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1. PELVIS 2 TRANS Trans SPACER SHAPE F6 PELVIS LEFT 1 Trans F6 SHAPE F6 PELVIS RIGHT 1 Trans F6 SHAPE BACK LEFT 1 SERVO Servo Fl BACK LEFT 1 TRANS Trans F1 SHAPE BACK LEFT 2 SERVO Servo AX12 BACK LEFT 2 TRANS Trans AX12_ SHAPE F3 BACK LEFT 3 TRANS Trans F3 CROSSED GRP AX12 BACK LEFT 3 TRANS Trans AX12_ SHAPE BACK LEFT 3 SERVO Servo F1 TRANS Trans F1 SHAPE CRUTCH BACK LEFT Trans CRUTCH FRONT LEFT BACK RIGHT 1 SERVO Servo Fl BACK RIGHT 1 TRANS Trans F1 SHAPE BACK RIGHT 2 SERVO Servo AX12 BACK RIGHT 2 TRANS Trans AX12 SHAPE F3 BACK RIGHT 3 TRANS Trans 24 F3 CROSSED GRP AX12 BACK RIGHT 3 TRANS Trans AX12_ SHAPE BACK RIGHT 3 SERVO Servo F1 TRANS Trans Fl SHAPE CRUTCH BACK LEFT F3 PELVIS RIGHT 1 TRANS Trans F3 PELVIS LEFT 1 TRANS Table 15 Simplified representation of the robot model the gray lines show the servo nodes
2. Reference Manual Servo Node http www cyberbotics com cdrom common doc webots refer ence section2 37 html 28 Number of world inhabitants http www worldpopclock com 29 P Turner Mathematics required for Legged Robotic Motion rev 1 September 2006 30 R M Alexander Locomotion of Animals Glasgow London U K Blackie 1982 31 Rules for the Four Legged Robot League http www tzi de 4legged pub Website Downloads Rules2007 pdf APPENDIX All the videos sources code and data files acquired during the different experiments will be posted on the project website The current project page is http wiki epfl ch wsrl This page is susceptible to change in the future in case the link is dead You will be able to look for additional information using the Biologically Inspired Robotic Group BIRG page at http birg epfl ch or http birg epfl ch page32024 html Animation Shape Webots Nodes inherits fields amp functions from Appearance Sphere Abstract class 1 Cannot be s instanciated can be used as Shape node Background TextureCoordinate TextureTransform Camera Color Viewpoint can be used as boundingObject boundingObject in a Solid node Charger Cone Worldinfo Connector Coordinate r DistanceSensor Cylinder ElevationGrid Emitter Extrusion GPS Gripper HyperGate 3 c v imageTexture m o IndexedFaceSet LightSensor Ind
3. R A A A A a i f A it fl f i f A f ig AN I aia n NAN AAA N IJl N x OM WNW N A l i l te ye de l i E A o ITATAYA u TATE al ata j y TET VOY J VN 2 y Y Y Y SY MB BS Y UF Y Y ba I 0 5 10 15 20 25 30 T T rr T T i 2 A A AAAA A A A AKA A A ft A i il 1 l f h N i f i l ae i gi i i i i JI i AJ Ilji fi j AANA UVY MAM YATATA MAA U YN y 2 vy YY _ 1 _ l A O 0 5 10 15 20 25 30 i LDAIT WW FPF 2r ot j Lf l I i N f i UA 1 i i f j f 1 A A fi A A i i EMME EY YVA V j Lj j iii j j j ave A V TAT y H j J J AVA 1 2r Figure 38 Example of synchronized oscillations Plot of the x states of four coupled oscillators over a period of 32 seconds the initial stabilization period is visible 15 When multiple coupled oscillators are used the resulting phase shifts between the oscillations is a function of the coupling strengths a and b however several different 14 combination of a and 5 can produce the same phase shift In fact the exact outcome of a particular coupling combination cannot be predicted by any general theory 19 Consequently the coupling strengths must be optimized by the search algorithms A slight variation 14 of the original oscillators model seen above was proposed in 20 With this modification the inpu
4. a Experiment I Optimized a function having 64 parameters is quite a challenge using a systematic search the cardinality of the space would have been 2 which implies approximatively 1 84 10 sets of possible parameters A way to distribute such a simulation doing a systematic search could be to ask each inhabitants of the world 25 to run 2 7810 evaluations Then considering each one of them has a computer able to run the simulation 32 times faster The 18 amount of time required if we distribute the systematic search to all world inhabitants would be 88 years Table 6 Experiment l Best performance Observing Table 6 we see that the robot moves hardly forward like it was swimming on the ground The gait obtained is not similar to what a real dog does Nevertheless it is safe to assume the optimization could be more successful doing hypothesis on the coupling That way the cardinality of the problem could be decreased PSO CPG Optimization experiment 1 Aa A i pii Y Peformance 100 120 140 160 180 200 220 240 Iterations 20 40 60 80 Figure 46 Experiment 1 Plot of PSO performance over 240 iterations b Experiment 2 Compared to the experiment 1 the cardinality of the problem is divided by two Doing the same analogy about the number of world inhabitants each one of them would have to run only one simulation for less than a seconds Observing Table 7 we can see the dog
5. 513 513 FL1 513 5143 0 0 513 513 513 513 513 FR1 513 513 513 513 513 513 513 513 513 FL2 205 819 819 819 867 513 513 513 513 FR2 819 205 513 513 513 166 513 513 513 FL 3 513 513 513 513 513 513 513 513 513 FR3 513 513 513 513 513 513 513 513 513 B_L_1 513 513 513 EE 513 513 513 513 513 BR1 513 513 573 513 513 513 513 513 513 BL_2 580 444 513 513 166 513 513 513 513 BR2 444 580 819 819 513 867 513 513 513 BL 3 513 513 513 513 513 513 513 513 513 BR 3 513 513 513 513 513 513 513 513 513 N1 513 513 513 513 513 513 513 513 513 N2 513 513 513 513 513 513 513 819 205 HEAD 513 513 513 513 513 513 513 513 513 Table 4 Initial servo position for each of the static experiments The gray cell shows the servos being updated during the experiment The results of the experiments done on the real robot have to compared to the one done on the modeled one B Results The Table 5 summarizes the outcome of the 9 tests The cross on the red cells states that the robot fall on the ground during the setup of the initial posture whereas the circle in the green cells depict that he robot didn t fall whatever was the position of the updated servo Exp 1 Exp 2 Exp 3 Exp 4 Exp 5 Exp 6 Exp 7 Exp 8 Exp 9 Real 57
6. The letter scale used before wasn t able to provide the right information concerning the X Y and Z location of the CoM A simple way to overcome that problem was to construct a CoM measurer Object Plate Axe Magnet Figure 14 Functional schematic of the CoM measurer As illustrated on Figure 14 the CoM measurer is composed of 3 main elements the plate the magnet and the axes Before using it the first step is to make the zero To achieve that purpose the magnet can be slided from left to right or from right to left until the plate is almost at equilibrium The second phase concerns the measuring of the CoM itself The body part is set on the plate and smoothly moved from left to right or right to left until the equilibrium state 1s reached That last step should be executed for the 3 axis X Y Z of the body part Particular attention has to be observed while the body part is set on the plate indeed the 3 axis should match as much as possible the one of the modeled shape That was the measured CoM can be directly reported in the model definition In order to measure the position of the CoM while the body part is disposed on the plate and the equilibrium state is reached or the closer possible to a pencil can be used to mark the position of a characteristic point of the body part Afterward with a ruler it s easier to measure the effective distance of the marked point to the central axis of the measurer After the
7. between the two segment is smaller then 90 degrees The Figure 28 b plots the servo values required to moved the leg given the current trajectory A part of the red curve as expected is flat This correspond to the maximum value the knee servo can t exceed To overcome this issue the solution is to consider the actual robot anatomy One of the initial rule of thumb needs to be updated Setting the x axis radius to b k y LI L2 fixes the problem 11 a Leg extermity trajectory 710 5 0 5 10 15 20 cm b AX 12 servo values shoulder servo knee servo time Figure 28 a Lower leg extremity trajectory b AX12 values for shoulder and knee servo 3 Experimental framework As explained in 30 the different possible gait in four legged animal locomotion are depicted on Figure 29 DiG y ye 0757 NO25 05 NO 05 0 6 WALK TROT TRANSVERSE AMBLE GALLOP TC TC pig TC 0 7 0 Q D5 5 Ds i CANTER PACE BOUND PRONK Figure 29 Gait used by four legged walking animals distinguished with respect to the relative relationships in units of 2r between their legs The front left leg serves as reference 30 Using the inverse kinematics model described before all the four legged gaits listed above are tried at different frequency ranging from 0 5Hz to 2Hz 4 Results Looking at the Figure 30 the trot gait presents from far and above all the best performance The performance is measured as a weight
8. from the 3D modeling of the different body parts the measure of the different physic properties the understanding of Webots simulator to the development of a central pattern generator or inverse kinematic model allowing the robot to move The project was built on the top of two cornerstones the elaboration of an accurate model both efficient and realistic and the development of a demo showing the capacities of Webots simulator to render a 3D model while simulating the physics Multiple component were developed allowing to ease the coding of the model to validate easily the static characteristics to distribute the optimization of a central pattern generator on cluster of computers Experimental results were gathered leading to clear conclusions However a additional test would validate the conclusions even further There is still a large amount of work to be done and with this document in hand any master level Report written July 04 2007 1 e mail jean christophe fillion robin epfl ch engineering student should be able to take the project further Despite of what is outstanding the overall satisfaction at this point in time from both team member and collaborators is high The remaining of this document aims at describing the Bioloid kit used to build the robot presenting the Webots simulator used to render and simulate the model and finally illustrating the different phases of the project Il Biotorw Ki
9. naxStop 0 O0 pi SFFloat Springtonstant 0 Os aLa SFFloat dampingtconstant 0 Ea iak SF Bool customForce FALSE SFBool forceaAndTorque TRUE MF Node animation Figure 12 Webots specification of the Servo node The realism of the simulation can be achieved setting the right physics parameters to the servo nodes It s safe to assume all the servos present similar characteristics No measure of the real performance has been done on the servo itself Instead the technical documentation has been considered see II C The different fields of the servo node are listed below the Figure 13 allows to get a better understanding of the influence of each one maxVelocity It specifies the default and maximum value for the desired motor speed 27 The value given in the specs is 0 196sec 60degrees which can be converted to 1 70 tr rad sec This later value will be used in the servo node initial rotation current rotation Servo s children Servo s parent translation p maxPosition minPositio maxStop minStop Figure 13 Rotational servo and the matching Webots servo node fields maxForce It specifies the default and maximum motor torque force F that is sent to the physics simulator 27 The documentation of the servo module talks about final max holding torque The given value is 16 5 KgForce cm which can be converted to 16181 N m acceleration It defines the default motor accelerat
10. open source 3D modeling and rendering studio allowing to import an object file and export it to POV 8 file format or VRML Virtual Reality Modeling Language file format Called Art of Illusion AOI 9 this Java based tool provides an easy way to model 3D shape or even edit existing one VRML is a standard file format to represent 3D interactive graphic vectors 10 VRML language allows to natively describe spheres cubes cones or extrusions If the modeled element is converted to a triangle mesh shape The efficiency of the rendering will be a direct function of the number of triangle meshes Some of the shape provided were too complex they presented a high degree of details and for the sack of the modeling it was not necessary to keep such low level details see Figure 8 and Figure 9 es a h e Figure 8 CM5 shape before simplification the VRML exported file is about 158 5Kb Figure 9 CM5 shape after simplification the VRML exported file is about 5 5Kb The 3D modeling of a model is a trade of between visual realism and rendering complexity 2 Webots scene description The description of scenes follows a VRML like language in that way all shapes modeled using the 3D modeling tool mentioned above can be easily imported There is two ways of describing a world scene either using the Webots built in VRML editor or using an external editor Kdevelop 24 revealed to be an interesting o
11. time step a particle s flight direction is driven by three factors first its own inertial speed second its tendency to return to the best solution it has discovered so far and third the tendency to go towards the best solution discovered by its neighbors This can be summarized in equation 15 which calculates the new flight speed of a particle at time t 1 and in equation 16 which calculates the new position a particle vg t 1 wv t rand Cera t orand p a xa t ue Xig t 1 x g t Via t 16 where v is the speed of a particle i is a particle index d represents the d dimension in the parameter space t is the discrete time index w is the particle speed inertia factor and where the function rand returns a uniformly distributed random number in the range 0 1 The coefficients and p control the individual and social levels of confidence e g how much a particle should follow its own best solution or his group s best solution Finally p is the best previous position of particle i and p is the best previous position in the neighborhood of particle i These principles are illustrated in Figure 39 v current speed xft J next position Py best solution in neighbourhood Oe Wrage tall aft current position Pi own best solution Figure 39 Principle of Particle Swarm Optimization In PSO we speak about the particles neighborhood A particle s neighborhood defines
12. 1 482 479 535 261 274 478 537 542 Webots 531 X X 363 375 466 527 531 Diff 40 X X 102 101 12 10 11 Diff deg 11 72 X X 29 88 29 59 3 52 2 93 3 22 Table 5 Equilibrium value of the updated servo for each of the experiments The issue of the experiment 1 7 8 and 9 can be accepted since the difference between the result obtained with the model and the one obtained within the simulator is below 15 degrees Nevertheless the issue of the of experiment 2 3 and 4 need to be observed carefully see Figures 19 20 and 21 Figure 22 Static test Experiment 5 In the context of experiment 3 the robot is really stable since in any position of the head the robot doesn t fall Plus the fact in experiment 2 and 3 it s not possible to set the robot in the initial posture It s safe to tell that the center of mass impacting the most is the one of the CM5 unit since it is the heaviest element The robot being really stable in the experiment 2 it s safe to assume the CoM is too much toward the left and or bottom of the CM5 unit Figure 23 Static test Experiment 6 Figure 24 Static test Experiment 8 Figure 25 Static test Experiment 9 To improve the issue of the experiments the update of the position of the 16 center of mass can be a tedious and long process The use of using a particle swarm optimization see VI B 2 is to optimize the location of the different center of mas
13. 2 15 c Synchronization By choosing the E and Tt parameters it is possible to control the amplitude and frequency of the oscillations However locomotion is efficient only when the phase shifts between the oscillations stays constant through time and 13 2 1 0 1 2 Xx Figure 35 Limit cycles of a standalone oscillator obtained with 30 oscillations started with random initial conditions x and v inthe range 2 2 With x 0 7 and E 1 15 therefore a strict synchronization is required In the model proposed in 18 synchronization is obtained by coupling the oscillators a signal proportional to the sum of the state of every other oscillator is added into each oscillator Equation 9 seen earlier is now completed into equation 12 18 2 X TV TV X T SeN D aero 12 TX V 13 where a and b represents the strength of the coupling of the x and v states of oscillator j into the oscillator i Synchronization happens only when the uncoupled frequencies match approximately 19 Figure 36 illustrates this fact the frequency difference A fof two uncoupled oscillators is plotted versus frequency detuning AF after coupling If the uncoupled frequencies are too different synchronization does not occur Synchronization region Figure 36 Frequency vs detuning graph 19 In order to facilitate synchronization the same time constant t is used for all the oscillators and therefore th
14. Modeling of a real quadruped robot using Webots simulation platform Jean Christophe Fillion Robin School of Computer and Communication Sciences I amp C Ecole Polytechnique F d rale de Lausanne CH 1015 Lausanne Switzerland Abstract The fundamental achievement of this project was the development of a three dimensional model that closely resembles the real quadruped robot While the static characteristics of the model were validated against the actual ones of the real robot the dynamical ones were defined by the results of applying the inverse kinematics model These were considered best when compared to the ones yielded by the particle swarm optimization PSO of central pattern generator CPG an alternate method to determine the properties in question The development of this model will serve as the foundation of a demonstration involving four to six robots playing on a virtual soccer field This paper highlights and contextualizes our implementation and outlines the crux of the problem in order to motivate future related research Index Terms Quadruped robot 3D model simulation four legged walking gait central patterns generators particle swarm optimization inverse kinematics I INTRODUCTION amp MOTIVATION he modeling of a real robot is a complex and passionating challenge On the crossing point of mechanics physics and computer science the development of a complete model involves multiple tasks ranging
15. TTOM SHAPE F3 NECK1 TRANS Trans F3 CROSSED GRP AX12 NECK1 TRANS Trans AX12_ SHAPE NECK1 SERVO Servo F2 NECK1 TRANS Trans F2 SHAPE NECK2_ SERVO Servo AX12_ NECK2 TRANS Trans AX12_ SHAPE F6 NECK2 LEFT TRANS Trans F6 SHAPE F6 NECK2 RIGHT TRANS Trans F6 SHAPE F2 NECK2 CENTER TRANS Trans F2_ SHAPE BRACKET NECK2 CENTER TRANS Trans BRACKET SHAPE Shape F1 NECK2 CENTER TRANS Trans F1 SHAPE BRACKET NECK2 LEFT EAR TRANS Trans BRACKET SHAPE BRACKET NECK2 RIGHT EAR TRANS Trans BRACKET SHAPE HEAD SERVO Servo AX12_ HEAD TRANS Trans AX12_ SHAPE F3 HEAD TRANS Trans 7 F3 CROSSED GRP AX12 HEAD 2 TRANS Trans AX12 SHAPE F3 FRONT RIGHT 1 TRANS Trans F3 FRONT LEFT 1 TRANS AX12 FRONT RIGHT 1 TRANS Trans AX12_SHAPE FRONT RIGHT 1 SERVO Servo F1 FRONT RIGHT 1 TRANS Trans Fl SHAPE FRONT RIGHT 2 SERVO Servo AX12 FRONT RIGHT 2 TRANS Trans AX12_ SHAPE F3 FRONT RIGHT 3 TRANS Trans F3_ CROSSED GRP AX12 FRONT RIGHT 3 TRANS Trans AX12_ SHAPE FRONT RIGHT 3 SERVO Servo F2 TRANS Trans F2_ SHAPE CRUTCH FRONT LEFT F3 PELVIS LEFT 1 TRANS Trans F3 SHAPE BRACKET PELVIS LEFT 1 TRANS Trans BRACKET SHAPE F6 PELVIS LEFT 1 TRANS Trans F6 SHAPE AX12 PELVIS Trans AX12_ SHAPE PELVIS SERVO Trans PELVIS 1 TRANS Trans SPACER SHAPE Shape F3 PELVIS LEFT 1 Trans F3 SHAPE AX12 BACK LEFT 1 Trans AX12_ SHAPE F3 PELVIS RIGHT 1 Trans F3_ SHAPE AX12_ BACK RIGHT 1 Trans AX12 SHAPE
16. ators are considered identical F L 3 F R 3 F_L 2 FR 2 LI EFRI BL3 BR 3 BL2 B R 2 B_L_1 B_R 1 It also safe to tell while a dog is walking that the frequency of the head and pelvis could be different from the the other joints That s why this time the frequency of the PELVIS and NECK 1 oscillator has been optimized between a value of 1Hz and 2Hz The number of parameters to optimized is now 33 HEAD O x2 NECK_1 Figure 43 CPG Model 2 c Experiment 3 This experiment is similar to the previous one except one detail concerning the frequency of the PELVIS and NECK 1 oscillator The frequency parameter is now removed the PELVIS and HEAD will oscillate at the same frequency the rest of the oscillators do The number of parameters is 32 17 d Experiment 4 Observing real dogs walking it seems their pelvis is moving much more from left to right than up and down In this experiment the influence of the PELVIS servo has been annihilated In the same time the NECK 1 has been removed since the pelvis and the head are considered to be linked in frequency The CPG Model 3 see Figure 44 being used the total number of parameter to optimized falls to 24 HEAD O NECK_2 O NECK_1 Figure 44 CPG Model 3 e Experiment 5 As in experiment 4 the PELVIS and NECK 1 oscillator are taken away CPG Model 4 see Figure 45 An additional hypothesis is done real dog can hardly move their front leg laterally far aw
17. ay from their torso As simplification in this experiment the F R 2 F L 2 B R 2 andB L 2 servos are kept in fixed position keeping their value as when the dog stand up Since the pair of oscillators F L 1 F_R_1 and B_R_1 BL 1 are identically optimized the number of parameters is 16 HEAD O NECK_2 O NECK_1 O Figure 45 CPG Model 4 f Experiment 6 Keeping the same hypothesis as in experiment 5 the pairs of oscillators F L 1 F R 1 and B R 1 B_L_1 have now their own set of optimized parameters The same model is used see Figure 45 Since the front and back top leg oscillator are unpaired the number of parameters is 24 4 Results and discussion The thumbnails showing the best performance obtained so far within the context of a given experiment are order from left to right and top to bottom These one were generated over a sequence of approximatively 5 seconds The aim of these sequence is too visualize the way the robot moves As we can see in the plots depicted in the subsection specific to each experiments a maximum of 240 iterations for the PSO seems to be a value allowing to converge toward a solution Indeed due to the random initialization of the 50 particles of the swarm the first iterations give wrong performance and then as the number of iterations increased the performance increases until it reached an asymptotic limit The performance for all experiments oscillated between approximatively 7 and gA
18. be carried out satisfactorily by the robot s motors Consequently an uncontrolled transition appears during which the robot performs an undesired brutal movement and is subject to fall This is in contrast to gait transitions in nature which always occur smoothly Furthermore with sinusoidal signals there is no simple way to incorporate sensory feedback To overcome this problem non linear oscillators were introduced as mathematical models of the natural CPGs 18 The state of oscillators changes smoothly and therefore gait transitions are soft In addition with oscillators feedback can be incorporated in the simulation For example sensors can detect that a foot is in contact with the ground and a feedback signal can be injected into the oscillators The oscillator proposed in 18 is based on these differential equations 2 2 TV gett a 9 TX V 10 where v and x represent the current state of the oscillator E is a positive constant that represents the energy of the oscillator determines the rate of convergence towards the limit cycle and T is the time constant that determines the oscillation s frequency This type of oscillator converges to a sinusoidal signal with amplitude VE and period 2rrt 18 lt t VE sin t t 11 where depends on the initial conditions This behavior is illustrated by the limit cycle presented on Figure 35 showing each run converges to the circular attractor of diameter 2VE
19. e uncoupled frequencies are similar A frequency of 1Hz tT 1 277 is chosen as baseline for all simulations This is because it corresponds to the pace of an ordinary animal and it is slow enough for the physical robot s servomotors to go once 180 back and forth A stabilization period is necessary before the frequencies become locked The duration of the stabilization period depends on the coupling strength Figure 38 shows an example of synchronized oscillations This stabilization period is bad because it results in disorganized steps of the robot Shorter stabilization periods are wished and can be obtained by increasing the coupling strength However unlike standalone oscillators the signals produced by coupled oscillators are not exact sine waves Discrepancy with the sine increases with the coupling strength and furthermore when the coupling becomes too strong the signals turn out to be chaotic Figure 37 and unsuitable for controlling locomotion For that reason coupling strengths are suitable only within an appropriate range that must be determined Figure 37 Chaotic oscillations resulting of too strong coupling Plot of the x states of four coupled oscillators over a period of 32 seconds 15 2r 4 A f NANANAAAAAR An j f A j i j A t fy i Hif V NV AN AVA AAA y yV WY vw yw y VJ y y J UVW y j Y V aL J fi l J i 0 5 10 15 20 25 30 T rr T T T 2 4
20. ease the likelihood of convergence it is better to hold down the dimensionality of the search space Therefore it 1s favorable to fix some parameters whilst the most relevant ones are kept free As explained in the previous paragraph the coupling strengths a and b must be free because the oscillators synchronization phase depends on them The oscillation amplitudes controlled by E must also be free because it is not known beforehand how large joint movements should be 15 180 Figure 40 Module s oscillations around xo 15 Oscillations in the region of the module s 0 angle the horizontal position in Figure 40 are too restricted For example in quadruped robots it is known 15 that the knee joints should oscillate in a region below the 0 angle In general this angle is not known beforehand and should therefore be another free parameter that we call here xo Different oscillator coupling models were validated The PSO used to optimize these models was initialized with a number of 50 particles According to 15 this value gives interesting results There is no defined method to determine the number of particle required to solve a given optimization problem but based on previous experiments the scientist can expect a convergence of the problem with a swarm size between 10 and 50 elements Computationally wise a PSO working with 50 particles is high demanding In fact using one computer and
21. ed from the improved gait Figure 52 Six quadruped playing on a soccer field As depicted on Figure 52 multiple robot are able to evolve simultaneously on the soccer field matchng the demo requirements 31 Additional work has to be conducted to allow the quadruped to detect the ball within his environment and try to kick it A plus to the current implementation could be the ability to cross compile the Webots controller into CM5 controllers ACKNOWLEDGMENT I gratefully acknowledge the technical support and the advices of Prof Auke Jan Ijspeert Olivier Michel Yvan Bourquin Peter Turner and Robin Fisher in the design and implementation of the quadruped robot model I would like to acknowledge Laurent Lessieux for his work on the X file processing Finally I also acknowledge Matteo Thomas DeGiacomi and Allessandro Crespi for their advices and help in the everyday lab life This work was made possible thanks to the Biologically Inspired Robotic Group REFERENCES 1 O Michel Cyberbotics Ltd Webots professional mobile robot simulation International Journal of Advanced Robotic Systems 2004 Volume 1 Number 1 pp 39 42 2 S Russell Open Dynamic Engine ODE open source and high performance library for simulating rigid body dynamics http www ode org 3 Research projects game or various tools that are using ODE http www ode org users html 4 Atmegal28 128 Kbyte self programming Flash Progra
22. ed sum of the absolute distance and the integrated distance done in between the 32 seconds of the simulation A detailed description of the performance calculation is available in the part VI B 3 page 16 12 Freq Hz 0 5 1 1 5 2 Mov e forward Walk backward Fall on the head or the side Stay on the spot Figure 30 Performance as function of gait type and frequency Trot Walk Gallop Canter Pace Bound Pronk The Figures 31 to 34 show the trotting gait for the four frequency 0 5Hz 1 0Hz 1 5Hz and 2 0Hz Since all the thumbnails are exactly generated every 62ms the difference of performance is also visible Indeed taking all the bottom right thumbnails of each figure and ordering them according to the position of the robot gives back the ranking of Figure 30 Figure 34 Trotting gait with f 1 5Hz B Using CPG model optimized with PSO The work of Yvan Bourquin 15 served as a basis for the design of the CPG models and their optimization The subsections 1 and 2 are largely inspired from his work 1 CPGs a Origins The concept of using non linear oscillators to control robotic locomotion is inspired from biology Experiments 13 showed that in a decerebrated cat the electrical stimulation of the brainstem is able to induce walking Furthermore an increase of the signal strength changes the walk velocity and the transition from a walking to a trotting gait happ
23. ens autonomously These experiments demonstrated that the brain is not involved in the generation of the rhythmic signals that produce locomotion in the cat Grillner 14 explained that the locomotory signals that produce sequences of muscle activation such as walk trot or gallop are generated by Central Pattern Generators CPG located in the spinal cord These CPGs are neural circuits that generate oscillatory output from a tonic input coming from the brain The brain appears to play a higher level role such as regulating the initiation velocity and termination of the locomotory activity 15 Figure 32 Trotting gait with f 1Hz b Non linear oscillator In animal locomotion the oscillations of the joint angles produced by the muscular activity can have different waveforms These waveforms are usually smooth brutal transitions are uncommon In order to facilitate numerical simulations a strong simplification is to model locomotion as sinusoidal variations of the robot s joint angles In practice sinusoidal signals are not flexible enough because they do not allow a soft transition from one gait to another For example if a walk gait in a robot is controlled by sinusoidal motor signals the transition to a different gait say trot requires the activation of different oscillations phases amplitudes and frequencies However with sinusoidal signals the transition from one gait to another is brutal and therefore cannot
24. exedLineSet joint CustomRobot DifferentialWheels TouchSensor Figure 53 Webots Nodes Chart outlining all the nodes available to build Webots worlds 11 Receiver Material Physics 9 uw f lt i co i i function el e2 e3 theta euler2vrml alphaX alpha alphaZ see http en wikipedia org wiki Rotation representation 28ma thematics 29 Sconvert degree to pi rad alphaX alphaX pi 180 alphaY alphaY pi 180 alphaZ alphaZ pi 180 compute the Direction Cosine Matrix DCM from euler angles Ax 1 O 0 0 cos alphaX sin alphaX 0 sin alphaXx cos alphax Ay cos alphaY O sin alphaY O 1 0 sin alphaY 0 cos alphaY Az cos alphaZ sin alphaZ 0 sin alphaZ cos alphaZ ee Ge Ee A Az Ay Ax Scheck DCM back to euler atan2 A 3 1 A 3 2 180 pi acos A 3 3 180 pi atan2 A 1 3 A 2 3 180 pi compute the euler angle rotation axis from the DCM theta acos A 1 1 A 2 2 A 3 3 1 2 el A 3 2 A 2 3 2 sin theta e2 A 1 3 A 3 1 2 sin theta e3 A 2 1 A 1 2 2 sin theta SPACER Fl F3 Table 13 List of shape needed to build the quadruped robot function alphaX alphaY alphaZ vrml2euler X Y Z theta see http en wikipedia org wiki Rotation representation 28ma thematics 29 compute the Direction Cosine Matrix DCM from e
25. from which other particles the information will be received The neighborhood size can vary from a few particles to the entire swarm The neighborhood type does also vary some PSO techniques are based on so called social neighborhood while others use geometrical neighborhood In social neighborhood the particles are associated with other particles from the beginning and their relationship is maintained throughout the process A geometrical neighborhood is defined in accordance with the current particles proximity in the parameter space In this case the particle to particle distances needs to be recomputed at every iteration The usually mentioned advantage of social neighborhood is its lower computational burden compared to geometrical neighborhood However in our case geometrical neighborhood was preferred because the processing power required by the optimization algorithm are insignificant anyway compared to that of the physics simulation The speed inertia factor w can either be fixed or decreased during the optimization process Some authors 17 suggest that a decreasing inertia factor gives better results and so this approach is used here 15 3 Experimental framework To summarize in order to obtain suitable oscillations different combinations of the tT E a and b of equation 14 must be tried out One option is to tune all parameters parameters with the optimization algorithms However in order to incr
26. gure 17 Figure 17 Approximation of the crutch bounding object A cylinder bounding object could be used but following discussion with the developers of Webots due to possible internal problems it was safer to use a box object V VALIDATION OF Bopy STATICS The 3D modeling and the setup of the physical properties is done The next step is to make sure the model answer the initial question of matching the real robot behaviors In this part a method is proposed to check the accuracy of the model static characteristics A Experimental protocol The main concept behind the validation of body statics is to avoid the dynamics to be involved in the process To achieve this purpose the position of the different servos has to be updated step by step to prevent any inertia factor to interfere the experiment The real quadruped robot is disposed in a stable position then updating step by step the position of one servo we check 1f the robot is falling down or not The measured value is so called the equilibrium value Then reproducing the same experiment on the simulator it s possible to compute the difference between the equilibrium value resulting from the real and the modeled experiment A series of nine experiment is realized The Table 4 shows for each experiment the initial value of all the sixteen servos of the robot Exp 1 Exp 2 Exp 3 Exp 4 Exp 5 Exp 6 Exp 7 Exp 8 Exp 9 PELVIS 513 513 205 819 513 513 513
27. ion A used by the servo controller to compute the current speed Ve 27 maxPosition and minPosition They define the soft limits of the servo Soft limits specify the software boundaries beyond which the servo controller will not attempt to move If the controller calls servo set _position with a target position that exceeds the soft limits the desired target position will be clipped in order to fit into the soft limit range Since the initial position of the servo is always zero minPosition must always be negative or zero and maxPosition must always be positive or zero When both minPosition and maxPosition are zero the default the soft limits are deactivated Note that the soft limits can be overstepped when an external force that exceeds the motor force is applied to the servo For example it is possible that the own weight of a robot exceeds the motor force that is required to hold it up 27 C Physics An accurate model is not only a visually realistic one its body dynamics need to match the ones of the real robot It s important to ask ourself the right questions about which physical characteristics need to be simulated and with which degree of abstraction or simplification The overall performance of the model will depend of the initial choices made by the scientist A simulation platform runs on a computer as a consequence the simulation can t be continuous in time The physics of the model need to be computed at
28. ion defined using the Motion editor see I E can be connected together depending on input from the sensors and programmatic logic Figure 5 Behavior editor GUI The commands provided with the Behavior Control Program include e program control commands START END e conditional branching commands IF ELSE IF ELSE CONT IF with conditional operations gt and gt lt and lt e program sequencing commands JUMP amp CALL RETURN e numeric commands COMPUTE and e assignment commands LOAD After a Behavior control program is defined this one can be tested remotely or uploaded to the CM5 unit E Motion editor The Motion Editor is a package that allows the user using a graphics based interface see Figure 6 to move the motors of a robot simply by increasing or decreasing the number that describes the motors current position Motions are built up frame by frame very similar to a story board in an animation sequence This allows quite complicated animations to be programmed and tested Once a motion has been defined it can then be downloaded into the CM5 memory and called from the Behavior Control Program He Eal i a i ee me ri j e j a a rE 7 EF Figure 6 Motion editor GUI There is two way of recoding the frame According to a function defined by the user all servo positions can be pre computed and entered manually in the motion editor This method
29. ion parameter is a floating point value ranging from 0 to 1 0 means that the surfaces are not bouncy at all 1 is maximum bounciness When two solids hit each other the resulting bounciness is the average of the bounce parameter of each solid If a solid has no Physics node and hence no bounce field defined the bounce field of the other solid is used The same principle also applies for to bounceVelocity staticFriction and kineticFriction fields 12 d bounceVelocity It defines the minimum incoming velocity necessary for bounce Incoming velocities below this will effectively have a bounce parameter of 0 12 e coulombFriction It defines the friction parameter which applies to the solid regardless of its velocity Friction approximation in ODE relies on the Coulomb friction model and is documented in the ODE documentation It ranges from 0 to infinity Setting the coulombFriction to 1 means infinity 12 f forceDependantsSlip t defines the force dependent slip FDS for friction as explained in the ODE documentation FDS is an effect that causes the contacting surfaces to side past each other with a velocity that is proportional to the force that is being applied tangentially to that surface It is especially useful to combine FDS with an infinite coulombFriction parameter 12 g centerOfMass It defines the position of the center of mass of the solid It is expressed in meters in the relati
30. iption of all the servo involved in the optimization and there is the list of all the connection between these ones A flag named bidir allows to enable or disable the mirroring of the coupling weight In fact a bidirectional connection is a connection were the weight of each direction are respectively opposed To be able to optimize only a subset of the parameters relative to all the oscillator a mapping mechanisms is developed The output of the PSO optimized gives a number X of values between 0 and 1 Then inside the implementation of the controller the parameters are mapped to their respective oscillators Bidirectional coupling are interesting if ones wants to increase the convergence speed of an oscillator and or consider feedback from sensors In between all the experiments the performance is measured the same way As the crux of PSO is the optimization of the performance returned by a function The function defined in 15 is used Every evaluation lasts 32 seconds in that time the robot has to go further possible However the performance could not be simply measured as the straight distance between the start and end location because in some cases the robot makes a circle and stops close to where it started In such cases the performance evaluates poorly even though only a tiny parameter change would be required in order to correct the robot s bent trajectory To overcome this problem the cumulated or integrated grou
31. is walking backward Since the control unit of the robot is heavy compared to the rest of the body this one being located toward the torso a backward gait could be a possible solution to overcome the stability problem That hypothesis seems to be suitable to justify the behavior observed Table 7 Experiment 2 Best performance PSO CPG Optimization experiment 2 Performance 4 20 40 60 80 100 120 140 160 180 200 220 240 Iterations Figure 47 Experiment 2 Plot of PSO performance over 240 iterations c Experiment 3 Looking at Table 8 the dog is in opposition to what was observed in the previous experiment walking forward The fact the direction is different is not especially in contradiction with the result observed previously Indeed in the present case the dog keeps the back leg lower while moving this way the center of gravity is kept close to the ground and the possible problems of stability are avoided 19 Table 8 Experiment 3 Best performance PSO CPG Optimization experiment 3 Performance 4 Ss 20 40 60 80 100 120 140 160 180 200 Iterations Figure 48 Experiment 3 Plot of PSO performance over 202 iterations d Experiment 4 As showed on Table 9 the robot moves backward and on the left keeping his back right leg up The resulting gait is a bit chaotic This leg being up the dog as to keep his balance on the three other legs while moving To overcome a possible fall on
32. iscussed with the Australian team responsible for the hardware development the initial design of the robot has been updated to give the quadruped an aibo style of walking Wedges were added between the knee and the lower leg to add a permanent offset of 18 degrees Adapting the inverse kinematics model and comparing the performance of the gaits given this new anatomy of the quadruped could be interesting Moreover the CPG optimization could also be redone considering these wedges According to the outcome of the different optimization following the parameters optimized and the coupling model of the CPG it could be interesting to implement a more sophisticated central pattern generator more sophisticated For example the inverse kinematics model developed could be implemented with oscillators being coupled at the same time to the pelvis and neck The function to measure the performance could also be improved Favored forward gait add bounding to the possible position of a body part For example give credit if the head stay above a given line or stay horizontal Al The most efficient gait implemented was discovered to be the trotting one obtained after using the inverse kinematics model However fat from being perfect the robot do not go always straight Given a target aim the robot could adapt and try to add correction to his current direction to keep the orientation The turning right and left operations could also be extrapolat
33. ition and speed can be controlled with a resolution of 1024 steps see Figure 4 150 300 Value 1023 Value 0 Figure 4 Rear view of the Dynamixel AX 12 module and the corresponding actuation position The AX12 module 22 can alert the user when parameters deviate from user defined ranges e g internal temperature torque voltage etc and can also handle the problem automatically e g torque off AX 12 Weight a Gear Reduction Ratio Input Voltage W Final Max Holding Torque kgf cm 12 16 5 Seci60degree 0 269 0 196 Resolution 0 35 Operating Angle 300 Endless Turn Voltage V 10 Recommended voltage 9 6 Max Current SOO nA Operate Temperature 5U 850 Command Signal Digital Packet Frotocol Type Half duplex Asynchronous Serial Communication 8bit 1stop No Parity Link Physical TTL Level Multi Drop daisy chain type Connector ID 254 ID 0 253 Communication Speed 7343bps 1 Mbps Feedback Position Temperature Load Input Voltage ete Material Engineering Plastic Table 2 AX 12 module technical specifications 22 D Behavior editor The Behavior Control Program allows to define a set of rules Then as a function of the robot current state and the outcome resulting in the application of these predefined rules actions are done The description of the different rules is done using a graphic based programming environment see Figure 5 in this way all mot
34. ll servos are linked with an oscillator the coupling between them is unidirectional The intrinsic frequency of all oscillator is the same Each oscillator having 4 parameters offset x amplitude V coupling weight w and w The number of parameters to optimize is 64 CPG Model 1 Figure 42 is used FR3 BRS BR2 F_R2 FRA BR HEAD NECK_2 NECK_1 O PELVIS mn r o Figure 42 CPG Model 1 b Experiment 2 The CPG Model 2 is used see Figure 43 We can consider the movement of the HEAD and NECK 2 servos as useful only in tern of vision stabilization capabilities In the framework of this optimization problem one s could argue that only the impact of the weight of the head on the dynamics of the body is important the servo HEAD and NECK 2 being used only to keep the vision stable or to look on the right or left they are kept in position Only the NECK 1 servo is used to move the head The connection within the body are all bidirectional that way the oscillator of the torso and pelvis are supposed to converge faster This experiment is improved compared to the first one Observing how a dog walks or runs we can tell that the joints of the leg move the same but are only shift in time Assuming this hypothesis is correct the size of search space is decreased and the chance to converge to a valuable optimum performance maximized Applying that concept the set of parameters of the following pairs of oscill
35. m Memory 4 kbyte SRAM 4 kbyte EEPROM 8 Channel 10 bit A D converter JTAG interface for on chip debug http www atmel com 5 Bioloid User Guide Understanding ID Address and data p27 http www tribotix info Downloads Robotis Bioloid Bioloid 20User 27s 20Guide pdf 6 A extended Object file format description http www eg models de formats Format_Obj html 7 http en wikipedia org wiki Wavefront_Technologies 8 Text File format of The Persistence of Vision Raytracer or POV Ray which is a ray tracing program available for a variety of computer platforms http en wikipedia org wiki POV Ray 9 Art of Illusion free and open source java based modeling and rendering studio http aoi sourceforge net 10 Virtual Reality Modeling Language http en wikipedia org wiki VRML 11 Webots Nodes Chart http www cyberbotics com cdrom common doc webots refer ence section4 1 html 12 Webots Reference Manual Physics Node http www cyberbotics com cdrom common doc webots refer ence section2 33 html 13 M L Shik F V Severin G N Orlovsku Control of Walking and Running by Means of Electrical Stimulation of the Mid Brain Biophysics 11 756 765 1966 14 S Grillner Neurobiological Bases of Rhythmic Motor Acts in Vertebrates Science New Series Vol 228 No 4696 Apr 12 1985 143 149 15 Y Bourquin Self Organization of Locomotion in Modular Robots MSc Disserta
36. making it possible to detect left center right distance angle as well as the light built in remote control sensor in center making it possible to transmit and receive infrared data between sensor modules built in micro internal microphone making it possible not only to detect current sound level and maximum loudness but also an ability to count the number of sounds for instance the numbers of hand clapping Built in buzzer allows the playback of musical notes and other special note effects Weight 379g Resolution 1Obit 1024 Voltage 7 10V Recommended voltage 9 6V Supply Current 40mA 6G 856 Digital Packet Operate Temperature Command Signal Frotocol Type Half duplex Asynchronous Serial Communication 8bit istop No Parity Link Physical TTL Level Multi Drop daisy chain type Connector ID 254 ID 0 253 Communication Speed 7343bps 1 Mbps Feedback Infra red Sensor Internal Mic Temperature Input Voltage IR Remocon Tx Rx Data etc Material Engineering Plastic Table 1 AX SI sensor module technical specifications 21 C AX12 module The AX12 module 22 is a smart modular actuator that incorporates a gear reducer a precision DC motor and a control circuitry with networking functionality all in a single package Despite its compact size it can produce high torque It also has the ability to detect and act upon internal conditions such as changes in internal temperature or supply voltage Pos
37. measure is done it s important to translate it into the coordinate system of the servo node see IV C 2 g centerOfMass The shape of the body parts should also be considered and when it s possible for example in case of symmetry relative to the servo axis and assuming the internal weight distribution 1s uniform or equally distributed the CoM value corresponding to the axis X Y or Z should be 0 2 Physics applied to Webots Within Webots the physical characteristics of any node derived from the solid node can be described adding the Physics node see Figure 15 which allows to define a given number of physics parameters to be used by the physics simulation engine Physics SFFloat density 1000 kg m if 1 use mass SFFloat mass ikg ignored if density 1 MFFloat inertiaMatrix 9 float values SFFloat bounce Os i01 SFFloat bounceVelocity 0 01 m s SFFloat coulombFriction 1 see ODE documentation SFFloat forceDependentSlip 0 see ODE documentation SFVec3f centerOfMass ood oy bnga ahga SFRotation orientation ae a of the inertia matrix Figure 15 Webots specification of the Physics node Accurate informations about the different physics parameters are given in the following subsections a density or mass It can be used to define the total mass of the solid If the density field is set different from 1 then it is used regardless of the mass field to compute the mass of the solid objec
38. most swimming on the ground In opposition to the previous experiment the F R 1 F L_1 B L I and B R I oscillators are optimized independently allowing to have different weight between them so different phases difference As in a real dog walking gait the four legs are phase shifted Table 11 Experiment 6 Best performance PSO CPG Optimization experiment 6 nT a Performance 5 20 40 60 60 100 120 140 160 180 200 220 240 Iterations Figure 51 Experiment 6 Plot of PSO performance over 240 iterations VII CoNcLUSION It is believed that the model of the Bioloid robot has been successfully designed The physics were applied to the model and the static validation of the model is on average good enough Despite the efforts made a lot of work remains outstanding and multiple aspects can be improved Developing a Bioloid specific modeling language helping at describing easily the connection in between the existing pre defined shape would be a cornerstone in the future development of model Validating the approximation of crutch bounding object is good enough and that the physic parameters concerning the coulomb friction and the bounciness are matching the behavior of the real quadruped robot And later on developing a test allowing to check if Webots behaves the same way when the simulation are done in run fast and batch mode would consolidate the results obtained so far As d
39. nd distance was also integrated into the performance evaluation Robot moving in a straight line should still be favored over zigzagging ones Therefore the performance needs to reflect both straight and the integrated distances For this reason the performance was calculated as the weighted sum of both using the formula 17 15 N 1 p alpy MEIDA P aimp 17 i l where represents the measured performance where p is the i point sampled on the robot trajectory where N is the total number of sampled point and where and are coefficients that allow balancing the respective weights of the absolute and integrated distances In our simulations these coefficients were set to 1 and 1 In order to avoid granting the robots performance scores for plain vibrations the trajectory points p are sampled at 1 0 second intervals such that a robot is always approximately in the same posture when sampling occurs Multiple optimization of CPGs are tried with a variable number of parameters below are described and motivated the different choices of coupling models their schematic diagrams are numbered from one to five 16 l Ww A Ny 7 u a Sensor HEAD NECK NECK_1 PELVIS B_L_1 F L1 B Ls EL 2 e ley Figure 41 Name of the servos The Figure 41 states the name of the different servos used through the experiments descriptions and later on in the discussion of the results a Experiment I A
40. obot The strength of the inverse kinematics model is to give the possibility of computing the different joint angles of a member knowing only the final trajectory of this one Using an elliptic trajectory for the leg extremity is known to be efficient for robotic walking The parametric equations for an ellipse are 7 and 8 x h acos 7 y k bsin 8 Where is the phase between 0 and 2m h k determining the center of the ellipse a and b being respectively the size of the radius for the x axis and y axis The value of these parameters is relative to the anatomy of the real robot Initially as stated in 29 the rules of thumb to determine the equation parameters are center of ellipse A k 0 Z Z 2 radius on y axis b L 2 radius on x axis a 0 95 L 2 These rules set the maximum sized ellipse possible given the robot anatomy not especially the most efficient Leg trajectory em 40 8 T ai 0 2 4 6 8 10 em Figure 27 Leg trajectory over 28 steps Applying the rules given in 29 the actual anatomy of the robot is not considered This one isn t able to bend the lower leg over 90 degrees The Figure 27 displays a red ellipse showing the lower leg extremity without considering the actual anatomy The segment depicted in blue corresponds to the upper and lower leg having a possible position whereas the red segment corresponds to impossible position since the angle
41. of the world file is also available in Appendix The complete listing will be accessible from the project web page Following the recent mails and over skype exchanges with the members team of Newcastle University responsible for the hardware design of the robot they updated the design of the Figure 10 Model of the quadruped robot rendered in Webots robot and added wedges below the knee actuator to add a permanent offset of 18 degrees Figure 11 The purpose of this update was to make the robot able to walk with an aibo style and ease the development of an efficient gait In the framework of this project and due to time constraints only the initial design of the robot has been used and validated Figure 11 Model of the updated quadruped robot rendered in Webots having the 18 degrees wedges B Animate the model The servo nodes see Figure 12 are the links between the controller and the visual representation of the model Giving orders to these servos the Webots rendering engine is able to recompute the new position of the different joints this way the model is animated and can interact with the physics of the world Serva SSe type Eetabienal SFFloat nmaxVelocity 10 e MO alge SFFloat wax Force 10 leit ts SFFloat controle 10 oO aera SFFloat acceleration m c we E Lar i 5 Elles position SFFloat winPosition T a a p SFFloat waxPosition 0 m O anai SFFloat minstap 0 pi SFFloat
42. ograms to several commercially available real mobile robots Webots lets you define and modify a complete mobile robotics setup even several different robots sharing the same environment For each object you can define a number of properties such as shape color texture mass friction etc You can equip each robot with a large number of available sensors and actuators You can program these robots using your favorite development environment simulate them and optionally transfer the resulting programs onto your real robots Webots has been developed in collaboration with the Swiss Federal Institute of Technology in Lausanne thoroughly tested well documented and continuously maintained for over 7 years 1 The core of Webots is based on the robust and powerful physics engine Open Dynamics Engine ODE 2 The two main components of ODE are the rigid body dynamics simulation engine and the collision detection engine As we Il see the development of a model involved multiple phases ranging from the drawing of the body parts see IV A the definition of the bounding objects see IV C 3 the setup of the physical properties see IV C 2 ODE is used both as a research helper package or as a computer game development library helping at providing more realistic behaviors Open source and freely available as of today ODE is involved in the development of almost 100 referenced projects 3 Started in 2001 and with the h
43. presents the advantages of being rigorous since all servo positions are set considering the shape and the geometry of the robot Since the servos can be aware of their own position the current position of the robot can be recorded and a sequence can be described step by step The cons of such a method is for example concerning the quadruped robot the in accuracy between the position recorded for each legs The position of the members being set manually plus the fact the robot can fall due to his proper weight makes this method a non rigorous way to implement gait or motion Nevertheless this later one allows to fast prototyping motion and could help to check ideas The motion editor is a valuable option if the user limits himself to program the existing example When a new robot is design since the 3D model is not existing in the motion editor the user isn t able to visualize the frames already entered He can only visualize the current position being reproduced remotely on the real robot while entering the frame IU Wesot SIMULATOR Webots is a commercial software developed by Cyberbotics Ltd It is a mobile robotics simulation software that provides you with a rapid prototyping environment for modeling programming and simulating mobile robots The provided robot libraries enable you to transfer your control programs to several commercially available real mobile robots Webots enable you to transfer your control pr
44. ption since it can handle VRML file easily and fold unfold VRML node This last feature of the editor allows to get a better overview of the work done so far The Webots Nodes chart see Appendix is useful to understand what are the existing nodes and from what kind 3 Model of the quadruped robot The elaboration of the quadruped robot model was a tedious and long process While at it I tried to keep the model clear efficient and simple to understand The various part used to construct the robot are referenced in the QuickStart manual 25 with a letter F and a number discriminating the part The same nomenclature is used in the world file The Table 13 available in the Appendix shows their names and their corresponding shapes A given shape is oriented in the world then depending on their location in the node hierarchy this one needs to be rotated Within VRML rotation are expressed with the notation euler angles axis 26 the 3D coordinate of one point and an angle 0 the field rotation allows to apply such a rotation The common way of expressing rotation and visualizing easily this one is the representation euler angle an angle of rotation corresponding to each axis To ease the development of the model a set of two Matlab functions allows the conversion between the two representations see Appendix Figure 10 shows the final quadruped robot model rendered in Webots A simplified and more readable release
45. regular time step One of the goals of the modeling was to be able to have at least 6 robots walking on the same ground in real time The real time constraint is not the least since if the simulation runs as wanted it shows how the real dogs would walk for real assuming the physic of the model is enough accurate and the model validated In case physic is added to the model Webots expects to see its definition under any Solid node type The Webots Nodes Chart helps in understanding the node inheritance model and their relationship to each other see Appendix 1 Measure of the real robot properties a Mass of the body parts Using a letter scale the different body parts of the robot has been weighted The term body part is used to describe a section between 2 servos Indeed the Webots simulator will apply the physics to all objects of the node hierarchy present between 2 servos Part id Mass g Part id Mass g BODY 692 N1 10 PELVIS 146 N 2 118 FL1 12 BL1 12 F R1 12 B R 1 12 FL2 126 BL2 126 FR2 126 BR2 126 FL3 32 BL3 34 FR3 32 BR3 34 HEAD 110 Table 3 Weight of the different body parts Table 3 summarizes the measures The robot presenting similar body part it s has been admitted their weight was equals That hypothesis explains the redundancy of the value b Center of Mass The next step was to determine the position of center of mass CoM of the different body parts
46. s could be considered The function to maximize would be the following N p mamae lreal webots 2 i 0 Where is the value to maximize MN the number of experiments real the outcome of the experiment with the real robot it s a fixed parameter during the optimization webots the outcome of the experiment within the simulator 10 VI EXPERIMENTATION OF THE Bopy DYNAMICS A Using inverse kinematics Model 1 Theoretical background There are two ways of solving the inverse kinematics problems either algebraically or geometrically Only the solution will be given here Further details are available in 29 ff 8X2 y2 L2 sin A2 12 d0s A2 y1 j x1 y1 x1 x2 Figure 26 Determining angles A and via geometric approach 29 From Figure 26 it s possible to extract the value for A and A 2 E Aley L L 4 COS i TiL 1 x 1 y A cos B sin 4 ay Jer where L and L are the respective length of both part of the robot leg The extremity x y being the bottom of the leg foot the point x y being the axis of rotation of the lower leg knee and the origin of the coordinate system being the axis of rotation of the upper leg shoulder x L cos A L cos A A 5 y L sin A L sin 4 4 6 Using 3 and 4 it s possible to compute 4 and A given a position of the foot 2 Applied to the quadruped r
47. t Bioloid Kit is a composed of a collection of block shaped parts see Appendix and servos see II C a sensor module see II B and a control unit see II A that the user can assemble together to build a sophisticated robots The connection between the different parts can be easily achieved using a simple screw driver the frames made from injection molded plastic fit and connect perfectly see Figure 1 Figure 1 Example of connection of a AX12 dynamixel servo A Control unit and Communication bus The control unit is so called the CM5 module and is based on a micro controller Atmel ATMega 128 4 The rechargeable battery pack of 9 6V is also embedded in the CM5 module All servos have a network ID programmed in their non volatile memory and are connected together via a TTL Serial Network see Figure 2 E Pi Gx B mmp PAT E D komi i Control Boe CM 5 94 Figure 2 Servos and sensors connected to CM5 unit via 3 wire TTL serial network Each unit in the Bioloid Kit has his own assigned ID 5 The CM 5 has ID200 The sensor module has ID100 The servos module can have IDs between 1 and 19 Figure 3 illustrates the connection of the different module of the real robot and the corresponding module IDs Figure 3 Wiring of the Dynamixel module B Sensor module The Sensor Module AX S1 is a Smart Sensor Module that integrates the following functions 21 embedded with three directions infrared sensor
48. t Otherwise the mass field which should be set to a positive value is used You should never set both the mass and the density to 1 otherwise the results will be undefined Rather it is highly recommended to set either the mass or density to 1 and the other field should be set to a positive value If the density field is a positive value and the mass field is set to 1 the actual mass of the Solid node will be computed based on the specified density and the volume defined in the boundingObject see IV C 3 of the Solid node However this computed mass will not be displayed in the mass field which will remain 1 12 b intertiaMatrix It defines the inertia matrix as specified by ODE If this parameter is empty or contains less or more than nine floating point values it is ignored Moreover if the mass field is 1 the inertiaMatrix field is ignored If it contains exactly nine floating point values and if the mass field is different from 1 then it is used as follow the nine parameters are the same as the ones used by the dMassSetParameters ODE function The parameters given in the inertiaMatrix 1 are C8 C8 Cg Las Loo L335 Lio Lig I where cg cg cg is the center of gravity position in the body frame The xy values are the elements of the inertia matrix expressed in kg m 12 la fio Lig inertiaMatrix cg I L 1 C amp S C8 PE c bounce It defines the bounciness of a solid This restitut
49. the side with one leg the dog moves on the opposite side with a tendency to walk backward to compensate the position of center of gravity being near the torso Table 9 Experiment 4 Best performance PSO CPG Optimization experiment 4 7 ppe AANA Performance 1 20 40 60 80 100 120 140 160 180 200 220 240 Iterations Figure 49 Experiment 4 Plot of PSO performance over 240 iterations e Experiment 5 In this experiment the dog is moving forward Front and back legs are respectively synchronized Since the oscillator parameters of the front left leg are mirrored to the right leg and respectively the same for the back leg As in a real dog gallop gait the phase shift between back and front oscillator is the same The center of gravity is closer to the torso then when the dog is falling his head and the fact the front leg are bended allows him to go back to his position Indeed while at this position the movement of the back leg backward give enough inertia to the body to make it stand back on the four legs Table 10 Experiment 5 Best performance 20 PSO CPG Optimization experiment 5 Performance 10 20 40 60 80 100 120 140 160 180 200 220 240 Iterations Figure 50 Experiment 5 Plot of PSO performance over 240 iterations f Experiment 6 Similarly to the experiment 5 the shoulder servos are in fixed position keeping the legs close to the body and avoiding gait where the dog is al
50. thinking to optimize a simulation of 32 seconds Considering the simulation runs in real time the total time required should be around 107hrs In case the simulation is slow down due to for example a high number of collision detection this amount of time will be increased In the case of our experiment the Webots simulator was running in batch mode Run a world in batch mode means there is no visual output of the simulation and the speed of the simulation is not constrained to real time If the simulation can run faster the simulator will do it On the computer used for the simulation Webots was able to run it 1 5 faster To speed up the optimization process the PSO has been distributed over a network of 50 nodes This way doing 240 iterations of the PSO the total time required was around 2 hours 32 1 5 240 The implementation of the CPG realized by 15 was the starting point That implementation didn t include the possibility to add bidirectional connection in the coupling of oscillators Moreover it was not possible to optimize only a subset of the servo modules For example sometimes it s interesting to optimize symmetrically the gait The number of parameters will be decreased and the likelihood of the gait optimized versus a gait existing in nature will be increased To overcome these limitations the initial implementation has been improved In the configuration file relative to a controller there is the descr
51. tion p16 p26 16 J Kennedy R Eberhart Particle Swarm Optimization Proceedings of the 1995 IEEE International Conference on Neural Networks pp 1942 1948 IEEE Press 17 Y Shi and R C Eberhart 1998 Parameter selection in particle swarm optimization In Evolutionary Programming VII Proc EP98 New York Springer Verlag pp 591 600 18 lt A J Ijspeert J M Cabelguen 2003 Gait transition from swimming to walking investigation of salamander locomotion control using non linear oscillators In Proceedings of Adaptive Motion in Animals and Machines 2003 22 19 A Pikovsky M Rosenblum and J Kurths 2001 Synchronization a universal concept in nonlinear sciences Cambridge Nonlinear Sciences Series 12 20 S Mojon 2004 Using nonlinear oscillators to control the locomotion of a simulated biped robot Unpublished Diploma Thesis http birg epfl ch page44565 html 21 User manual of Dynamixel Sensor module AX S1 release of 06 14 2006 22 User manual of Dynamixel module AX 12 release of 06 14 2006 23 Microsoft Direct X API http en wikipedia org wiki DirectX 24 KDE development Environment http www kdevelop org Bioloid QuickStart Comprehensive Kit Manual http www tribotix info Downloads Robotis Bioloid QuickSta rt Comprehensive Kit pdf 26 Rotation representation http en wikipedia org wiki Rotation_ representation _ mathem atics 27 Webots
52. ts are normalized and therefore the strength of the signal carried by a particular connection does not depend on the energy of the emitting oscillators Mojon 2004 This modified model 14 is used in this project 2 X Fy apx Dey TV a AA a 5 nest by a j 14 E To ox tvi According to the simulation done the coupling strengths were determined to be satisfactory in the range 0 7 0 7 15 2 Particle Swarm Optimization Particle Swarm Optimization PSO was originally developed in 1995 by James Kennedy and Russell Eberhart 16 Like genetic algorithms PSO is based on a population that slowly converges towards one or more solutions However with PSO the particles are preserved throughout the entire process they do not die Contrary to GA which is based on competition for better chances of survival and reproduction PSO uses a kind of cooperation between the particles This is achieved through the exchange of the coordinates of the best solutions that have been encountered so far PSO s particles are simple search agents that fly through the search space Whilst moving they record the best position that they have discovered so far They communicate with their neighbors and learn from them the best local solution PSO is based on the concepts of social interaction or more exactly the tendency of an individual to go his own way as opposed to his tendency to follow his group s way At every
53. uge number of contributors as a mature C API and a platform independent package ODE is known to be a successful and promising Physics engine VVebots ODE Engine Vorldinfof Viewpoint Background Supervisor controller chief controller chief CustomRobot controller slave controller slave CustomRobot controller slave World definition Figure 7 Webots functional diagram The basic behind the design of a Webots model are quite simple A fully functional model see Figure 7 is composed of at least a world file see III 2 and a controller A controller is a program mapped to an entity represented in the world allowing to give it instruction regarding his surrounding environment his internal state instruction received from an other controller The execution of world starts with the opening of a world file WBT file extension Webots parses the file and check for inconsistencies Then it extracts the controller s name s corresponding to the different entities customRobot Supervisor node Finally each entity has his own instance of controller running Webots with the help of ODE engine can animate and render the scene in respect of the physics The specificities of the simulator regarding the development of the model will be reviewed in the subsidiary parts of this paper IV MoDELING As stated in 1 the design of a model out of one s imagination co
54. uld be done in few hours In our case it s a quite more sophisticated problem since we have the real robot and we want to build its most accurate representation both in respect of its visual and its body dynamics A Visual Aspect The Bioloid kit comes with a set of example assembly instructions For each of them a motion file and behavior file are provided Since the motion file contains the 3D model with the exact shape of all the body parts it could be interesting to be able to extract the useful informations and generate one file for each ones A collaborator Laurent Lessieux specialist of robotic modeling and simulation provided me with some code able to create OBJ files for each part from the X file provided with the Bioloid Kit The X files are the 3D description files used by Microsoft DirectX API 23 Indeed there is already a set of examples provided with the kit and each example has the corresponding 3D model allowing to visualize it in the motion editor Thanks to his work the initial phase involving the shaping of the 3D body parts was speed up 1 Shape simplification using 3D modeling tool Having all 3D files corresponding to all the different shapes is a good advantage The OBJ format corresponds to the standard 3D object file format created for use with Waveftront s Advanced Visualizer Object Files are text based files supporting both polygonal and free form geometry curves and surfaces 6 7 It exists an
55. uler angle rotation axis E X Y alt Snormalized vector E E norm B A eye 3 cos theta 1 cos theta E E 0 Z Y Z 0 X Y X 0 sin theta Stranspose matrix A Ars compute the euler angle rotation axis from the DCM alphaX acos A 3 3 alphaY atan2 A 3 1 A alphaZ pi atan2 A 1 3 Spee A 2 3 Sconvert pi rad to degree alphaX alphaX 180 pi alphaY alphaY 180 pi alphaZ alphaZ 180 pi Table 12 Matlab script to convert from Euler angle notation to VRML angle euler axis angle notation Table 14 Matlab script to convert from VRML angle euler axis angle notation to Euler notation ANOUKA Supervisor CMS TRANS Trans CM5 SHAPE Shape CMSUNIT TRANS Trans CMSUNIT SHAPE Shape F3 FRONT LEFT 1 TRANS Trans F3 SHAPE Shape F3 FRONT LEFT 2 TRANS Trans AX12_ FRONT LEFT 1 TRANS Trans AX12 SHAPE Shape FRONT LEFT 1 SERVO Servo F1 FRONT LEFT 1 TRANS Trans Fl SHAPE Shape FRONT LEFT 2 SERVO Servo AX12 FRONT LEFT 2 TRANS Trans AX12_ SHAPE F3 FRONT LEFT 3 TRANS Trans F3_ CROSSED GRP Group F3 SHAPE F3_CROSSED1 TRANS Trans F3 SHAPE AX12 FRONT LEFT 3 TRANS Trans AX12_ SHAPE FRONT LEFT 3 SERVO Servo F2 TRANS Trans F2 SHAPE Shape CRUTCH FRONT LEFT Trans CRUTCH DISC SHAPE CRUTCH TRANS Trans CRUTCH SHAPE CRUTCH PLASTIC TOP TRANS Trans CRUTCH PLASTIC TOP SHAPE CRUTCH PLASTIC BOTTOM TRANS Trans CRUTCH PLASTIC BO
56. ve coordinate system of the Solid node It is affected by the orientation field as well 12 The measure of the CoM X Y or Z location is relative to a side of the body part or an other noticeable point before using it in the physics node definition One s should take care of translating that value into the servo coordinate system h orientation It defines the orientation of the local coordinate system in which the position of the center of mass centerOfMass and the inertia matrix intertiaMatrix are defined 12 3 Bounding objects Since the modeled shapes are complicated triangle meshes these one can t be used by the collision detection engine It will result in too complex computation and the overall simulation will be slow down An approximation of the bounding object should be done There is no automatic process to determine there bounding object According to the specificities and the purpose of the simulation the user should define them using simple object like sphere box or cylinder Within Webots when the user click on the robot model Figure 16 the bounding object are highlighted Figure 16 Robot model rendered in Webots with his bounding objects highlighted Particular attention should be consider while defining the bounding object of the crutches Indeed the crutches are the contact point of the robot with the ground This one was approximated using a box and a sphere see Fi

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