Structure Design and Locomotion Analysis of a Novel Robot for
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12th IFToMM World Congress, Besançon (France), June18-21, 2007 Structure Design and Locomotion Analysis of a Novel Robot for Lunar Exploration Zhiying Wang * Xilun Ding † Alberto Rovetta ‡ Beihang University Beihang University Politecnico di Milano Beijing, China Beijing, China Miliano, Italy Abstract— 1 Two kinds of hexapod robot, for lunar exploration, are investigated: hexagonal and rectangular. II. Hexapod Legs Typical gaits are analyzed for these two kinds of hexapods’ locomotion. A comparative study, based on agility, stability and Humans, with two legs, are the most agile animal, but redundancy, concludes that the robot with hexagonal need a very complex controller: a brain. Lunar rovers architecture is better than the rectangular one. Finally, cannot have that kind of brain because of knowledge and simulations are done based on a novel hexagonal lunar technology limitations. Other mammals have four legs exploration robot. and are also every agile. It seems that a four-leg-rover is a good choice. However, the Moon is far from Earth, Keywords: optimal design, accuracy, parallel robot traveling to the Moon costs a lot, we cannot afford maintenance if one or two legs are broken. On the other hand, almost all insects have six legs. According to I. Introduction bionics, six-leg/hexapods robot may be a better choice. Planetary rovers have become a popular topic in recent There are several benefits for hexapods rover. years. Several types robot systems for planetary (a)Hexapod robot is easy to keep balanced. exploration have been proposed , wheeled types, (b)Hexapod technology is a redundant locomotion legged types and hybrid wheel/leg types. The wheeled system which increases reliability. It is workable even if type robot includes the single wheel of Gyrover , four one, two or three legs broken. wheels of RATLER  and others. The most famous (c)Hexapods makes it possible for the robot to use one, Mars Rovers, Opportunity and Spirit have six wheels . two or three legs to work as hand and perform complex The legged type includes Ambler, Dante and Dante II of operations. Carnegie Mellon University, and many others. Both Dante and Dante II have eight legs . Go-For from JPL III. The structure of the robot and Chariot II from Tohoku University of Japan is a There are two basic architectures of hexapod robots (see leg/wheel robot. Track 1 of VNIITRANSMASH, Fig.1) , rectangular and hexagonal. Generally, the ANDROS Mark V-A from USA and ACEC robot from hexagonal architecture is axi-symmetric. It can have many ACES are pedrail robots. Other types such as hopper robot kind of gaits and can easily change direction. For can jump forward. However, until now, the robots that example, to realize 0o, ±60 o, ±120 o and ±180 o turning have landed on planets successfully are all wheeled type. with the waving gait, it needs only regroup its legs and/or The lunar environment is very different from that on change the leader leg. The leader leg changes from leg 1 Earth. It is far from Earth, there is almost no air, the to leg 3 in group ‘1+3+5, 2+4+6’, the direction will gravity on the Moon is 1/6 of that on Earth and there is a change from 0o to 120 o ( see Fig.2). In contrast, for the deep layer of dust on the Moon. The strong friction rectangular architecture, a special gait is required for prevents wheels from running well. Wheels can also get turning action. Generally, it requires four steps for a stuck easily in dust. The leg-type robot is more agile than rectangular robot to realize a turning action(see Fig.3). wheel-type robot; however, it has very low locomotion 1 velocity. Legs incorporated with wheels can integrate the 2 advantages of these two kinds of locomotions . 3 2 Therefore, leg/wheel-type rover have becomes our main selection for lunar exploration. 4 3 4 1 *E-mail: email@example.com † E-mail: firstname.lastname@example.org 6 ‡ E-mail: email@example.com 5 5 1 This work is partially supported by China NSFC Grant #50475001 and 6 by HI-TECH RESEARCH AND DEVELOPMENT PROGRAM OF Fig. 1 hexagonal and rectangular robots  CHINA (863 PROGRAM: Grant # 2006AA04Z207) 12th IFToMM World Congress, Besançon (France), June18-21, 2007 Leg 2 Leg 1 Leg 3 Group 2 1 2 3 4 Group 1 Leg 4 Fig. 2 120 o turning Leg 5 Leg 6 Fig.5 Wave gait z θi1 Bi x e θi2 d Hi θi3 Fig. 3 Four steps to implement a turn  b a Li Ai S (a) Fig. 4 Configuration of rover R R Compared with recetangular structure, a hexagonal chassis with a hemisphere body is better for lunar R rover(Fig. 4) R R R R IV. Implementation and results Gait analysis and R simulation R For hexagonal hexapod robot, the wave gaits were studied mostly. However, it can have several different R gaits even for straight walking. S A. Wave gait (b) Robot with wave gait (Fig.5) is the easiest gait to turn around. But it is very complex to control because every Fig.6 Structure of a wave leg leg has a different gait. For the wave gait, the leg’s During walking, there will be three legs to support the structure is as in Fig. 6. There are two revolute joints body, and three legs wave ahead (Fig. 5). The whole along axes Y, one along axes Z, its foot, contacting with body’s simple structure is as Fig. 6(b). There are 12 links, the ground becomes a spherical joint (with three revolute 13 revolute joints, two spherical joints in this freedoms). 12th IFToMM World Congress, Besançon (France), June18-21, 2007 configuration. The positon is described in a space 9 and Fig. 10 listed the steps of 60 degrees and 90 degrees coordinate frame. turning cases. The number of degrees of freedom of the robot is computed as follows : F=12*6-5*12-3*2=6 In this case, every supporting leg has three freedoms, which makes control very complex. B. Crab gait Fig.8 Small angle turning while walking Another gait for hexagonal robot is ‘crab gait’ or ‘kick- up gait’ , which is a continuous gait.. Six legs are also grouped into two patterns, 1+3+5 and 2+4+6. There will be 3 legs for supporting while three legs rise to walk ahead at every time. The track of foot is a parabola ( see Fig.7): y=-ax^2+b ‘b’: is the maxmimal height that the robot’s feet can raise. While passing small obstacles, ‘b*fh’ is the height of Fig9. Three steps to realize turning left (60 o) obstacle, ‘2*sqrt(b-y)*fw’ is the width of obstacle, given that, ‘fh’ and ‘fw’ are factors of obstacle’s height and width, 0<‘fh, fw’<1. Fig10. Four steps to realize turning (90 degrees) Quadrangles in the above figures are areas of support; the white circle is the robots’ mass centre. It can safely turn through 90 degrees using four steps (Fig. 10). (a) B.2 Simulation L2 When the robot walks in a straight line, the body should L be kept horizontal. Three drivers are needed. The L1 θ1 kinematics can be simply denoted by geometric equations. The relationship between joint angles are shown in the h following equations: θ4 θ1 =θ1 (b) θ2 =π-arcsin[(h+L 1sinθ1)/L2] - θ1 Fig. 7 crab gait and simple structure θ3 =π-arcsin[(h+L 1sinθ4)/L2] - θ4 (1) L2cos(θ4)+L1 cos(π- θ4 -θ3) In figure 7(a), legs in solid line are in the supporting = L1cos(θ1)+L2 cos(π- θ1-θ2) + L phase, legs in dashed line are in the walking phase. From simple structure (see Fig.7 (b)), the number of degrees of freedom of the robot is: F=3*5-2*6=3. Therefore, the result can be obtained as follows: From the above analysis, the crab gait is simpler than θ1 =θ1 (2) the wave gait. However, it also needs special gaits for θ2 = f1(θ1) turning. θ3= f2(θ2) B.1 Turning Figure 11 shows the simulation of the robot walking To realize turning motion, there are two cases. For small straight using ADAMS with crab gait. angle turning, turning can be realized during walking, the robot does not need to stop. The turning angle must be less than 30 degrees to avoid walking legs colliding with supporting legs. See in Fig.8. For large angle turning, three steps are needed. There are always four legs standing on the ground to support the body, and the other two legs rise to adjust direction. Fig. Fig. 11 Simulation of walking (3 3 gait) The trajectories of joints are shown in Fig.12 12th IFToMM World Congress, Besançon (France), June18-21, 2007 The simulation results for the displacement of the mass centre using MATLAB & ADAMS are shown in Fig.13- Fig. 16. B.3 Gaits with sick legs - Fault Tolerant Locomotion Because of the complex lunar environment, the robot’s legs may be damaged during working. If one or two legs (a) The thigh joint (b) The thigh joints of leg 2 are broken, it still can run with wheels and walk with the of leg 1 and leg 6 other four or five legs with two kinds of gait. Even if three legs are broken, the robot can still walk with a suitable gait . However, if two interphase legs are out of action, the crab gait is impossible. It is still possible for supporting and running, but if three adjoining legs are broken (see Fig. 17) walking is almost impossible. Figure 18 shows how the robot can run with two legs out of action. (c) The thigh joints of (d) The thigh joints of leg 3 and leg 5 leg 4 4 5 6 Fig.17 Three adjoining legs broken case Fig.18 Two legs broken case B.4 Gaits with wheels (e) The calf joint of (g) The calf joint of leg 1 leg 2 and leg 6 Because wheels can provide higher speed locomotion than legs, our robot will run with wheels in the case of a smooth surface on the Moon. All wheels will be grouped into two branches, one on the left, the other on the right. The robot runs like a car. It can realize turning through changing the velocity difference between these two groups of wheels, which had been studied intensively. (h) The calf joint of leg 3 (i) The calf joint of leg 4 The ideal velocity for forward motion is, and leg 5 v(t)=(vl(t)+vr(t))/2 (3) Fig.12 Curves of joints’ angles vl (t):velocity of left group; vr (t):velocity of right group. The radius of turning is, p=D*( vl (t)+ vr (t))/(2*( vl (t)- vr (t))) (4) D-the distance between group one and group two. The angular velocity of turning is: w(t)=(v1(t)- vl (t))/D (5) If |vl (t)|=|vr(t)|, then w(t)=0, robot runs straightly; If | vl (t)|>|vr (t)|, then robot turns right; If | vl (t)|<|vr (t)|, then robot turns left; Fig.13 Horizontal displacement of mass centre Fig.14 Vertical displacement of mass centre If vl (t)=- vr (t), then w(t)>0 and v(t)=0, robot turns without displacement. According to experience, Fuzzy Logic is most suitable for controlling the wheel velocities. V. Prototype test Based on system design and simulation, one prototype was build (see Fig.18). The prototype has 24 motors Fig.15 Horizontal displacement of a single leg (Servos Hitec HS-475HB) and a main board (Servopod). Fig.16 Vertical displacement of a single leg The Servopod has the ability to control more than 26 12th IFToMM World Congress, Besançon (France), June18-21, 2007 servos, it is the best choice for a limited budget prototype,  Shigeo Hiros. Three Basic Types of Locomotion in Mobile Robots. Advanced Robotics, 1991. 'Robots in Unstructured Environments', but it will be changed in the next stage when more 91 ICAR., Fifth International Conference, Page(s):12 - 17 vol.1, computational power will be needed. Figure 19 also June 19-22, 1991. shows the motion of the prototype.  Reumoat, P.Alezandre, Ff D.Ghuya. GAIT ANALYSIS AND IMPLEMENTATION OF A SIX LEG WALKING MACHINE, Advanced Robotics, 1991. 'Robots in Unstructured Environments', 91 ICAR., Fifth International Conference, Page(s):941 - 945 vol.2, June 19-22, 1991.  SU Jun, CHEN Xue dong, TIAO Wen gang. A Study of the Omnidirectional Gait for a Hexapod Walking Robot. Mechanic and Electron, pages:48-52, 2004 (3).  Yun-Jung Lee, Shigeo Hirose. Three-Legged Walking for Fault Fig.19 Prototype walking on smoothing surface Tolerant Locomotion of a Quadruped Robot with Demining Mission. Proceedings of the 2000 IEEE/RSJ International VI. Conclusion and Future work Conference on lntelligent Robots and Systems. Pages :973-978, 2000. Robots with wheel type locomotion can have high  Ruan Feng, The Research on Mobile Robot Control System, velocity on smooth surfaces, but cannot run on rough issertation of Master's Degree of Zhejiang University, Feb. 2004. terrain. Robots with leg type locomotion are more agile, Mechanism and Machine Theory, 38(3):227–240, March 2003. but usually only walk with low speed. Therefore, the robot with a hybrid locomotion using both legs and wheels will be a good choice for a lunar rover. From the above analysis, the hexagonal structure for a hexapod is more agile than the rectangular one. Because the crab/kick-up gait is like a human’s gait, it is simpler to control and easier to implement. The wave gait is more complicated,. However, when one or two legs are damaged, the crab gait is very hard to use while the wave gait is still available. Therefore, the locomotion of the crab gait coupled with the wave gait is more suitable for a lunar rover. This papaer mainly focus on a comparative study of rectangular hexapod robot and hexagonal hexapod robot, and the analysis of the wave gait and crab gait was investigated. There are still many other gaits for this kind of lunar robot, such as climbing slope, overtaking gouge, and detailed gaits when one or two legs are broken. As for fault tolerant gaits, only runing with wheels is studied here, more work will be done on fault tolerant leg- walking gaits in the future. VII. Acknowledgment Thanks to the China NSFC (Grant no. 50475001), HI- TECH RESEARCH AND DEVELOPMENT PROGRAM OF CHINA (863 PROGRAM: Grant no. 2006AA04Z207) AND the S&T cooperation program (2006-2009) of the governments of China and Italia for financial support, and also thanks to Professor Alberto Rovetta and his research group on the Italian side for joint research work. References  http://www.ri.cmu.edu/projects/project_102.html  http://www.sandia.gov/isrc/fuelcellrat.html  http://apod.nasa.gov/apod/ap040803.html  Su Jun. The Research of the Gait Planning and Control of the Multilegged Walking Robot. A Thesis of Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Engineering, 2004.03.