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2 7 Acquston of Obstacle Avodance Actons wth Free-Gat for Quadruped Robots Tomohro Yamaguch*, Kego Watanabe** and Kyotaka Ium** * Department of Electrcal, Electroncs and Informaton Engneerng, Kanagawa Unversty ** Department of Advanced Systems Control Engneerng, Saga Unversty Japan Open Access Database Introducton Although legged moble robots are nferor to wheeled or crawler types n moblty effcency on the flat ground, they demonstrate hgh moton performance and adaptaton capablty to the ground by utlng ther hgh degrees of freedom (DOF). Snce such robots choose stable leg-placement, stable movements can be performed on rregular terrans (afak & Adams, ). Moreover, they demonstrate some unque functonaltes, e.g., the scaffold of a stable actvty at the tme of rest can be formulated from takng the posture of legs whch are hard to topple (Hrose & Yoneda, 993). However, t s very dffcult to decde robot gat due to ts hgh DOF. When the legs of the robot are smply controlled by a fed command, adaptaton capablty to the terran s remarkably restrcted and sometmes t s mpossble to mantan a stable walk. Moreover, when a leg s unable to be placed properly an optmum leg placement must be effcently found from among other canddates. Therefore, t needs for a legged moble robot to sequentally decde the progresson of legs. For that purpose, the robot predctvely perceves and recognes geographcal features of the terran, and t consequently gets over any obstacle by usng an adaptve ablty acqured n advance. From ths fact, legged robots are not necessary to avod all the obstacles by alterng ther path, unlke wheeled or crawler types, because they can avod an obstacle by crawlng-over or strdng, accordng to the obstacle s nature and the current state of the robot. Thus, t can be found that the moblty effcency to reach a destnaton s mproved by such acton. Moreover, when robots have many legs lke 4-legged or 6-legged types, the movement range s affected by the order of swng leg. We studed path to a destnaton and obstacle avodance of a quadruped robot consderng free-gat. In general, quadruped robots can reale two types of walk: one s the statc walk whch retans the stablty statcally, keepng the center of gravty (COG) n the polygon constructed by the support legs, and the other s the dynamc walk whch retans dynamc stablty, though t s statcally unstable. In the statc walk, one feature s that an rregular-terran walk s easly realed, whereas ecellng n walkng-speed or consumpton energy s a feature of the dynamc walk (Kmura et al., 99, Kmura, 993). Thus, statc walk s sutable for acton acquston of quadruped robots n geographcal envronments where obstacles, such as a level dfference, est (Chen et al.,, Chen et al., ). Source: Moble Robots, Movng Intellgence, ISBN: X, Edted by Jonas Buchl, pp. 576, ARS/plV, Germany, December 6

3 536 Moble Robots, movng ntellgence In ths research, snce obstacle avodance s taken nto consderaton, the statc walk s adopted as a basc walk and the order of swng leg s determned. A free gat plannng n the statc walk was already formulated as a condtonal optmaton problem and the soluton method by the Monte Carlo method was proposed by Nakamura et al. (Nakamura et al., 999). However, assumed, fed envronment specales the result obtaned from ths method; t has no flebltes to the outsde of search envronment. Dmensons of the obstacle and the current state of the robot can be perceved accurately, because of the presence of force sensors, ultrasonc sensors and potentometers on the present quadruped robot. A smulator s bult based on the robot s structure and the path to the destnaton s acqured from the smulator. When avodng an obstacle by quadruped robot, there are many combnatoral solutons, such as combnatons of turn and forward movements, combnatons of sdeway and forward movements, etc. The robot s body heght must be regulated because leg movement s restrcted by heght. When the leg s placed on a corner of an obstacle, the robot may fall, so robot acton must be determned from the relatve poston between the obstacle and the robot. We propose a method for determnng the acton of a quadruped robot usng neural network (NN) from the poston of the destnaton, the obstacle confguraton, and the robot s self-state. Note, however, that no any free-gat moton s taken nto consderaton at the frst research. The order of swng leg n free-gat s determned n the second research usng the amount of movements and the robot s self-state. The statc walk of the quadruped robot has 4 knds of the order of swng leg. Snce the statc walk always needs to set the COG of the robot n the polygon constructed by the supportng legs, the amount of movements of the body s dfferent, dependng on the order of swng leg. Therefore, the order of swng leg s determned by another NN. Furthermore, an NN for determnng the robot acton s acqured by re-learnng the NN that was bult n the case when the order of swng leg was fed. To reach a destnaton wth a mnmum number of walkng cycles (Furusho, 993), NN desgn parameters are optmed by a genetc algorthm (GA) usng data from several envronments, n whch each envronment has dfferent destnatons and obstacle dmensons.. Quadruped Robot Fg. shows the epermental setup. TITAN-VIII (Hrose & Arkawa 999) (see Fg. ) s the quadruped robot. TITAN-VIII has four legs, one wth three DOF, and each jont has a potentometer. Force sensng resstors (Interlnk Electroncs, FSR Part # 4) are used on the leg sole to measure force eerted on each leg. Ultrasonc sensors (NceRa, T/R4-6) are used on the forelegs to detect an obstacle; each foreleg has three ultrasonc sensors. Potentometer measurement and force sensng resstor are transferred to a personal computer through a robot nterface board (Fujtsu, RIF-) and an A/D converter board (Interface Corporaton, PCI-333). The ultrasonc sensor measures the tme dfference between emttance and recepton of ultrasonc waves, whch s reflected on an obstacle by unversal pulse processor (UPP), part of RIF-. The computer sends jont angle commands to a motor drver (Okaak Sangyo Co. Ltd., Ttech Motor Drver) on the robot through the robot nterface board. Snce sensor nformaton n feedback control must be processed n real tme, RT-Lnu s used as the computer OS.

4 Acquston Of Obstacle Avodance Actons Wth Free-Gat For Quadruped Robots 537 RIF- D/A converter A/D converter UPP PCRT- Lnu FSR Force sensor Leg 4 PCI-333 A/D converter Ultrasonc sensor Potentometer Motor controller Leg 3 Ultrasonc sensor Fg.. Robot control system. Leg TITAN-VIII Leg Fg.. TITAN-VIII.

5 538 Moble Robots, movng ntellgence y y y ),, ( s s s s y r ),, ( f f f f y r l l l 3 l Fg. 3. Coordnate system of TITAN-VIII s leg. The coordnate system of one leg of the robot s defned n Fg. 3. For any leg, assumng poston coordnates of a shoulder are r s ( s, y s, s ) and poston coordnates of a sole are r f ( f, y f, f ), jont angles, (,, ) are obtaned by s f s f o d r d d r d y y tan tan tan () where cos s f l r () cos tan l s f (3) cos l l l l d s f (4) cos l l l l d s f (5)

6 Acquston Of Obstacle Avodance Actons Wth Free-Gat For Quadruped Robots 539 (6) Here, denotes the leg number ( =,, 3, 4). Wth reference to, l, l, and l are lengths of lnks. The ultrasonc sensor and the force sensor are on the foot at l 3, where l 3 = 3 [mm]. Gven the ntal postons for soles and shoulders, jont angles of legs ncludng the swng leg are obtaned from Eq. (). Note, however, that the operaton of each jont s , , , , and n degrees. Actons should be determned to not eceedng operatonal range. 3. Obstacle Detecton and Recognton To avod an obstacle, ts estence and heght must be recogned usng sensory nformaton. For the robot, obstacles are detected and recogned by ultrasonc sensors. Ultrasonc sensors detect obstacles perpendcular to sgnals emtted by them. If the ultrasonc sensor was on the robot, the measurement of sensors would be shortened, so the ultrasonc sensors are on legs so that the emsson of ultrasonc waves s changeable. As a result, obstacles not perpendcular to the robot s forward drecton can be detected. When a leg s swngng, t can move up to a poston where the ultrasonc sensor does not detect anythng. Usng ths concept, the heght of the obstacle s measured roughly. Ultrasonc sensors on forelegs detect obstacles n the robot s forward drecton. A downward sensor detects the unevenness of terran. When the center of the robot s body s set as the orgn, the poston of an obstacle, ( ob, y ob ), detected by the robot s front sensors s gven by f l l cos l sn cos Lso sn l l cos l sn sn Lso cos ob s yob ys s (7) (8) The poston of an obstacle detected by the robot s left and rght sensors s gven by l l cos l sn cos Lso cos l l cos l sn sn Lso sn (9) ob s yob ys () Here, denotes the front leg numbers (=, ). The poston of the detected obstacle s calculated wth the dstance L so measured by ultrasonc sensor, together wth the body poston and the jont angles of the foreleg. Leg Leg Leg 3 Leg 4 Center of gravty 5 [mm] Fg. 4. Movement path of quadruped robot. Obstacle

7 54 Moble Robots, movng ntellgence 5 5 Ultrasonc sensor Obstacle 5 [mm] Fg. 5. Recognton result of the obstacles n the forward drecton. Postons of obstacles, detected where the robot moves (Fg. 4) are gven n Fgs. 5 and 6. Fg. 5 shows nformaton regardng obstacles from foreleg sensors. We found that one sde of each obstacle s detected. Fg. 6 shows postons and heghts of obstacles when a leg passed over them, detected by the downward sensor. Robot acton must be determned usng such nformaton. Fg. 6. Recognton result of the ground. Ultrasonc sensor Obstacle Acton Determnaton of Quadruped Robot Usng an NN For an actual robot, nformaton obtaned from sensors ncludes leg jont angles and dmensons and heghts of obstacles. We assumed that destnaton nformaton s gven n advance. Actons of the quadruped robot are determned by the above nformaton. For each acton, there are several combnatoral solutons such as the combnaton of forward- and turnng-motons, one of forward- and sdeway-motons, etc. The robot acton s decded by a three-layered NN (Fg. 7). Ths NN s traned offlne so as to acheve an acton usng a mnmum number of walkng cycles. Inputs to the NN are assumed to be the poston of each sole { f (k), y f (k)},, { f4 (k), y f4 (k)}, the robot s body heght Zr(k), -drectonal mamum and mnmum dstances to an obstacle at rght { orma (k), ormn (k)}, the y-drectonal mamum and mnmum dstances to the obstacle at rght {y orma (k), y ormn (k)}, and the heght of the obstacle at rght { orma (k), ormn (k)}, the - drectonal mamum and mnmum dstances to the obstacle at left { olma (k), olmn (k)}, the y-

8 Acquston Of Obstacle Avodance Actons Wth Free-Gat For Quadruped Robots 54 drectonal mamum and mnmum dstances to the obstacle at left {y olma (k), y olmn (k)}, and the heght of the obstacle at left { olma (k), olmn (k)}; -drectonal dstance error,.e., dstance between the COG of the robot and destnaton de (k), y-drectonal dstance error y de (k), and drecton error,.e., the drecton between the destnaton and forward drecton of the robot de (k). Postons of each sole and obstacles are defned n the frame whose orgn s fed to the body center. Outputs of the NN are the amount of - and y-drectonal movement of the robot {Xr(k), Yr(k)} and the turnng angle of the robot r(k). If no obstacles est n front of the robot, measured values of obstacles are set to ( orma, y orma, orma )=(.,.99,.), ( ormn, y ormn, ormn )=(.99,.,.), ( olma, y olma, olma )=(.99,.99,.), and ( olmn, y olmn, olmn )=(.,.,.) [m], assumng the obstacle s behnd the robot. Poston of the robot Rght obstacle Left obstacle Destnaton nformaton f k k f 4 or mak, or mn k ol mak, ol mn k dek yf k yf 4k yor ma k, yor mn k yol ma k, yol mn k ydek Zrk or mak, or mn k ol ma k, ol mn k de(k) Input layer Hdden layer Output layer Xrk Yr(k) r(k) Movement quantty of robot Fg. 7. Three layered neural network for determnng the acton of the quadruped robot. A radal bass functon neural network (RBFNN) (Elanayar & Shn, 994, Sakawa & Tanaka, 999), known as an NN that can reale varous appromaton functons, s used n the control system. Wth an RBFNN, a nonlnear functon s epanded by any bass functon havng a crcular contour, and s used as functon appromaton or pattern recognton. Unt functons at the hdden (or ntermedate) layer of RBFNNs are gven by ( k) c ( ) ep () where denotes th unt output at the hdden layer, and desgn parameters of RBF are center c and standard devaton for each nput. jth unt output at output layer o j s gven by

9 54 Moble Robots, movng ntellgence o ( ) j k m ( ) () whch s calculated by a lnear combnaton of outputs of the hdden layer. Here, j denotes the connecton weght between the th hdden unt and the jth output unt, and m denotes the number of unts at the hdden layer, where the number of hdden unts s determned by tral and error. The number of hdden unts was set to m=, because a good result was obtaned when m was four tmes the number of nputs. Usng ths RBFNN, an acton of the quadruped robot s determned from the nformaton of the obstacles, the current state of the robot, and the destnaton nformaton. 4. Acquston of Obstacle Avodance by Smulaton A block dagram of obstacle avodance control system s shown n Fg. 8. To avod obstacles, the system responds to the envronment by alterng the path and gettng over or strdng obstacles. To do so, the robot changes ts heght to that of an obstacle. Such actons constran how much the robot can adjust the heght. The RBFNN determnes the movement of the robot usng obstacle dmensons, the poston of each leg, and robot heght, collectvely consdered durng walkng. Postons of shoulders and legs are computed from the amount of movement. Each jont angle s calculated by Eq. (), and the output s communcated to the robot. Dstance error s updated by change n the current COG poston of the robot, after computng the COG poston by consderng postons of shoulders and legs. Although the poston of an obstacle s measured by ultrasonc sensors of the robot, poston nformaton of obstacles n smulaton s updated by change of the COG poston of the robot. Each leg s changed based on the amount of robot movement. The range of leg placement s assumed as follows: when placng the leg on the ground, ts range should be 5 [mm] away from a corner of an obstacle, whereas, when placng the leg on an obstacle, ts range should be 3 [mm] away from a corner. If a leg cannot be placed n a poston, the robot places t at the nearest poston from the scheduled poston. j Informaton of corner Ultrasonc Zr(k) sensor Rght obstacle Obstacle Obstacle orma ( k),, ormn ( k) recognton recognton Left obstacle Xr(k) olma ( k),, olmn ( k) Yr(k) RBFNN Destnaton de( k), yde( k), de( k) RBFNN Robot s r(k) Robot s c.g. c.g. f, y f Poston Poston calculaton calculaton r, y, ) s r, y, ) f ( s s s ( f f f Zr(k) Jont Jont (,, ) angle angle Potentometer Robot Robot Fg. 8. Obstacle avodance control system wth consderaton to the destnaton. 4.. Smulaton condton The smulaton envronment s shown n Fg. 9. The y-as s set to the forward drecton of the robot. The robot s assumed to start from pont (.,.,.3) [m] and approach the goal, a crcle havng radus. [m], centered on the destnaton pont.

10 Acquston Of Obstacle Avodance Actons Wth Free-Gat For Quadruped Robots 543 Smulaton s performed three tmes by settng dstance error to ( de, y de )=(.,.8), (.5,.), (.5,.) [m]. We assume that one obstacle ests at the robot s rght and the other at the left. Coordnates of legs and the obstacle are shown n Fg.. Intal postons for legs are set to ( f, y f )=(.5,.3), ( f, y f )=(.5,.5), ( f3, y f3 )=(.5,.5), and ( f4, y f4 )=(.5,.3) [m]. Postons of - and y- coordnates of obstacles are shown n Table, where each row represents coordnate data combned to produce coordnates of any two obstacles. Heght coordnates or and ol of obstacles are set to.6,.,.3 [m], where the data can be combned to produce a combnaton of heghts. Coordnate or ( ol )=.3 [m] mples that t s an obstacle the robot cannot get over, so that the combnaton of or =.3 [m] and ol =.3 [m] s not consdered n smulaton. One of the two obstacles s assumed to be the obstacle that the robot cannot get over, so that smulaton s conducted for 96 obstacles. Walkng s a crawl n whch the body s supported by three or more legs. The order of swng leg selecton s the rght hnd-leg, rght foreleg, left hnd-leg, and left foreleg. Realaton of stable statc walkng s smlar to the crawl. The COG of the robot should be n the polygon constructed by the supportve legs; therefore the body s moved so that the COG of the robot s always n the supportve leg polygon. We assume that the robot s parallel to the ground. Obstacles Start Goal Fg. 9. The envronmental setup for the acquston of quadruped robot s acton. y, ) ol, y ) ( ol yol ( ol yol Left obstacle ( 4 ol 4, ) ol, y ) ( 3 ol 3 ( or, yor) ( or, yor ) Rght obstacle ( or 4, yor 4) ( or 3, yor 3) y Leg Leg f, y ) f, y ( f ( f ) Leg 3 Leg 4 ( f 3, yf 3) Quadruped robot ( f 4, yf 4) Fg.. Coordnates of the robot s legs and the obstacles.

11 544 Moble Robots, movng ntellgence No or or or3 or4 ol ol ol3 ol No y or y or y or3 y or4 y ol y ol y ol3 y ol Table. - and y- drectonal coordnates of obstacles. 4.. Setup of ftness functon In smulaton, connecton weghts of the NN and parameters (center and standard devatons) of RBFs are optmed by a GA (Mchalewc, 996) so that the robot avods obstacles and reaches the destnaton wth a mnmum number of walk cycles. Table shows desgn parameters for the GA used n smulaton. The assocated ftness functon of an ndvdual s defned by ftness ob n ( ftness ftness ftness ) (3) o whose soluton s searched for as a mnmaton problem. ob n s the number of envronments consdered n optmaton. ftness o s an evaluaton functon assocated wth penalty for collson wth an obstacle. ftness o s gven by a., f there s no collson ftnesso (4) [ de ( k) yde( k)], otherwse Walkng stops f the robot colldes wth an obstacle. ftness a s an evaluaton functon related to jont constrants,.e., whether each jont angle s n an admssble range or not. ftness a s gven by., f there s no outsde of the range ftnessa (5) [ de ( k) yde( k)], otherwse Walkng stops f the jont eceeds jont constrants. ftness c s an evaluaton functon related to walk cycles requred to reach the destnaton, and gven by ftness c T c [ de ( k) yde ( k)] (6) 5 T denotes the walk cycles requred to move from the startng pont to the destnaton whle avodng obstacles by stable walkng. The mamum number of walk cycles T ma n one envronment s set to 5 and walkng stops f the walk cycles eceed T ma. The number of ndvduals Crossover rate.6 (unform crossover) Selecton strategy Tournament selecton (3 ndvduals) Eltst preservng strategy Table. Desgn parameters for GA.

12 Acquston Of Obstacle Avodance Actons Wth Free-Gat For Quadruped Robots Smulaton Result 4.. Performance for tranng data A typcal control result after tranng the RBFNN usng the above procedure s shown n Fg.. Envronmental condtons for one of 96 combnatons were as follows: - and y-drectonal ntal dstance error of the destnaton were ( de, y de )=(.5,.) [m]; - and y-drectonal coordnates of two obstacles were ( or, y or )=(.,.85), ( or, y or )=(.,.65), ( or3, y or3 )=(.5,.55), ( or4, y or4 )=(.5,.75), ( ol, y ol )=(.5,.85), ( ol, y ol )=(.5,.65), ( ol3, y ol3 )=(.,.66), and ( ol4, y ol4 )=(.,.86) [m]; and -drectonal coordnates were or =.3 and ol =. [m]. The robot turned to the left to avod an obstacle at rght, n whch t could not get over but conquered the obstacle at left. Legs and 3 were used to get over the obstacle at left and the robot reached the destnaton. The number of walk cycles to the goal was 9 and the fnal dstance error was ( de, y de )=(.37,.46) [m]. Leg Leg goal Leg 3 Leg 4 Center of gravty Obstacle 5 5 [mm] Fg.. Obstacle avodance acton for the traned envronment. Leg Center of gravty Obstacle Leg 3 Center of gravty Obstacle 4.. Performance for untraned envronment In ths secton, we eamne RBFNN performance n an untraned envronment. We set the ntal dstance errors at ( de, y de )=(.35,.) [m], and - and y-drectonal coordnates of two obstacles at ( or, y or )=(.,.87), ( or, y or )=(.,.56), ( or3, y or3 )=(.57,.55), ( or4, y or4 )=(.57,.86), ( ol, y ol )=(.56,.9), ( ol, y ol )=(.56,.59), ( ol3, y ol3 )=(.4,.66), and ( ol4, y ol4 )=(.4,.99) [m], together wth -drectonal coordnates at or =.7 and ol =.3 [m]. Fg. shows the results. In smulaton, snce the obstacle at left could not be gotten over by the robot, t moved to the rght and got over t. We found that legs and 4 were used for gettng over the obstacle at rght so that the robot reached the destnaton. The number of walk cycles to the goal was 9 and the fnal dstance error was ( de, y de )=(.36,.4) [m]. Leg Leg goal Leg 3 Leg 4 Center of gravty Obstacle 5 5 [mm] Fg.. Obstacle avodance acton for an untraned envronment. Leg Center of gravty Obstacle Leg 4 Center of gravty Obstacle

13 546 Moble Robots, movng ntellgence 4.3 Eperments Eperments were conducted by quadruped robot TITAN-VIII. Walk was at a crawl and the robot recogned an obstacle by ultrasonc sensors on the forelegs. - and y-drectonal movement and the turnng angle of the robot were determned by the NN from smulaton. We assumed that the robot could not get over an obstacle taller than.5 [m]. Placement of a swng leg s decded by nformaton retreved by the downward ultrasonc sensor, dependng on whether the placement s a corner of the obstacle. Whether the leg s a swng leg or not s decded by the force sensor. TITAN-VIII Fg. 3. Envronment of an eperment. Obstacle Destnaton The epermental envronment s shown n Fg. 3. One obstacle s on the rght and the other on the left. The obstacle at left can not be gotten over by the robot. Intal dstance error was set to ( de, y de )=(.,.9) [m]. Postons of obstacles are detected by the robot (Fgs. 4 and 5). Fg. 4 shows nformaton on obstacles gathered by sensors on the forelegs, whose results show that only one sde of each obstacle could be detected. Fg. 5 shows postons and heghts of obstacles when the leg has passed over them, whch were detected by downward sensors. The path to the destnaton and the presence of obstacles s shown n Fg. 6. We found that the robot turned to the rght to avod the obstacle at left, whch could not be gotten over, but got over the obstacle at rght. Legs and 4 were used for gettng over the obstacle at rght and the robot reached the destnaton. The number of walk cycles to the goal was 9 and the fnal dstance error was ( de, y de )=(.37,.75) [m]. Ultrasonc sensor Obstacle 5 5 [mm] Fg. 4. Recognton result of the obstacles gathered by sensors on the forelegs.

14 Acquston Of Obstacle Avodance Actons Wth Free-Gat For Quadruped Robots Ultrasonc sensor Obstacle Fg. 5. Recognton result of the obstacles detected by downward sensors. 4 4 Leg Leg goal Leg 3 Leg 4 Center of gravty Obstacle 5 5 [mm] Leg Center of gravty Obstacle Fg. 6. Obstacle avodance acton n an actual eperment. Leg 4 Center of gravty Obstacle 5. Determnaton of the Order of Swng Leg for Free-Gat Robot s body heght Zr(k) Amount of movements for the robot Xr(k) Yr(k) r(k) Order of swng leg : 3 4 : 4 3 : 3 4 3: 3 4 Input layer 3: 4 3 Output layer Hdden layer Fg. 7. Three layered neural network for determnng the order of swng leg. Snce obstacle avodance s taken nto consderaton, t s assumed that the statc walk s adopted as a basc walk and the order of swng leg s determned. 4 knds of the order est n a statc walk of the quadruped robot. Although 4 knds of the order can be tred to mplement whenever the

15 548 Moble Robots, movng ntellgence quadruped robot walks, n ths research, the order of swng leg s determned by a three-layered NN shown n Fg. 7. Inputs to the NN are assumed to be the robot s body heght Zr(k), the amount of - and y-drectonal movements of the robot {Xr(k), Yr(k)} and the turnng angle of the robot r(k). Moreover, we prepare 4 unts at the output, correspondng to 4 knds of the order (Table 3). The order of swng leg fed to the quadruped robot uses the order assocated to the unt whose output value s closest to one among output unts. RBFNN s also used for the NN, where the number of unts n the hdden layer s set to 5. Output number Order of swng leg Output number Order of swng leg Table 3. Order of swng leg to each output of NN. 5. Acquston of the Order of Swng Leg In a statc walk of quadruped robot, snce the amount of movements of the body changes wth the order of swng leg, the robot produces dfferent movable range for each order of swng leg. For ths reason, f the stablty of statc walk s mantaned by less movement of the body, then the movable range of each leg becomes large; t can msequently enlarge the movable range of the robot. For teacher sgnal used for ths research, when the robot s body heght Zr(k) was changed from 3 [mm] to 37 [mm], the amount of -drectonal movement of the robot Xr(k) s changed from [mm] to [mm], the amount of y-drectonal movement of the robot Yr(k) s changed from 5 [mm] to 35 [mm] and the turnng angle of the robot r(k) s changed form 5 [degree] to 5 [degree], respectvely, the order of swng leg that the movement of the robot s body s a mnmum and the stablty of statc walk s satsfed s set as one, and the other order s set to ero. Here, there were 9 knds of the order of swng leg that the amount of movements of the robot s body became the mnmum. Note however that when the amount of changes of Zr(k), Xr(k), Yr(k), and r(k) s fed, the number of selectons s changed, dependng on the order of swng leg. Therefore, the amount of change of Zr(k), Xr(k), Yr(k), and r(k) s enlarged for the case of hgh number of selectons, whereas the amount of change of movement s made small for the case of low number of selectons, and data are prepared for each order of swng leg. Moreover, t s assumed that ntal leg postons of quadruped robot are set to ( f, y f )=(.5,.3), ( f, y f )=(.5,.5), ( f3, y f3 )=(.5,.5), and ( f4, y f4 )=(.5,.3) [m]. Here, the subscrpt number denotes the leg number.

16 Acquston Of Obstacle Avodance Actons Wth Free-Gat For Quadruped Robots 549 In ths research, the order of swng leg s determned usng RBFNN. Connecton weghts of the NN and parameters (center and standard devatons) of RBFs are optmed by a GA so that the relaton between an nput and an output s satsfed. There s 9 knds of the order of swng leg chosen when changng Zr(k), Xr(k), Yr(k), and r(k), respectvely, and data are prepared for each one. Here, there are a total of 38 knds of combnaton optmed by usng GA. The assocated ftness functon of an ndvdual s defned by ftness n ( ftness A ftneess B ) (7) whose soluton s searched for as a mnmaton problem. n s the total number of combnatons n optmaton. ftness A s an evaluaton functon only appled when a teacher sgnal ts j s one, whch s gven by ftness A ( oj tsj ) jj (8) where j denotes any unt number of output layer and j denotes the unt number of ts j. Contrarly, ftness B s an evaluaton functon appled when a ts j s ero, whch s gven by ftness B ma{( o ts),,( o ts ),,( o4 ts4) } (9) j j ftness B denotes the largest value n the dfference of o j and ts j. j denotes the unt number to 4 ecept for the case of j that denotes the unt number of ts j. 5. Obstacle Avodance wth Consderaton to the Free-Gat A block dagram of obstacle avodance control system consdered here s shown n Fg. 8. The avodance acton of quadruped robot s determned by the upper NN. Furthermore, the order of swng leg s determned by the lower NN from the amount of movements of the robot. The smulaton envronment s the same as secton 4.. The y-as s set to the forward drecton of the robot. The robot s assumed to start from pont (.,.,.3) [m] and approach the goal, a crcle havng radus. [m], centered at the destnaton pont. Ultrasonc sensor Destnaton Rght obstacle Obstacle Obstacle orma k),, recognton recognton Left obstacle k),, Robot s Robot s c.g. c.g. olma ( ormn ( olmn ( k) ( k) de( k), yde( k), de( k) f, y f Informaton of corner Zr(k) RBFNN RBFNN Xr(k) Yr(k) r(k) Poston Poston calculaton calculaton r, y, ) s r, y, ) f ( s s s ( f f f Zr(k) Jont Jont (,, ) angle angle Potentometer Robot Robot y f RBFNN RBFNN Order of swng leg Fg. 8. Obstacle avodance control system wth consderaton to the order of swng leg.

17 55 Moble Robots, movng ntellgence We set the ntal dstance errors at ( de, y de )=(.5,.) [m], and - and y-drectonal coordnates of two obstacles at ( or, y or )=(.,.85), ( or, y or )=(.,.65), ( or3, y or3 )=(.5,.66), ( or4, y or4 )=(.5,.86), ( ol, y ol )=(.5,.75), ( ol, y ol )=(.5,.55), ( ol3, y ol3 )=(.,.65), and ( ol4, y ol4 )=(.,.85) [m], together wth -drectonal coordnates at or =. and ol =.3 [m]. Here, although a robot can get over an obstacle at rght, an obstacle at left shall not be get over. The robot s body heght Zr(k) s adjusted and changed to the heght of the obstacle whch can be get over. 5.. When the order of swng leg s fed The movement path of the quadruped robot when fng the order of swng leg and avodng an obstacle s shown n Fg. 9, and the correspondng amount of movements of the robot s body Br s shown n Table 4. Here, the leg number used as swng leg s assgned as the left foreleg to, rght foreleg to, left hnd-leg to 3 and rght hnd-leg to 4, as shown n Fg.. The robot s body heght changes as shown n Fg.. Furthermore, t can be checked from Fg. that both the leg and 4 were used for a gettng over to the obstacle at rght. Leg Leg goal Leg 3 Leg 4 Center of gravty Obstacle 5 5 [mm] Fg. 9. Movement path of the quadruped robot when fng the order of swng leg. Xr(k) [mm] Yr(k) [mm] r(k) [deg] Zr(k) [mm] Br [mm] Order of swng leg Table 4. The amount of movements of the robot s body when fng the order of swng leg.

18 Acquston Of Obstacle Avodance Actons Wth Free-Gat For Quadruped Robots 55 Leg Center of gravty Obstacle Fg.. Movement path of the leg and 4. Leg 4 Center of gravty Obstacle 5.. When all 4 knds of the order are tred The movement path of the quadruped robot, when tryng all 4 knds of the order and avodng an obstacle, s shown n Fg., and the amount of movements of the robot s body Br s shown n Table 5. Here, the robot s body heght changes wth obstacles. For ths reason, the robot s body heght vares as shown n Fg.. Compared to the case where the order of swng leg s fed, t s found that the amount of movements of the robot s body s relatvely small. Leg Leg goal Leg 3 Leg 4 Center of gravty Obstacle 5 5 [mm] Fg.. Movement path of the quadruped robot when tryng all 4 knds of the order. Xr(k) [mm] Yr(k) [mm] r(k) [deg] Zr(k) [mm] Br [mm] Order of swng leg Table 5. The amount of movements of the robot s body when tryng all 4 knds of the order.

19 55 Moble Robots, movng ntellgence 5..3 When the order of swng leg s determned by RBFNN After tranng the lower RBFNN, the movement path of the quadruped robot, determnng the order of swng leg and avodng an obstacle, s shown n Fg.. The correspondng amount of movements of the robot s body Br s shown n Table 6. Note here that the robot s body heght s the same as that shown n Fg.. Compared to the case where the order of swng leg s fed, t s observed that the amount of movements of the robot s body s small. However, compared wth the case where all 4 knds of the order are tred, the amount of movements of t he body was slghtly large. Leg Leg goal Leg 3 Leg 4 Center of gravty Obstacle 5 5 [mm] Fg.. Movement path of the quadruped robot when determnng the order of swng leg usng RBFNN. Xr(k) [mm] Yr(k) [mm] r(k) [deg] Zr(k) [mm] Br [mm] Order of swng leg Table 6. The amount of movements of the robot s body when determnng the order of swng leg usng RBFNN. 6. Re-learnng of the NN for Determnng the Robot Acton NN for determnng the robot acton s acqured by re-learnng the NN that was bult n the case when the order of swng leg was fed. A block dagram of obstacle avodance control system s the same as secton 5.. Moreover, the smulaton condton and ftness functon are the same as secton When the Obstacle at Rght s a Wall We set the ntal dstance errors at ( de, y de )=(.5,.) [m], and - and y-drectonal coordnates of two obstacles at ( or, y or )=(.,.85), ( or, y or )=(.,.65), ( or3, y or3 )=(.5,.55), ( or4, y or4 )=(.5,

20 Acquston Of Obstacle Avodance Actons Wth Free-Gat For Quadruped Robots ), ( ol, y ol )=(.5,.85), ( ol, y ol )=(.5,.65), ( ol3, y ol3 )=(.,.66), and ( ol4, y ol4 )=(.,.86) [m], together wth -drectonal coordnates at or =.3 and ol =. [m]. Here, although a robot can get over an obstacle at left, an obstacle at rght shall not be get over. The smulaton result usng the learned RBFNN s shown n Fg. 3. The number of walk cycles to the goal was, and the dstance from the COG of the robot to the destnaton pont was ( de, y de )=(.7,.7) [m]. Moreover, the amount of movements of the robot and the order of swng leg are shown n Table 7. It was found that the order of the swng leg changes wth the amount of movements of the robot. In the smulaton result of the case where unlearned RBFNN s used, the number of walk cycles to the goal was 9, and the dstance from the COG of the robot to the destnaton pont was ( de, y de )=(.37,.46) [m]. Leg Leg goal Leg 3 Leg 4 Center of gravty Obstacle 5 5 [mm] Fg. 3. Movement path of quadruped robot when changng the order of swng leg usng RBFNN (n the case where an obstacle at rght s a wall). Xr(k) [mm] Yr(k) [mm] r(k) [deg] Zr(k) [mm] Order of swng leg Table 7. The amount of movements of the robot n the case where an obstacle at rght s a wall. 6. When the Obstacle at Left s a Wall Leg Center of gravty Obstacle Leg 3 Center of gravty Obstacle We set the ntal dstance errors at ( de, y de )=(.5,.) [m], and - and y-drectonal coordnates of two obstacles at ( or, y or )=(.,.85), ( or, y or )=(.,.65), ( or3, y or3 )=(.5,.66), ( or4, y or4 )=(.5,.86), ( ol, y ol )=(.5,.75), ( ol, y ol )=(.5,.55), ( ol3, y ol3 )=(.,.65), and ( ol4, y ol4 )=(.,.85) [m], together wth -drectonal coordnates at or =. and ol =.3 [m]. Here, although a robot can get over an obstacle at rght, an obstacle at left shall not be get over. The smulaton result s shown n Fg. 4. The number of walk cycles to the goal was, and the dstance from the COG of the robot to the destnaton pont was ( de, y de )=(.8,.4) [m].

21 554 Moble Robots, movng ntellgence Moreover, the amount of movements of the robot and the order of swng leg are shown n Table 8. In the smulaton result when unlearned RBFNN s used, the number of walk cycles to the goal was, and the dstance from the COG of the robot to the destnaton pont was ( de, y de )=(.68,.7) [m]. Leg Leg goal Leg 3 Leg 4 Center of gravty Obstacle 5 5 [mm] Leg Center of gravty Obstacle Leg 4 Center of gravty Obstacle Fg. 4. Movement path of quadruped robot when changng the order of swng leg usng RBFNN (n the case where an obstacle at left s a wall). Xr(k) [mm] Yr(k) [mm] r(k) [deg] Zr(k) [mm] Order of swng leg Table 8. The amount of movements of the robot n the case where an obstacle at left s a wall. 7. Conclusons We epermentally have proved a method for acqurng a path to a destnaton and obstacle avodance of a quadruped robot. Robot actons were determned through an RBFNN, whose nput conssted of destnaton nformaton, obstacle confguraton, and current robot status. Usng tranng data on envronmental condtons, focusng on -, y-, and -coordnates of dfferent obstacles and certan destnatons, RBFNN desgn parameters were optmed usng a GA so that the robot reached the destnaton wth a mnmum number of walkng cycles. For an untraned (unknown) envronment, we found that the RBFNN was useful for acqurng an obstacle avodance path to the destnaton. Effectveness of ths approach was eamned by actual eperments. However, free-gat moton was not taken nto consderaton n the frst reseach. A method of determnng the order of swng leg n free gat by an RBFNN, whose nputs are the amount of movements for the quadruped robot and the heght of the body, has been proposed for the second research. In the tunng of desgn parameters of the RBFNN, data to whch the amount of movements for the robot was changed are prepared for each order of swng leg. Such desgn parameters were optmed usng GA so that the relaton between an nput and an output s satsfed.

22 Acquston Of Obstacle Avodance Actons Wth Free-Gat For Quadruped Robots 555 As a result, compared to the case where the order of swng leg s fed, the amount of movements for the robot body was small. However, compared to the case where all 4 knds of the order are tred, that for the robot body was slghtly large. It seems to be attrbuted to the fact that there was few data used for the study of the RBFNN. In order to make the amount of movements for the robot body much smaller, more data need to be used for the study of RBFNN. In order to acqure the obstacle avodance acton of quadruped robots wth consderng to the order of swng leg, the acton of a quadruped robot has been determned through an RBFNN, whose nputs were the destnaton nformaton, the obstacle confguratons, and the robot s self-state. The NN for determnng the robot s acton s acqured by re-learnng the NN that was bult n the case where the order of swng leg was fed. Compared to the case where the unlearned RBFNN s used, the fnal dstance error to the destnaton of the present approach was small; however the walk cycle was comparable to each other. It s attrbuted to the fact that a prorty was assgned to the error dstance n the evaluaton of GA. For ths reason, n order to make a walk cycle smaller, further ftness functon of GA needs to be re-eamned. Moreover, the effectveness of the proposed system needs to be verfed by usng the actual system. Obstacles are recogned by an ultrasonc sensor that detects reflected ultrasonc waves on a flat surface. Obstacles were assumed to be flat,.e., rectangular blocks and oblque obstacles were not consdered. Snce the order of the swng leg was assumed to be constant, ths assumpton appears to have slghtly restrcted the robot acton. We wll mprove the moblty effcency of the robot by constructng a system that changes the sequence of the swng leg based on envronmental condtons and mprove recognton system by addng a vson sensor (Chow & Chung, ). 8. References Chen, X.; Watanabe, K.; Kguch, K. & Ium, K. (). An ART-based fuy controller for the adaptve navgaton of a human-coestent quadruped robot, IEEE/ASME Transactons on Mechatroncs, Vol. 7, No 3, pp Chen, X.; Watanabe, K.; Kguch, K. & Ium, K. (). Path trackng based on closed-loop control for a quadruped robot n a cluttered envronment, ASME, Journal of Dynamc Systems, Measurement, and Control, Vol. 4, pp. 7-8 Chow, Y.H. and Chung, R. (), VsonBug: A heapod robot controlled by stereo cameras, Autonomous Robots, Vol. 3, No. 3, pp Elanayar, V. T. S. & Shn, Y. C. (994). Radal bass functon neural network for appromaton and estmaton of nonlnear stochastc, IEEE Transactons on Neural Networks, Vol. 5, No. 4, pp Furusho, J. (993). Research deployment of the walkng robot, Journal of Robotcs Socety of Japan, Vol., No 3, pp Hrose, S. & Arkawa, K. (999). Development of quadruped walkng robot TITAN-VIII for commercally avalable research platform, Journal of Robotcs Socety of Japan, Vol. 7, No 8, pp Hrose, S. & Yoneda, K. (993). Toward development of practcal quadruped walkng vehcle, Journal of Robotcs Socety of Japan, Vol., No 3, pp Kmura, H. (993). Dynamc walk of the quadruped robot, Journal of Robotcs Socety of Japan, Vol., No 3, pp

23 556 Moble Robots, movng ntellgence Kmura, H.; Shmoyama, I. & Mura, H. (99). Dynamcs n the dynamc walk of a quadruped robot, Advanced Robotcs, Vol. 4, No. 3, pp Mchalewc, Z. (996). Genetc Algorthms + Data Structure = Evoluton Programs, 3rd, revsed and etended edton ed., Sprnger, Germany Nakamura, T.; Sek, M.; Mor, Y. & Adach, H. (999). Free gat plannng usng Monte Carlo method for locomoton on rugged terran, 999 JSME Conference on Robotcs and Mechatroncs, A-4-6 (CD-ROM) afak, K. K. & Adams, G. G. (). Dynamc modelng and hydrodynamc performance of bommetc underwater robot locomoton, Autonomous Robots, Vol. 3, No. 3, pp. 3-4 Sakawa, M. & Tanaka, M. (999). Introducton to Neurocomputng, Tokyo, Morkta Shuppan Co., Ltd.

24 Moble Robotcs, Movng Intellgence Edted by Jonas Buchl ISBN X Hard cover, 586 pages Publsher Pro Lteratur Verlag, Germany / ARS, Austra Publshed onlne, December, 6 Publshed n prnt edton December, 6 Ths book covers many aspects of the ectng research n moble robotcs. It deals wth dfferent aspects of the control problem, especally also under uncertanty and faults. Mechancal desgn ssues are dscussed along wth new sensor and actuator concepts. Games lke soccer are a good eample whch comprse many of the aforementoned challenges n a sngle comprehensve and n the same tme entertanng framework. Thus, the book comprses contrbutons dealng wth aspects of the Robotcup competton. The reader wll get a feel how the problems cover vrtually all engneerng dscplnes rangng from theoretcal research to very applcaton specfc work. In addton nterestng problems for physcs and mathematcs arses out of such research. We hope ths book wll be an nsprng source of knowledge and deas, stmulatng further research n ths ectng feld. The promses and possble benefts of such efforts are manfold, they range from new transportaton systems, ntellgent cars to fleble assstants n factores and constructon stes, over servce robot whch assst and support us n daly lve, all the way to the possblty for effcent help for mpared and advances n prosthetcs. How to reference In order to correctly reference ths scholarly work, feel free to copy and paste the followng: Tomohro Yamaguch, Kego Watanabe and Kyotaka Ium (6). Acquston of Obstacle Avodance Actons wth Free-Gat for Quadruped Robots, Moble Robotcs, Movng Intellgence, Jonas Buchl (Ed.), ISBN: X, InTech, Avalable from: tons_wth_free-gat_for_quadruped_robots InTech Europe Unversty Campus STeP R Slavka Krauteka 83/A 5 Rjeka, Croata Phone: +385 (5) Fa: +385 (5) InTech Chna Unt 45, Offce Block, Hotel Equatoral Shangha No.65, Yan An Road (West), Shangha, 4, Chna Phone: Fa:

25 6 The Author(s). Lcensee IntechOpen. Ths chapter s dstrbuted under the terms of the Creatve Commons Attrbuton-NonCommercal-ShareAlke-3. Lcense, whch permts use, dstrbuton and reproducton for non-commercal purposes, provded the orgnal s properly cted and dervatve works buldng on ths content are dstrbuted under the same lcense.