch was constructed by OpenGL. The smulated gat of the bped robot s shown n Fg. 4. VI. CONCLUSION It s dffcult to drectly obtan the natural gat pattern of the smplfed bped robot from the complcated human model. In order to solve these problems, ths paper proposed the adaptve gat pattern generaton of the bped robot usng the genetc algorthm, whch s based on the energy analyss of the human s gat and the desred of the bped robot. Expermental results have shown that the proposed algorthm has the gat pattern of the bped robot convergng to the natural one of the human. (a) trajectory (b) Frontal plane gat pattern( θ ) frontal Fg. 3 Frontal plane gat pattern Fg. 3(a) shows that the optmzed trajectory s much closer to the desred one. And Fg. 3(b) shows the θ frontal generated from analyss. REFERENCES [] Cap, Masao Yokota, Optmal Mult -crtera humanod robot gat synthess-an evolutonary approach, Int. Journal of Innovatve Computng, Informaton and Control, Vol.2, 2006, pp [2] M.-y.Cheng, C.-S. Ln, Genetc Algorthm for Control Desgn of Bped Locomoton, Journal of Robotc System, Vol.5,, 997, pp [3] Hasagawa Y, Arakawa T, Fukuda T, Trajectory generaton for bped locomoton robot,mechatroncs, Vol.0, 2000, pp [4] Jong Hyeon Park, Moosung Cho, Genraton of an Optmal Gat Trajectory for Bped Robots Usng a Genetc Algorthm, JSME Internatonal Journal, Vol.47, No.2, 2004, pp [5] Genc Cap, Masao Yokota, and Kazuhsa Mtobe, A new Humanod Robot Gat Generaton based on Multobjectve Optmzaton, n Proc IEEE Int. Conf. Advanced Intellgent Mechatroncs, 2005, pp [6] Zhe Tang, Zengq Sun, Changju Zhou, GA Based Optmzaton for Humanod Walkng, ICGST-ARAS nternatonal Journal on Automaton, Robotcs and Autonomous Systems, vol 5, 2006, pp. 0. [7] A. Borghese, L Banch, F Lacquant, Knematc determnants of human locomoton, Journal of Physology, 996, pp [8] Xupng Mu, A Complete Dynamc Model of Fve-Lnk Bped Walkng, n Proc. Amercan Control Conf, vol, 2003, pp [9] Momr Vokobratovc, Branslav Borovac, Zero-Moment Pont Thrty Fve Years of ts Lft, Int. Journal of Humanod Robotcs, vol, 2004, pp [0] Davd A. Wnter, Bomechancs and Motor Control of Human Movement, Wley, 990. (a) Gat on the sagttal plane (b) Gat on the frontal plane Fg. 4 Bped robot gat PWASET VOLUME 23 AUGUST 2007 ISSN WASET.ORG