IROS2019国际学术会议论文集 1034

Effects of a Bio mimicked Flapping Path on Propulsion Effi ciency of Two segmental Fish Robots Majid Abedinzadeh Shahri Ali Rouhollahi Majid Nili Ahmadabadi Abstract Having an appropriate fl apping path to yield effi cient propulsion is an interesting issue in fi sh robotics In most works especially two segmental structures the fl apping motion is limited to sinusoidal functions In this paper to cope with the aforementioned limitation a conceptual non sinusoidal path is proposed The proposed fl apping path and the conventional one both are optimized for a sample fi sh robot According to some simulation results it is shown that if a proper actuator is employed to generate both optimized paths the proposed approach yields more propulsion effi ciency Furthermore it is discussed that our method can better imitate fi sh muscle output power Finally through experiments some practical issues are considered I INTRODUCTION Underwater robots are commonly used in oceanic appli cations A key feature of such robots is mobility which in directly highlights the problem of energy effi ciency Clearly the propulsion method in water drastically affects the con sumed energy of underwater vehicles In that regard some engineers shifted their focus on the development of new techniques for improving the propulsion system 1 2 The effi ciency of aquatic locomotion attracts great under water robotics researchers 3 Obviously the most interest ing locomotion type of marine animals is swimming Most fi shes propel their body by using two swimming modes body and or caudal fi n BCF and median and or paired fi n MPF 4 However the former swimming mode is more frequently employed by fi shes for propulsion BCF swimming mode is further categorized into Anguilliform Subcarangiform Carangiform Thunniform and Ostraciiform Fish like robots are expected to be more effi cient than tra ditional underwater vehicles In this context an appropriate approach to modeling the swimming patterns of fi sh robots is required A well known method to study the hydrody namic interactions between a robotic fi sh and its surrounding water is Lighthill s large amplitude elongated body theory LAEBT 5 Recently this theory has been improved to be applicable for analytical modeling of mobile multi body robots in three dimensional swimming 6 8 Usually the body motion of fi sh follows a harmonic pat tern Most researches consider the fi sh movement to be a pure sinusoidal motion 8 10 However the advantages of using non sinusoidal paths for moving airfoils were studied in 11 12 Now a question arises here that if fi sh swimming Corresponding author e mail m abedinzadeh ut ac ir Principle investigator e mail mnili ut ac ir All authors are with Cognitive Systems Lab School of Electrical and Computer Engineering University of Tehran Tehran Iran m abedinzadeh rouhollahi 74 mnili ut ac ir motions are precisely mimicked by robots then how more effi ciency can be obtained In this paper according to LAEBT a limitation of sinu soidal paths is mentioned Accordingly a conceptual non sinusoidal fl apping path is proposed to cover more possible solutions For comparison between the two aforementioned paths we consider the planar motions of a tail actuated robotic fi sh approximately like Ostraciiform swimming mode see Fig 1 It is worth mentioning that the two segmental body is usually interesting in fi sh robots 9 10 13 Assuming that the motor yields the same effi ciency to generate the two reciprocating motions both paths are optimized for a sample fi sh robot According to the simula tion results it is shown that the optimized proposed method yields improvements in terms of propulsion effi ciency Also it is shown that the output mechanical power of the motor to generate the optimized proposed path is better matched with the fi sh muscles behavior Finally both optimized fl apping paths are implemented on a real two segmental robot fi sh to study more practical issues The rest of the paper is organized as follows in Section II the proposed method is described Optimization procedure and simulation results are presented in Section III Also a behavioral analogy among the proposed method and fi sh muscles is presented in Section IV Section V presents more simulation and experiment tests We conclude this paper in the last section II TWO SEGMENTAL FISH ROBOT AND PROPOSED FLAPPING METHOD In fi sh swimming the fi sh body propels the surrounding water and as a result the water reaction forces propel the fi sh to swim through water According to LAEBT in the planar case the main portion of water reaction forces which produce the thrust force is exerted on the caudal fi n The effects of this reaction force are determined according to the fi n direction and its velocity vector 8 Now consider a 2 segmental fi sh robot which includes a body a motor and a tail fi n see Fig 1 For swimming in the horizontal plane the motor moves the tail fi n according to a desired cyclic task In this case with neglecting the body movement the tail velocity vector is determined according to its angular velocity through a cycle Therefore the tail angular motion through each stroke1affects on the thrust force Accordingly if the path function of the tail movement has more redundancy solutions with more propulsion effi ciency might be achievable 1 Each side to side movement of the tail fi n is called a stroke 2019 IEEE RSJ International Conference on Intelligent Robots and Systems IROS Macau China November 4 8 2019 978 1 7281 4003 2 19 31 00 2019 IEEE1721 q 1 u 2 h 3 fh 4 V 5 e 6 l1 7 l2 8 w 2 9 d1 10 d2 11 12 Corresponding author e mail m abedinzadeh ut ac ir Principle investigator e mail mnili ut ac ir All authors are with Cognitive Systems Lab School of Electrical and Computer Engineering University of Tehran Tehran Iran m abedinzadeh a rouhollahi mnili ut ac ir Fl 13 Fr 14 15 16 17 l 18 r 19 ACKNOWLEDGMENT PREPRINT TO IEEE TRANSACTIONS ON ROBOTICS1 A Non Sinusoidal Flapping Path for Two Segmental Fish Robots to Improve Propulsive Effi ciency Majid Abedinzadeh Shahri Ali Rouhollahi Majid Nili Ahmadabadi Abstract Index Terms I INTRODUCTION q 1 u 2 h 3 fh 4 V 5 e 6 l1 7 l2 8 w 2 9 d1 10 d2 11 12 Corresponding author e mail m abedinzadeh ut ac ir Principle investigator e mail mnili ut ac ir All authors are with Cognitive Systems Lab School of Electrical and Computer Engineering University of Tehran Tehran Iran m abedinzadeh a rouhollahi mnili ut ac ir Fl 13 Fr 14 15 16 17 l 18 r 19 ACKNOWLEDGMENT l2 8 w 2 9 d1 10 d2 11 12 Corresponding author e mail m abedinzadeh ut ac ir Principle investigator e mail mnili ut ac ir All authors are with Cognitive Systems Lab School of Electrical and Computer Engineering University of Tehran Tehran Iran m abedinzadeh a rouhollahi mnili ut ac ir Fl 13 Fr 14 15 16 17 l 18 r 19 ACKNOWLEDGMENT l1 7 l2 8 w 2 9 d1 10 d2 11 12 Corresponding author e mail m abedinzadeh ut ac ir Principle investigator e mail mnili ut ac ir All authors are with Cognitive Systems Lab School of Electrical and Computer Engineering University of Tehran Tehran Iran m abedinzadeh a rouhollahi mnili ut ac ir Fl 13 Fr 14 15 16 17 l 18 r 19 ACKNOWLEDGMENT e 6 l1 7 l2 8 w 2 9 d1 10 d2 11 12 Corresponding author e mail m abedinzadeh ut ac ir Principle investigator e mail mnili ut ac ir All authors are with Cognitive Systems Lab School of Electrical and Computer Engineering University of Tehran Tehran Iran m abedinzadeh a rouhollahi mnili ut ac ir Fl 13 Fr 14 15 16 17 l 18 r 19 ACKNOWLEDGMENT V 5 e 6 l1 7 l2 8 w 2 9 d1 10 d2 11 12 Corresponding author e mail m abedinzadeh ut ac ir Principle investigator e mail mnili ut ac ir All authors are with Cognitive Systems Lab School of Electrical and Computer Engineering University of Tehran Tehran Iran m abedinzadeh a rouhollahi mnili ut ac ir Fl 13 Fr 14 15 16 17 l 18 r 19 ACKNOWLEDGMENT fh 4 V 5 e 6 l1 7 l2 8 w 2 9 d1 10 d2 11 12 Corresponding author e mail m abedinzadeh ut ac ir Principle investigator e mail mnili ut ac ir All authors are with Cognitive Systems Lab School of Electrical and Computer Engineering University of Tehran Tehran Iran m abedinzadeh a rouhollahi mnili ut ac ir Fl 13 Fr 14 15 16 17 l 18 r 19 ACKNOWLEDGMENT Fig 1 Schematic of a two segmental fi sh robot Usually the tail angle is limited as q t Acos t where A is the motion amplitude and t is a monotonic variable which represents the motion phase It is worth men tioning that the t 0 and t 2 separate the forward and backward strokes Inconventional fl appingmethod onechooses t 2 t T t where Tis the period of cyclic motion In the following due to t being constant this fl apping type is called uniform Using the uniform approach the tail angular velocity can be expressed as q t A sin t Obviously this fl apping path does not have this potential to yield angular velocities with different magnitudes for a specifi c angular position in both strokes Here the motion phase is defi ned as t t 0 t 0 t 2 where t is a cyclic non uniform variable defi ned as T 2 t dt t constant 0 t With this defi nition although a cyclic behavior is repeated through each stroke having a non uniform motion from t makes the velocity magnitude of the tail independent of its angular position unlike in the uniform motion Now togenerateanon uniformcyclic motion we defi neanauxiliaryvariableas t atan2 sin t cos t l 0 2 where atan2 represents the four quadrant arctangent function and t is a uniform monotonic variable Due to the constant value of l 0 1 the input uniform motion t constant is converted to a non uniform monotonic motion t constant 0 seeFig 2 Choosing t 2 t the cyclic non uniform motion t with a period of T 2 is obtained Here is a constant value that specifi es the phase shift between t and t Finally the presented cyclic non uniform motion is used as t t 0 2 III OPTIMIZATION PROCEDURE To compare the performance of the aforementioned paths both fl apping motions are optimized for a sample two PREPRINT TO IEEE TRANSACTIONS ON ROBOTICS1 A Non Sinusoidal Flapping Path for Two Segmental Fish Robots to Improve Propulsive Effi ciency Majid Abedinzadeh Shahri Ali Rouhollahi Majid Nili Ahmadabadi Abstract Index Terms I INTRODUCTION q 1 u 2 h 3 fh 4 V 5 e 6 l1 7 l2 8 w 2 9 d1 10 d2 11 12 Corresponding author e mail m abedinzadeh ut ac ir Principle investigator e mail mnili ut ac ir All authors are with Cognitive Systems Lab School of Electrical and Computer Engineering University of Tehran Tehran Iran m abedinzadeh a rouhollahi mnili ut ac ir Fl 13 Fr 14 15 16 17 l 18 r 19 ACKNOWLEDGMENT PREPRINT TO IEEE TRANSACTIONS ON ROBOTICS1 A Non Sinusoidal Flapping Path for Two Segmental Fish Robots to Improve Propulsive Effi ciency Majid Abedinzadeh Shahri Ali Rouhollahi Majid Nili Ahmadabadi Abstract Index Terms I INTRODUCTION q 1 u 2 h 3 fh 4 V 5 e 6 l1 7 l2 8 w 2 9 d1 10 d2 11 12 Corresponding author e mail m abedinzadeh ut ac ir Principle investigator e mail mnili ut ac ir All authors are with Cognitive Systems Lab School of Electrical and Computer Engineering University of Tehran Tehran Iran m abedinzadeh a rouhollahi mnili ut ac ir Fl 13 Fr 14 15 16 17 l 18 r 19 ACKNOWLEDGMENT PREPRINT TO IEEE TRANSACTIONS ON ROBOTICS1 A Non Sinusoidal Flapping Path for Two Segmental Fish Robots to Improve Propulsive Effi ciency Majid Abedinzadeh Shahri Ali Rouhollahi Majid Nili Ahmadabadi Abstract Index Terms I INTRODUCTION q 1 u 2 h 3 fh 4 V 5 e 6 l1 7 l2 8 w 2 9 d1 10 d2 11 12 Corresponding author e mail m abedinzadeh ut ac ir Principle investigator e mail mnili ut ac ir All authors are with Cognitive Systems Lab School of Electrical and Computer Engineering University of Tehran Tehran Iran m abedinzadeh a rouhollahi mnili ut ac ir Fl 13 Fr 14 15 16 17 l 18 r 19 ACKNOWLEDGMENT PREPRINT TO IEEE TRANSACTIONS ON ROBOTICS1 A Non Sinusoidal Flapping Path for Two Segmental Fish Robots to Improve Propulsive Effi ciency Majid Abedinzadeh Shahri Ali Rouhollahi Majid Nili Ahmadabadi Abstract Index Terms I INTRODUCTION q 1 u 2 h 3 fh 4 V 5 e 6 l1 7 l2 8 w 2 9 d1 10 d2 11 12 Corresponding author e mail m abedinzadeh ut ac ir Principle investigator e mail mnili ut ac ir All authors are with Cognitive Systems Lab School of Electrical and Computer Engineering University of Tehran Tehran Iran m abedinzadeh a rouhollahi mnili ut ac ir Fl 13 Fr 14 15 16 17 l 18 r 19 ACKNOWLEDGMENT PREPRINT TO IEEE TRANSACTIONS ON ROBOTICS1 A Non Sinusoidal Flapping Path for Two Segmental Fish Robots to Improve Propulsive Effi ciency Majid Abedinzadeh Shahri Ali Rouhollahi Majid Nili Ahmadabadi Abstract Index Terms I INTRODUCTION q 1 u 2 h 3 fh 4 V 5 e 6 l1 7 l2 8 w 2 9 d1 10 d2 11 12 Corresponding author e mail m abedinzadeh ut ac ir Principle investigator e mail mnili ut ac ir All authors are with Cognitive Systems Lab School of Electrical and Computer Engineering University of Tehran Tehran Iran m abedinzadeh a rouhollahi mnili ut ac ir Fl 13 Fr 14 15 16 17 l 18 r 19 ACKNOWLEDGMENT 0 2 0 2 l 0 0 l 0 4 l 0 8 tan r sin r cos lr sin cos l Fig 2 Geometric demonstration of the proposed function to convert a uniform motion to a non uniform motion segmental fi sh robot to swim with maximum propulsion effi ciency The parameters of the robot are presented in Tab I The robot dynamics are modeled by a LAEBT based modeling approach presented in 8 Generally the propulsion effi ciency is expressed as 14 e Pout e Pin F eV Ein T where F is the time averaged value of the thrust force e V T V dt T is the time averaged vector of the robot velocity V and Einrepresents the robot consumed energy over a cycle Here we assume that the fl apping types do not affect the motor effi ciency Therefore the consumed energy is calculated as Ein T q dt Also the time averaged value of the thrust force is derived as F T fh edt T where fhis the vector of the instantaneous hydrodynamic force and e e V eV see Fig 1 For a desired forward swimming Vd the uniform fl ap ping method is distinguished by Xuni A T and the non uniform one by Xnonuni A T l Therefore defi ning fopti X eV as the cost function the optimization problem for both fl apping methods is expressed as X argmin fopti X subject to eV Vd The optimal parameters of both fl apping methods for TABLE I Parameters of the sample robot dynamic model ParameterUnitValue l1 Body length m0 25 m1 Body mass Kg0 50 I1 Body angular inertia Kg m20 02 l2 Tail length m0 15 m2 Tail mass Kg0 10 I2 Tail angular inertia Kg m20 001 Water density Kg m31000 h Immersed height cm6 0 Cm Shape coeffi cient 0 5 Cf Friction coeffi cient 0 01 Cd Drag coeffi cient 2 0 1722 TABLE II Optimization results Flapping method Forward velocity m s Optimal parametersCriteria T s A rad l rad T q dt J T 2dt N2m2 Uniform0 10 970 19 7e 3 ref 3 2e 2 ref 1 5e 4 ref Non uniform0 10 730 170 43 0 075 6e 3 21 4 8e 2 47 4 9e 4 233 Uniform0 20 440 18 3 1e 2 ref 3 3e 2 ref 1 4e 3 ref Non uniform0 20 550 220 43 0 091 8e 2 39 4 9e 2 46 2 1e 3 46 achieving different forward velocities 0 1 0 2 m s are ob tained by using the Genetic Algorithm in MATLAB toolbox The optimal solutions are compared with each other in terms of energy consumption Ein propulsion effi ciency and actuation cost T 2dt The obtained results presented in Tab II indicate that for this robot the optimal non uniform fl apping approach for all desired velocities yields approxi mately 45 improvement in terms of propulsion effi ciency and in average 30 improvement in terms of energy consumption However the proposed method signifi cantly increases the actuation cost The effects of this feature are discussed in Section V IV BEHAVIORAL ANALOGY Here we present a behavioral analogy of the motor torque of the sample robot in the presence of both fl apping approaches and fi sh muscles The sample robot includes two segment bodies with a motor on the single revolute joint Hence the fi sh muscular system is modeled as a simple two segmental structure which is equipped with two virtual muscle fi bers see Fig 3a In this fi gure Fland Fr represent the output force of each virtual muscle fi ber The single revolute joint of the muscular system is moved according to reciprocating motion and accordingly the virtual muscle fi bers are lengthened or shortened The be havior of each virtual muscle is specifi ed according to the force displacement profi le which is extracted from 15 see Fig 3b It is worth mentioning that in 15 it is shown that the fi sh muscle fi bers yields maximum useful power with the presented profi le Finally the effects of the virtual muscles forces through a reciprocating motion are mapped on the single joint to yield the torque angle profi le These profi les were extracted according to three confi gurations of the muscle fi bers see Fig 3c As it can be seen in all of the simulated confi gurations the output torque of the virtual muscles increased rapidly at the end of each stroke and thereafter yielded maximum torque at the beginning phases of the opposite stroke For Vd 0 3m s the torque angle profi les of the sample fi sh robot for both optimized fl apping methods are shown in Fig 4 Obviously the fi sh robot in the presence of the proposed approach could better imitate the aforementioned behavior of the fi sh muscles In other words the non uniform path in the optimization procedure could obtain a behavior similar to the fi sh muscles to yield more propulsion effi ciency The optimized non uniform method yields the maximum torque at the beginning phases of each stroke So hereinafter this method is named as impulsive fl apping Although the im pulsive method has more similarity to the best performance of the fi sh muscles in case of a fi sh robot this condition might be improper for the robot actuator In the next section this problem is studied in more details V FURTHER SIMULATIONS ANDEXPERIMENTAL RESULTS In the previous simulations to obtain the optimal fl ap ping path it was assumed that the motor has an equal effi ciency for generating the two fl apping approaches Now we consider more realistic conditions to study the propulsion