Loop Forming Snake-like Robot ACM-R7 and Its Serpenoid Oval Control

The 21 IEEE/RSJ International Conference on Intelligent Robot and Sytem October 18-22, 21, Taipei, Taiwan Loop Forming Snake-like Robot ACM-R7 and It Serpenoid Oval Control Taro Ohahi, Hiroya Yamada and Shigeo Hiroe Abtract Thi paper dicue the deign of a new nakelike robot without wheel, named ACM-R7. It ha 18 DOF, i 1.6m in length and weigh 11.7kg. It feature a water-tight tructure, a large motion range pitch joint of ±9 degree and a high output-power actuator arrangement, baed on the coupled drive concept. Furthermore the control method Loop Gait i dicued. For thi gait the ACM-R7 form a loop hape and roll like a wheel on the rim. We introduce the Serpenoid Oval for the loop hape. It formed by a mooth inuoidal angular motion of the joint. Moreover we conider the modification of the Serpenoid Oval for teering and obtacle avoidance. The performance i then verified by everal motion experiment. I. I NTRODUCTION A the nake-like robot and manipulator can make new type of future field robot, we have named the nakelike robot, or the robot forming the cord-like linear hape by the erial connection of unified unit a Active Cord Mechanim (ACM). Since after the world firt experiment of Hiroe nake-like robot of 1972, we have been contructing everal type of ACM and tudied about it control method [1]. Mot of the former ACM model that we have made o far had multiple wheel attached along the body to generate low frictional motion toward the longitudinal direction and high frictional motion toward the normal direction of the body. The difference of friction can generate a mooth and fat gliding motion. However, on andy off-road ground for example, the wheel may ink into the and and and may get tuck in the rotational haft of the wheel. ACM without wheel have impler and moother bodie and thu are uitable for the motion on andy or uneven environment. However, frictional reitance of the wheelle body on the ground i high, and large energy will be lot in the locomotion, if the normal erpentine motion i ued. We proved that the Sinu Lifting, oberved in real nake, i one of the effective way to improve the locomotion efficiency of the wheel-le ACM, and we already proved that the mooth erpentine motion can be generated [2]. However, the rate of the improvement of the energy efficiency i limited, becaue of the liding motion between the body and the ground. Therefore, we focued on the Loop Gait for the wheelle ACM. The loop gait i the motion of the ACM when forming a loop hape. Firt, the front and the rear egment of the ACM are connected to each other to form a loop hape. Then, by the ynchronized winging motion of each Author are with Tokyo Intitute of Technology, 2-12-1 Ohokayama, Meguro-ku, Tokyo 152-855, Japan, hiroe@me.titech.ac.jp 978-1-4244-6676-4/1/$25. 21 IEEE Fig. 1. ACM-R7 Yaw Link-B Roll Link-A Yaw Joint Ball Joint 143 mm Ball Joint Pitch (a) Pitch Axi Link-B (b) Yaw Axi Pit ch nt Joi Link-A Motor (c) Joint Mechanim Fig. 2. Joint Mechanim of ACM-R7 Fig. 3. Joint Motion joint, the looped body of the ACM generate a whole-body rolling motion, jut like a pinning wheel rim on the ground. The loop gait i much uitable for moving on flat terrain, becaue there exit everal drawback, uch a the intability problem, due to comparatively high center of ma. However, the loop gait ha the amazing advantage of high efficiency. Becaue, although joint of the ACM body make winging 413

B C A Fig. 4. Gripper and Rod O TABLE I SPECIFICATION OF ACM-R7 Dimenion 1589 14 74 mm Ma 11.7 kg Number of Joint 18 Motor 6W DC Motor 18 Joint Torque 16 Nm Joint Angle Range ± 9 deg CPU SH2 747 (Renea) Battery NiMH 7.2V 9mAh 9 motion, jut a in the cae of erpentine motion, the looped ACM can create infinite pinning motion of the whole body and there i no liding motion between the body and the ground, the motion i fat and energy efficient. Until now, everal robot which make the loop gait have already been propoed, uch a Polybot [3] [4] and MTRAN [6]. They are moduler robot, which tranform into a nake, a loop and other variou hape. They can move traight, and make accelerated motion by changing their ellipe hape [5]. MTRAN accomplihed it with the neural ocillator CPG [7]. In addition, the terrain adaptive motion by uing touch enor ha alo been tudied and Polybot ha already achieved the tep climbing motion with the loop gait [8]. However, mot of them are in the experimental tage and the performance of the mechanim were limited. Of coure they were not made a a watertight tructure. The control method were alo in the preliminary tage and imple ellipe were introduced for their baic hape. In thi paper, we dicu about the development of a new type of nake-like robot, ACM-R7, having the mechanim to form a loop hape and having a rugged watertight tructure. We alo propoe the new fundamental hape of the loop gait named Serpenoid Oval and dicu the modified erpenoid oval for teering and obtacle avoidance. The performance of the developed ACM-R7 and it control method baed on erpenoid oval i uccefully verified by the everal motion experiment. II. DESIGN OF ACM-R7 CAPABLE OF LOOP GAIT We have developed the nake like robot ACM-R7 which ha the above-mentioned propertie (Fig. 1). It ha 18 joint and the total length i 1.6 m. The orthogonal rotation 1 DOF joint are connected alternately. The pecification of ACM- R7 i hown in Table I. A. Joint Mechanim The joint torque hould be large to lift the body in the loop gait. The wide motion range of the joint i required to form a loop hape. Therefore, the coupled drive mechanim Curvature [rad/m] Fig. 5. Standard Shape of Serpenoid Oval κp 2π B κy A.5 C 1. (Arc Length) Fig. 6. Curvature of the Serpenoid-oval (C f = 1, C t =, C 1 = ) i intalled to each joint to increae the output torque and the motion range. In thi mechanim, the output of two motor are combined and drive two joint a hown in Fig. 2 (a) (b). The detail of the joint mechanim i hown in Fig. 2(c). Firt, the two Link-A are rotated by two motor independently. Link-A i connected to the fore unit with Link-B and ball joint. Then, the pitch joint i driven when the Link-A are rotated in the ame direction. If the Link-A are rotated in the different direction, the yaw joint i driven. The output torque of the pitch axi joint i twice a large a a mechanim in which one joint i moved by one motor. Furthermore the joint angle range i 9 degree (pitch axi). The pitch axi joint are mainly ued in the loop gait. The wide angle range make it eay to archive a loop hape. The joint mechanim i covered with bellow and oil eal, o that ACM-R7 can move in wet and duty environment. It i believed that the importance of the loop gait wa increaed, becaue a waterproof and dutproof robot capable of the loop gait in outdoor environment ha been developed. B. Connecting Mechanim with the Gripper A gripper i attached to the end of ACM-R7 (Fig. 4). ACM-R7 become a loop hape by graping the rod at the oppoite end with the gripper. The gripper i driven by a worm gear to prevent it accidental opening. Therefore, the gripper i able to keep the graping, even if the motor output i turned off. III. SERPENOID OVAL FOR THE KINEMATICS OF THE LOOP GAIT A. Propoal of Serpenoid Oval There are variou loop hape like circle, ellipe and combination of circular arc and line. However, a combination of circular arc and line i not mooth. An ellipe ha part of which curvature varie widely. Further, it i difficult to apply an ellipe to a robot a we dicu later. Therefore, we propoe the erpenoid oval which i an applied hape of 414

.3.2 Circle & Line Ellipe Serpenoid Oval -2 6π Y [m].1. -.5 -.4 -.2..2.4 X [m] -1 Fig. 9. κp [rad/m] Fig. 7. Comparion of the Loop Shape 14 12 Serpenoid Oval Ellipe 1 8 Circle & Line 6 4 2..2.4.6.8 1. 1.2 1.4 (Arc Length) [m] Fig. 8. dκp /d [rad/m 2 ] Comparion of Curvature of Loop Shape + + 6 4 Serpenoid Oval Ellipe 2 2 4 Circle & Line 6 - -..2.4.6.8 1. 1.2 1.4 (Arc Length) [m] Comparion of Derivative of Curvature of Loop Shape a erpenoid curve. The hape of a erpenoid oval i mooth, becaue the curvature of it change inuoidally. Serpenoid oval i defined by a hape control method, which ha been developed for nake-like robot [9]. In thi method, the hape of a nake-like robot i expreed in 3D curve by defining two curvature. The curvature are function of body trunk length. The curvature of a erpenoid oval are defined by the following equation. κ p, κ y : Curvature : Body Trunk Arc Length t: Time : Total Length of the Loop T t : Cycle Time C f : Coefficient of Flatne C t : Coefficient for Turning C 1 : Coefficient for Poture Offet κ p (,t) = 2π { 1 C f co 2π [( ) κ y (,t) = 2π C t + C 1 2 { 1 + co 2π ( 2 ( 2 t T t t T t )} )} C 1 ] The cycle time T t change locomotion velocity, not affecting the hape of a erpenoid oval. Therefore, we dicu the equation with t = to ignore the influence of T t. The meaning of the coefficient (C f, C t, C 1 ) are decribed in the following part. Firt of all, the tandard hape of a (1) (2) Cf Fig. 1. 1 2.5 1. (Arc Length) 2π 6π Change of the Flatne of Serpenoid Oval erpenoid oval i hown in Fig. 5 (C f = 1, C t =, C 1 = ). The relationhip between the arc length and the curvature i hown in Fig. 6. Compared to the other loop hape, the moothne of the change of the curvature i the mot characteritic point of a erpenoid oval. The change of the joint angle i mooth if the change of the curvature i mooth. Thu the loop gait baed on a erpenoid oval i able to move fat. The comparion of the loop hape (a erpenoid oval, an ellipe and a combination of circle arc and line) i hown in Fig. 7. The relationhip between the arc length and the curvature are hown in Fig. 8. The derivative of Fig. 8 are hown in Fig. 9. Thi erpenoid oval i the tandard hape which i hown in Fig. 5. The total length and the apect ratio of all hape are equal. The curvature and the derivative of curvature of the erpenoid oval change moothly. However, the derivative of curvature of the combination of the circle arc and the line reache an infinite value. It mean that the joint peed become very fat when the hape i applied to the robot. The change of the curvature of the ellipe i alo larger than erpenoid oval. In addition, it i difficult to expre the curvature of an ellipe by the arc length, becaue an ellipe i generally defined by other parameter. Therefore a erpenoid oval i uitable a a baic hape for the loop gait. B. Change of Flatne It i poible to change the flatne of the erpenoid oval by changing the definition of the curvature with the coefficient of the flatne C f. The relationhip between C f and the flatne of erpenoid oval i hown in Fig1. The flatne can be changed by the control of the value of C f. The tandard value i C f = 1. A erpenoid oval become a flat hape when C f become large. In contrat, the hape change to a κp (Curvature) [rad/m] 415

.15 H H /.1.5.5 1. 1.5 2. Cf (Coefficient of flatne) Fig. 11. Height of the Center of Serpenoid Oval circle, if C f i cloe to zero. If C f ha a negative value, the hape i rounded 9 degree from the hape in which C f i poitive. Fig. 11 how the relationhip between C f and the height of the center of the erpenoid oval. When a erpenoid oval become flat, the poition of the center of ma i lowered and it i difficult to fall. Therefore, the flat loop hape i effective, when ACM move over obtacle or climb a lope with the loop gait. On the other hand, a erpenoid oval which i cloe to a circle i uitable for high peed locomotion, becaue the bending peed of the joint i low when the hape i cloe to a circle. The bending peed i determined by the derivative of κ p. The maximum value of the derivative of κ p i calculated from the following equation. dκ p d max = 8π2 L 2 C f (3) t Therefore, the maximum locomotion peed become fat by increaing C f intead of by riing of the poition of the center of ma. C. Turning We introduce the coefficient for turning and the coefficient for poture offet to make the turning motion. The lower part, which touche the ground, ha to be bent horizontally to make turning motion in the loop gait. However, it i difficult to bend only the lower part becaue of the loop hape. In our method of turning, the whole loop hape i bent horizontally. The degree of bending i determined by C t. The relationhip between C t and the hape of a erpenoid oval i hown in Fig. 12. Serpenoid oval i not bent when C t =. The whole hape become bent when C t i increaed. Even if the flatne of a erpenoid oval i changed, it i bent. Fig. 12 how the hape of the erpenoid oval with different value of C f and C t. It i bent to the oppoite direction when the value of C t become negative. The relationhip between the arc length and the curvature (C f = 1., C t =.5, C 1 =.2) i hown in Fig. 13. κ p i the ame a in traight motion, and κ y i alo changed inuoidally. The meaning and calculation method of C 1 i defined a follow; The poition gap between the head and the tail will be oberved (Fig. 14), when the loop hape i bent with C 1 =. C 1 i the coefficient to offet the gap. The calculation method of C 1 wa developed a follow. Fig. 12. Curvature [rad/m] 2π Relationhip between Serpenoid Oval and C t κp κy.5 1. (Arc Length) Fig. 13. Curvature of the Serpenoid Oval (C f = 1, C t =.5, C 1 =.2) Error (a) Top View Front View (b) Top View Front View Fig. 14. Difference of the Shape by C 1 Firt, it i aumed that C f i contant, and the loop hape i calculated. C t i changed in increment of.1. The value of C 1 which make the gap minimum i calculated in each C t. Next, the relationhip between C t and C 1 i calculated in each C f (C f = to 1.5, with increment of.1). The relationhip between C t and C 1 in each C f i approximated by a linear function. Fig. 15 how them. For example, the function of C 1 i approximated by the following equation. C 1 =.41 C t (4) Then the relationhip between C f and the gradient of the Fig. 15 i approximated by a quadratic function. Therefore C 1 i expreed in the following equation with C t and C f. C 1 = (.136C 2 f.298c f +.841 ) C t (5) The erpenoid oval i bent horizontally without the gap by defining C 1 from Eq. 5. An approximation error i oberved when the continuou model i approximated to the dicrete model. There may be a gap in the dicrete model, even if there i no gap in the continuou model. A large gap hould be reduced by recalculation and adjutment of the joint. However we did not make adjutment, becaue the gap i thought to be mall enough to be aborbed with mechanical elaticity. 416

C1 (Coefficient for Poture Offet).4.3.2.1.1.2.3.4.5 Ct (Coefficient for Turning) Cf.1.2.3.4.5.6.7.8.9 1. 1.1 1.2 1.3 1.4 1.5 Fig. 17. Experiment of the Change of the Flatne of Serpenoid Oval with ACM-R7 Fig. 15. Relationhip between C t and C 1 Gradient of the Graph Ct - C1.8.6.4.2.2.4.6.8 1. 1.2 1.4 1.6 Cf (Coefficient of Flatne) Fig. 16. Relationhip between C f and the Gradient of the Fig. 15 A. Control Method IV. EXPERIMENT The loop gait with a erpenoid oval wa teted uing ACM- R7. In order to control a nake-like robot with a erpenoid oval, a continuou model ha to be approximated to a dicrete model. The joint angle of the dicrete model i calculated by integration of the curvature of the continuou model in the following equation [9]. i: Joint Axi (p or y) j: Joint Order in Each Axi θ: Joint Angle L u : Length between Joint Axe : Length from the Edge to the Firt Joint θ i,j =,i + j+1 2 L u,i+ j 1 2 L u κ i ()d (6) ACM-R7 calculate the joint angle uing Eq.6 with the main CPU mounted on the tail unit. The joint angle value i tranmitted to the local CPU in each unit with CAN BUS. The joint are proportionally-controlled. B. Flatne 1) Change of Flatne: The change of flatne of the erpenoid oval wa teted. It wa confirmed that the flatne of a erpenoid oval i changed by C f. The limitation of the value of C f wa 1.5 becaue of the maximum joint angle of the pitch axi joint. Fig. 18. Step Climbing (Step Height: 9cm) 2) Locomotion Velocity: When C f wa 1. (tandard hape), the fatet locomotion velocity wa 1. m/. In the experiment, the locomotion acceleration wa not controled. Therefore, the loop hape rolled backward by it acceleration, when ACM-R7 wa moved fater than it. 3) Step Climbing: Step climbing experiment wa conducted. ACM-R7 wa made to climb the 9cm tep with C f =.5, 1., 1.5. It wa not able to climb the tep when C f =.5, 1., becaue it rolled backward before the center of ma got over the edge of the tep. When the erpenoid oval i flat (C f =1.5), it wa able to climb the ame tep. The flatne and the dent of the center of a erpenoid oval were effective to climb the tep. The dent fit to the hape of the edge of the tep (Fig. 18(b)). 4) Slope Climbing: The lope climbing performance wa teted on an outdoor lope. The inclination angle wa about 33 degree. The locomotion direction wa parallel to the lope. When the loop hape wa a tandard erpenoid oval (C f = 1.), ACM-R7 rolled down the lope. However, the flat haped ACM-R7 (C f = 1.5) wa able to go up the lope (Fig. 19). C. Turning The turning motion wa experimented, which i hown in Fig. 2. ACM-R7 wa able to turn, even if the erpenoid oval i tranformed to flat or rounded hape by changing C f. The turning radiu wa controlled by the coefficient of turning C t. The relationhip between C t and the turning radiu i hown in Fig. 21. The curve hown in Fig. 21 i the minimum radiu of the curvature of the continuou model, which i theoretically calculated from κ y. When C t i increaed, the radiu of the curvature of the continuou model become mall. Then, the experimental turning radiu become mall, 417

Radiu [m] 2.5 2. 1.5 1. Turning Radiu (Experimental Value) Minimum Curvature Radiu of Continuou Model (Theoretical Value).5...1.2.3.4.5 Ct (Coefficient for Turning) Fig. 21. Relationhip between C t and Turning Radiu Fig. 19. Slope Climbing on Gra (The Angle of the Slope: 33 deg) Fig. 2. Steering Motion too. Therefore, it became poible, that the ACM in the loop gait make turning motion in arbitrary radiu. Outdoor experiment were made on gra, becaue ACM- R7 i waterproof and dutproof. The traight and turning motion i hown in Fig. 22. A. Concluion V. CONCLUSIONS AND FUTURE WORKS The new nake-like robot ACM-R7, which i uitable for loop gait, wa developed, with waterproof tructure. The new mooth hape Serpenoid Oval wa propoed for the loop gait. The hape control method of a erpenoid oval wa formulated to make turning and tep climbing. The experiment confirmed the uefulne of thoe method uing ACM-R7. B. Futurework There will be more hape control method of a erpenoid oval. Future work will include the formulation of thoe method. In addition, another loop hape that conider the effect of it own weight hould be examined, becaue only the kinematic of the loop gait were dicued. The joint torque i able to be adjuted by the new hape becaue a loop hape ha redundant joint to fix the poture. Fig. 22. Locomotion on Gra with Serpenoid Oval [3] M. Yim, D. G. Duff and K. D. Roufa, PolyBot: a modular reconfigurable robot, Proceeding of IEEE International Conference on Robotic and Automation (ICRA2), Vol. 1, pp. 514-52, 2. [4] J. Satra, S. Chitta, M. Yim, Dynamic Rolling for a Modular Loop Robot International Journal of Robotic Reearch, Vol. 28, No.6, pp.758-773, 29. [5] D. Mellinger, V. Kumar and M. Yim, Control of Locomotion with Shape-Changing Wheel, Proceeding of IEEE International Conference on Robotic and Automation (ICRA29), pp. 175-1755, 29. [6] S. Murata, E. Yohida, K. Tomita, H. Kurokawa and S. Kokaji, Self- Reconfigurable Modular Robotic Sytem, Proceeding of International Workhop on Emergent Synthei (IWES 99), pp. 113-118, 1999. [7] A. Kamimura, H. Kurokawa, E. Yohida, S. Murata, K. Tomita, S. Kokaji, Automatic Locomotion Deign and Experiment for a Modular Robotic Sytem, IEEE ASME Tranaction on Mechatronic, Vol. 1, Iue 3, pp. 314-325, 25. [8] Y. Zhang, M. Yim, C. Elderhaw, D. Duff and K. Roufa, Phae Automata: A Programming Model of Locomotion Gait for Scalable Chain-type Modular Robot, Proceeding of the 23 IEEE/RSJ International Conference on Intelligent Robot and Sytem (IROS23), Vol. 3, pp. 2442-2447, 23. [9] H. Yamada and S. Hiroe, Study on the 3D Shape of Active Cord Mechanim, Proceeding of IEEE International Conference on Robotic and Automation (ICRA26), pp. 289-2895, 26. REFERENCES [1] S. Hiroe, Biologically Inpired Robot, Oxford Univerity Pre, 1993. [2] H. Yamada and S. Hiroe, Study of Active Cord Mechanim - Generalized Baic Equation of the Locomotive Dynamic of the ACM and Analyi of Sinu-lifting -, Journal of the Robotic Society of Japan, Vol. 26, No. 7, pp. 81-811, 28 (in Japanee with Englih Summary). 418