arXiv:0908.4464v2 [cs.RO] 2 Sep 2009  Proceedings of the ASME 2009 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 2009 August 30-September 2, 2009, San Diego, USA  DETC2009/MR-86328  THE EEL-LIKE ROBOT  F. Boyer 1 , 2 , D. Chablat 1 , P. Lemoine 1 , 3 , P. Wenger 1 1   Institut de Recherche en Communications et Cybern  ́ etique de Nantes UMR CNRS n ◦   6597, 1 rue de la No  ̈ e, 44321 Nantes, France  2   Ecole des Mines de Nantes, 4 rue Alfred-Kastler, Nantes 44307, France  3   Ecole Centrale de Nantes, 1 rue de la No  ̈ e, 44321 Nantes, France Email:   { Frederic.Boyer, Damien.Chablat, Philippe.Lemoine, Philippe.Wenger } @irccyn.ec-nantes.fr  ABSTRACT  The aim of this project is to design, study and build an “eel- like robot” prototype able to swim in three dimensions.   The study is based on the analysis of eel swimming and results in the realization of a prototype with 12 vertebrae, a skin and a head with two fins. To reach these objectives, a multidisciplinary group of teams and laboratories has been formed in the frame- work of two French projects.  INTRODUCTION  As compared with our technological achievements, the per- formances of fish make the human dream. Among them include their prodigious capacity for acceleration up to 20 times gravity, their speed exceeding 70 km/h, their extraordinary maneuver- ability: 180 ◦   turn without slowing down and radii of curvature about 10 times their length, while the current vehicles must slow down by half and take radius of about 10 times their length. Ef- ficiency is about 10 times higher than our best submarines, etc... These features alone justify current efforts to understand and re- produce solutions used by the fish in our robotic systems. In this area, under the biomimetics, the first difficulties encountered is described as follows: “Replicate the performance of a fish by simple imitation of its form and function would be impossible because the development of a vehicle bending so smooth and continuing is beyond the current possibilities of robotics.” [1]. Thus, the continuing fish is an essential difficulty of research in this area. The purpose of this project is to enhance biomimetics by producing a prototype eel-like robot that is “more continu- ous” than its counterparts today. The mechanical architecture of the prototype consists in stacked parallel modules sheathed by a continuous flexible part playing the role of the skin.  THE EEL SWIMMING  The object of the biomimetic robotics is to mimic life, to im- itate biological systems or to conceive new technologies drawn from the lesson of their study [2]. In nature, there are two main types of fish, each being sub- servient to a type of swimming. The first were carangid swim- ming, as jacks, horse mackerel or pompano [2]. The latter are anguilliform such as the moray or the eel whose handling ca- pacity reached records. It is this second type of swim that our project is to achieve.   An anguilliform swimmer propels itself forward by propagating waves of curvature backward along its body [1].   In this case, the maneuverability is the result of the high redundancy (hyper-redundant) induced by the deformation of the fish body on the dimensions of the task. Before any inves- tigative technique, the project started with a literature review of biomimetic fish in general and eel in particular. The designers studied the system skeleton - muscles - ten- dons. For the control, we studied the biomimetics of swimming under the “fluid mechanics” or more generally, as the allure of swim [3].   Finally, data on experimental zoologists style swim eels are limited to the planar motion and take the form of films. We can extract displacement and orientation laws of vertebrae 1
as well as bending inter-vertebral taking in our terminology, the sense of curvature [4]. From these data we are committed to characterize and iden- tify swimming simplified underlying parameters of minimum distorted set.   Thus, we have updated the laws of wave propa- gation sine curve progressive or retrograde combined with bends (pitch and yaw) [5]. To compensate coupling induced by bending, twisting laws are under study. Each vertebra includes 3 degrees of freedom, bending around two planes (yaw / pitch) and twisting around its column.   The prototype includes 12 vertebrae (36 dof), a rigid head and a passive and flexible tail. The head is equipped with side wings mimicking the pectoral fins dedicated to control ani- mal roll and pitch.  PROTOTYPE DESIGN Introduction  Since the beginning of robotics, engineers have constantly adapted their current design technology.   For robots, when it comes to technology, is means mainly technology actuators, computers or materials. Thus, browsing history catalogs robots, we find that for the same robot morphology increasing the power of electric motors and their miniaturization has first resulted in the replacement of hydraulic motors, then simplified and re- duced the number of parts by removing parallelograms or bal- ance weights. In another vein, increasing the power of comput- ers has helped to devise more complex mechanical structures and the integration of dynamic models. Thus, from simple mechan- ical architectures such as Cartesian robots or anthropomorphic, new mechanical architectures appear, called parallel mechanism as the Gough-Stewart platform [7]. For the design of an eel-like robot, we must adapt our con- straints in mature technologies.   Indeed, we could have used shape memory of piezoelectric actuators if they had owned the dynamics and power requirements for moving a robot in the wa- ter. Also, we have chosen micro-motors with direct current that has the main advantage of being commanded in couple.   In a similar vein, we can choose technologies that were unsuitable for mass production for our prototype unit.  Choice of the mechanical architecture  From the study of biomimetics, it was decided to build the prototype by stacking 12 vertebrae, each with 3 degrees of free- dom of rotation. For our study, the following points were consid- ered: - minimize the inter-vertebral space in order to draw up a continuous deformation model (Figure 1); - maximize the use of the elliptical section on each vertebra (Figure 1); - balance the placement of the mechanical to ensure hydro- static balance; - find the most robust mechanisms with regard to the assem- bly uncertainties.  0,15 0,13 0,18  Figure 1.   DECOMPOSITION OF THE BODY OF THE EEL VERTEBRA WITH THEIR DIMENSIONS [m]  To accommodate the mechanical parts, the computer and the electronics in the body of the eel, we set the dimensions for each vertebra: focal lengths of 0.18m and 0.13m, height of 0.15m. This amounts to build an eel over 2 meters long when one takes into account the head and tail. On the basis of an observation of muscular fish, one is tempted to use only linear actuators. For small volume however, there are few robust alternatives to the rotary actuators. Indeed, for a translation, most linear actuators use a rotary actuator, coupled with a ball screw.   A lot of en- ergy is lost due to friction. In addition, there are two additional drawbacks as the size of the motor and its guidance and the small amplitude of motion. Similarly, the realization of vertebrae from a serial architec- ture has been ruled out. Indeed, the use of a serial mechanism as represented in Figure 2 has the following issues: - the motors location is asymmetric; - the coupling between motor 1 ©   and 3 ©   requires a complex assembly for the transfer of constraints between the verte- brae; - the displacement of motor 2 ©   causes the displacement of large masses.    ‚ ƒ     ‚ ƒ     ‚ ƒ  Figure 2.   PROTOTYPE OF THE EEL-LIKE ROBOT BASED ON A SE- RIAL ARCHITECTURE  2
Finally, we chose a parallel architecture. There are many solu- tions for a spherical wrist with parallel structure. They are usu- ally classified according to the following properties [8]: - symmetrical / unsymmetrical - isostatic / overconstraint - linear actuators / rotary actuators. However, few technological achievements of “spherical wrist” exist today.   Among these few prototypes, the best known in robotics is probably the agile eye developed by Clement Gos- selin [9]. This architecture was used to guide a camera in space (hence its name agile eye) or haptic device [10]. It consists in three rotary motors, of which axes intersect at the center of the wrist and three “legs” consisting of two revolute joints each, which also cut the main center of the wrist (Figure 3).   They are the legs making the connection between the fixed part of the mechanism and the camera or the handle of the user.  Figure 3.   THE AGILE EYE AND SHADE DEVELOPED AT LAVAL UNI- VERSITY IN QUEBEC  Finally, when one assembles in series such many identical mechanism, all efforts pass through each motor, requiring to strengthen the pivot joints. To eliminate this problem, we stud- ied a family of wrists with a passive ball-and-socket joint in the center of rotation (Figure 4). Thus, an intermediary solution between the agile eye and a spherical parallel wrist with 4 feet can be obtained by actuat- ing the leg with a ball-and-socket joint. Then, a leg is obtained, consisting of a central motorized pivot followed by a universal joint.   By affecting the other 2 legs to the control of both uni- versal joint rotations, we get the wrist represented in Figure 5. This mechanism is derived from the wrist mechanism defined by Agrawal [11] with rotary actuators instead of linear actuators. This architecture was chosen in [12]. It is very compact and can be easily located in the elliptical shape of eels. In addition, the kinematics can be reproduced, through the action of the two rods 1 ©   and 2 © , the role of muscles attached to the skeleton and working in addition (in the sense of yaw, for propulsion) and sub- traction (in the pitch, for diving). The motor on leg 3 ©   allows for the rolling motion. Several motors placements have been testes  Figure 4.   EXAMPLE OF SPHERICAL WRIST WITH THE CENTER OF ROTATION CONSTRAINED BY A PASSIVE BALL-AND-SOCKET JOINT WITH (a) LINEAR ACTUATORS AND (b) ROTARY ACTUATORS  (Figures 5 (a), (b) and (c)). The solution (c) has been chosen be- cause in this case, the spindle motors is collinear to the axes of the largest focal length of the ellipse. In this case, when the rolling angle is zero, the two coaxial motors operate as a differential gear. Based on this choice, kine- matics and geometric models (direct and inverse) of this parallel robot have been developed. During the swimming, only the in- verse kinematics is calculated. This model is written as quadratic equations, which can be solved algebraically. This aspect is cru- cial because of limited processing power of computers shipped. To prevent this actuator from large axial effort, we placed two parallel gears deporting the motors relative to the axis vertebrae. This feature allows to use a motor whose long axis is important. 3
x y z  C 1  B 1  C 2  B 2  A 1  A 2 q 1  q 2  q 3  O  x   y     ‚ ƒ  m m m  C 1 B 1   C 2 B 2  A 1   A 2  O  Motors  (a)  C 1 B 1   C 2 B 2  A 1   A 2 O  Motors  (b)  C 1 B 1   C 2 B 2  A 1   A 2  O  Motors  (c)  Figure 5.   MODELLING VERTEBRAE BASED ON A PARALLEL ARCHI- TECTURE AND ITS PLACEMENT IN THE ELLIPTICAL ENVELOPE  Assembly of vertebrae  The body of the eel is done by mounting vertebrae in serie. In this assembly, the location of actuators, on-board computers and electronics power must be taken into account.   After ana- lyzing the needs of on-line calculation, the choice is to allocate a micro-controller to two vertebrae. The motors controlling the pitch and yaw are side by side while the motor controlling the roll is in opposition. This solution is chosen to balance the masses on two vertebrae. Finally, on each section will be set the elliptical skin of the eel-like robot. Figure 6 represents the position of dif- ferent elements in the prototype.  Computer and power electronics  Row motor   Pitch and yaw motors  Figure 6.   ARRANGEMENT OF THE MECHANICAL, COMPUTER AND POWER ELECTRONICS  Modeled with CATIA, each vertebra is used to simulate the movement of actuators motion and to avoid interferences be- tween the moving parts (Figure 7). The joint limits were com- puted and integrated in the control loop in [13].  Figure 7.   DIGITAL MOCKUP OF A VERTEBRA ON CATIA  Figure 8.   PROTOTYPE OF TWO VERTEBRAE MADE BY TECHNICAL STAFF OF THE IRCCyN  Design of the skin  The skin of the eel is attached to each vertebra; the objective of our design is to maintain this body to achieve a continuous contact. The difficulty that arises here is the tension between two contradictory goals, which both play a role in the distortion of the body. Indeed, the skin should offer a very easy distortion in bending-twisting while providing significant resistance to pres- sure of the fluid. Thus, there are significant distortions that the prototype must undergo.   This is illustrated in Figure 9 on the plane yaw. When the yaw angle is 30 degrees, the external cur- vature increases by 24% while the inside curvature decreases by 28%. To prevent the skin from pleating, a first option would be to precharge the skin when the external curvature is a minimum. Unfortunately, if the skin is made of elastic material (rubber, ly- cra), its axial stretching is accompanied by an inevitable trans- verse narrowing (Figure 10). 4
o  q  C A  B Radius of curvature External curvature 0.075  Internal curvature  Radius of curvature [m]  0 0,2 0,4 0,6 0,8 1,0 1,2 1,4  0   10   20   30  Yaw angle [deg]  Figure 9.   LINK BETWEEN THE RADIUS OF CURVATURE OF EELS AND THE YAW ANGLE  Also, we have chosen to support such a skin of an underly- ing structure. For example, this could be based on the stacking of intermediate hollow vertebrae connected by rubber rings (Fig- ure 10).   Such solution permits to guarantee the continuity in curvature: high deflection, ease of assembly, and its low radial size.  Figure 10.   DEFORMATION OF THE SKIN WITHOUT REINFORCE- MENT AND WITH THE PROPOSED REINFORCEMENT  The skin is made with three types of materials, plastic rings for reinforcements, chains of rubber to ensure continuity in cur- vature, and a latex skin to seal and lift between the fluid and the eel-like robot.  Figure 11.   PROTOTYPE OF TWO VERTEBRAE WITH A PART OF THE SKIN WITH RUBBER RINGS AND INTERMEDIATE RIGID SECTIONS  Motor Fin  Figure 12.   CLOSED-LOOP MECHANISM FOR THE CONTROL OF ONE FIN  Figure 13.   PROTOTYPE OF THE HEAD MADE IN RAPID PROTOTYP- ING WITH TWO CLOSED-LOOP CHAINS TO CONTROL THE FINS  Figure 14.   PROTOTYPE OF THE HEAD MADE IN RAPID PROTOTYP- ING WITH ITS SKIN  Design of the head  In the head of the eel-like robot, we have to integrate many sensors (tilting sensor, accelerometers, a measure of relative speed, camera...), a computer as the brain of the fish and two fins to assure the stability. The main problem for the integration of the fins is the size of both motors. We need to have collinear axis and we wish to use the same actuators as the vertebrae. Two closed-loop mechanisms are used to shift the actuators (Figure 12). To simplify the design, we used a set of identical parts to the one used for the vertebrae. For the first prototype, the head is made by rapid prototyping which allows us to test the volume used by the wires (Figure 13). The skin of the head is rigid and it is made in rapid prototyping (Figure 14).   At the end, it will be covered by a skin made in latex. 5
SOFTWARE AND HARDWARE IMPLEMENTATION Technology constraints  For this type of project where actuators and control systems are on-board, the definition of space, weight and energy con- sumption are essential. Another aspect is the wiring system. We must ensure that the various wires for power and data transport do not reduce the manoeuvrability of the eel by introducing cou- ples or additional forces to overcome during the movement. To achieve the deformation of the body of the eel, each joint is pow- ered by three motors located in adjacent vertebrae. The motors are distributed over the whole length of the eel. This architecture provides a natural distribution of mass along the body of the eel, unlike a system actuated by rods or cables with a concentration of actuators in the robot. During the design phase, we have to integrate all these concepts to minimize: - the volumes filled by actuators, electronic and drive control to allow a maximum amplitude of deformation of the body of the eel, - the number and the section of the wires in order to obtain a wiring harness that disrupts the least possible movement of deformation, - overall power consumption, so as to ensure a self-sufficient in energy, - overweight related to electrical and electronic components, so as not to penalize the buoyancy of the whole robot. Finally, we have to check that all the components are well distributed to obtain a good balancing of the masses. It is to be noted that the purpose of the swimming process is to guide the head of the eel-like robot. Indeed, it is its position, direction and speed of motion, which are given by the operator. The propulsion for such a motion is generated by the distortion of the eel. Thus,   all information concerning position,   direction or progress of the robot are relevant to the head of the eel.   It is therefore natural that the head is instrumented with sensors and that it should be taken as reference for the deformations of the rest of the body. Even if some information is not necessary when the robot is tele-operated, they are used to assess the performance of the prototype (mechanical power and rebuild of its trajectory relative to surroundings), making use of a minimum of instru- mentation relevant. As the prototype is tele-operated, it is necessary to establish a communication channel between the operator and the eel. The operator is then a part of the control loop by giving the instruc- tions to adjust the trajectory like an airplane pilot does. Finally, it is necessary to periodically perform a number of sequentially computations for each link (calculation of the de- sired joint angles and position control loop for each motor). The calculations to perform in a given period of time depend on the number of joints or vertebrae. This imposes constraints in terms of overall computing power of control system depending on the number of vertebrae.  Solution for the prototype  With all these considerations we have chosen a solution based on a set of computers distributed on the vertebrae and on the head of the eel (and whose number depends on the number of actuated joints). With this architecture, the head of the eel has its own com- puter to manage different sensors, communication with the oper- ator and to act as the supervisor of the whole robot. Other com- puters release the supervisor from operations to be conducted pe- riodically to determine the instructions to be sent to each motor and to control the local position loops. This solution allows at first to establish a true parallel exe- cution and secondly to increase the number of computers when the number of vertebrae grows up. The computing power of the system is automatically adjusted in function of the number of vertebrae. For the material of our application, our choice is on a module of the society Phytec built around the Motorola microprocessor MPC565 and presented in Figure 15. This 32-bit RISC processor of the PowerPC MPC500 family is running at 56 MHz, has a 64-bit floating point unit, and offers opportunities to interface 6 actuators (2 joints) and a set of input/output functions based on the performance of an independent firmware. Finally, the MPC565 integrates the management of 3 CAN buses, which can transmit messages of 8 bytes long with a maxi- mum speed of 1Mb/s for each bus. These transmissions are stan- dard asynchronous multi-master and priority management type (the message of the highest priority is not destroyed in case of collision). Thus, Phytec MPC565 module dissipates a maximum of 2.15W (0.8W for the Motorola processor core),   it is only 84x57x3mm (format similar to credit card) and weights only 27g.   Of course in our application we only use a reduced set of the module capabilities, thus reducing overall consumption. The possibility for each MPC565 processor to drive 6 motors al-  Flash memory SRAM memory   MPC565  Figure 15.   FRONT AND BACK VIEWS OF THE MODULE PHYTEC MPC565  6
Command module 2x3 motors Vertebra 2   Vertebra 3 Vertebrae 1  3 motors  Head Main computer 2x3 motors Vertebra 11   Vertebra 12 Vertebra 10  3 motors  Tail Actuated joints   Passive joint  Command module  Figure 16.   DISTRIBUTION OF THE MODULES ALONG THE EEL  lows us to use a single module to manage 2 joints. This option is used as stated in Section   in alternating motors and electron- ics/computer bearing vertebrae. The batteries can be distributed along the eel to balance the masses despite the alternation of the vertebrae. So far, this fea- ture is not used in the prototype and the volume is replaced by a mass of lead.   Figure 16 shows the distribution of the mod- ules along the body of the eel.   Today all the batteries are put in the head thus providing an easy way to exchange them with another set.   To obtain a density of 1 the weight of each ver- tebra must be 2.7Kg and the head 4.5Kg.   The total weight of the Lithium-Polymer accumulators is 1.1Kg with a total size of 268x88x72mm. By bringing together elements by functional modules (actu- ation and control modules) allows confining in compact and well defined spaces, reduces wiring interconnection between the com- puter and electronics (control modules), and helps limit the num- ber of wires needed for electric supply and communication be- tween all the elements. To ensure greater flexibility of the wires, their section is reduced by using for all the modules the same voltage of 37 V (used for motors). Thus reducing the intensity necessary, and converting tension as needed as close as possible to fuel elements with very efficient micro-choppers. Furthermore, the formation of functional modules creates physical blocks easier to waterproof than a multitude of separate elements. The application software is based on an OSEK/VDX com- patible real-time executive developed at the IRCCyN [14]. It is a real-time operating system integrating tasks management with fixed priorities, tasks, synchronization, mutual exclusion, events treatment (interrupts, alarms) and communication services of- fered by the CAN bus. Some very specific tasks, such as the management of in- cremental encoders (actuators position sensors) are managed di- rectly by functions performed by an independent firmware run- ning in real parallelism with respect to the main processor exe- cution. This possibility is offered by some embedded functions that discharge the MPC565 core from many disruptions related to these tasks. The global application is built in a distributed ar- chitecture, and consists of a supervisory task, supported by the module located in the head of the eel, and tasks of local control, supported by the modules in the vertebrae. However, it is necessary to consider the communication as- pect and the synchronization between these various tasks as de- fined above. Indeed the supervisor task must convey to all the tasks of local control the information corresponding to the cur- rent behavior of the eel imposed by the operator. This informa- tion relates to the parameters of the undulation to distribute along the body of the eel, and a possible overall curvature, which can be added to the undulation. These data can be transmitted simul- taneously to all the tasks of local control through the broadcast on the CAN bus of a single message. With this information, each local task can calculate the joint values with respect to time and location of joints in the chain of the eel. The synchronization of the undulation distributed along the body of the eel is provided by this periodic broadcast whose mes- sage contains a current time topic. These functions of synchronization and communication are based on the first CAN bus. The second bus is used for diagnosis and feedback from the vertebrae to the head of the eel. This so- lution avoids conflicts between control and monitoring/diagnosis messages.  EXPERIMENTAL RESULTS  The validation of the prototype (i.e. kinematics, electronics and skin) is in progress and applied to a piece of eel (6 vertebrae). These tests aim to validate the watertightness of the skin and the buoyancy of the robot (Figure 17).  Figure 17.   PICTURE OF A 6 VERTEBRAE IN A SWIMMING POOL TO TEST THE WATERTIGHTNESS AND BUOYANCY  7
Initial results have validated the watertightness of the skin and showed that the volume of the prototype is very dependent on the differential of the pressure between the inside and outside parts of the robot. So we are testing an autonomous mechanical system based on a calibrated relief valve and a calibrated diving pressure regulator to respectively reduce or increase the inside pressure of the robot with respect to the outside pressure. The purpose of this system is to balance the inside air and outside water pressures to obtain a constant volume of the robot in order to stabilize its buoyancy. The variation of the weight of the em- bedded air supply during the swimming of the robot should be negligible. This air supply will be a rigid compressed air bottle localized in the head of the eel. Electrical power consumption and capability of body distortion of the eel have also been eval- uated and validated during these tests.   The theoretical power required for swimming is 15W and the mechanical power de- livered by the actuators is 102W, but there was an uncertainty concerning the power consumed by the skin deformation. It was shown that the available mechanical power is sufficient to gener- ate the swimming movement when the eel robot is immersed in water. The capacity of the accumulators is 4Ah and can provide the energy for at least 20 minutes of swimming. The definition of the tail is not achieved. However, we have decided that a part of the tail will be flexible and it will be made of a part of some rubber, like a flipper.  CONCLUSIONS  From the eel-like robot project, many results have been ob- tained concerning the mechanical design, which led, on the basis of a serial stacking of parallel modules, to the first version of our prototype. From this, three key issues can be addressed a) the kinematics of the vertebrae, b) the skin, which, even if solutions were proposed, many uncertainties remain, and c) the buoyancy of the prototype, which will be extended in the future and will lead to systems or ballast bladder.  ACKNOWLEDGMENTS  This research was partially supported by the CNRS (“An- guille” Project) and the ANR project RAAMO (“Robot Anguille Autonome en Milieu Opaque”). The prototype was built by the IRCCyN technical department. F. Brau, M. Canu, G. Branchu, G. Gallot, A. Girin, P. Molina and S. Jolivet are gratefully ac- knowledged for their technical help for the manufacturing and assembly of the prototype as well as the master students, G. Fadel and P. Lorne.  REFERENCES  [1] Triantafyllou, M.S. and Triantafyllou, G. S.,   “An effi- cient swimming machine,” Scientific American, pp. 65–70, March 1995. 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