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 AbstractHaving 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 Lighthills 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.abedinzadehut.ac.ir Principle investigator; e-mail: mniliut.ac.ir All authors are with Cognitive Systems Lab., School of Electrical and Computer Engineering, University of Tehran, Tehran, Iran. (m.abedinzadeh; rouhollahi.74; mniliut.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.abedinzadehut.ac.ir Principle investigator; e-mail: mniliut.ac.ir All authors are with Cognitive Systems Lab., School of Electrical and Computer Engineering, University of Tehran, Tehran, Iran. (m.abedinzadeh; a.rouhollahi; mniliut.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.abedinzadehut.ac.ir Principle investigator; e-mail: mniliut.ac.ir All authors are with Cognitive Systems Lab., School of Electrical and Computer Engineering, University of Tehran, Tehran, Iran. (m.abedinzadeh; a.rouhollahi; mniliut.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.abedinzadehut.ac.ir Principle investigator; e-mail: mniliut.ac.ir All authors are with Cognitive Systems Lab., School of Electrical and Computer Engineering, University of Tehran, Tehran, Iran. (m.abedinzadeh; a.rouhollahi; mniliut.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.abedinzadehut.ac.ir Principle investigator; e-mail: mniliut.ac.ir All authors are with Cognitive Systems Lab., School of Electrical and Computer Engineering, University of Tehran, Tehran, Iran. (m.abedinzadeh; a.rouhollahi; mniliut.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.abedinzadehut.ac.ir Principle investigator; e-mail: mniliut.ac.ir All authors are with Cognitive Systems Lab., School of Electrical and Computer Engineering, University of Tehran, Tehran, Iran. (m.abedinzadeh; a.rouhollahi; mniliut.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.abedinzadehut.ac.ir Principle investigator; e-mail: mniliut.ac.ir All authors are with Cognitive Systems Lab., School of Electrical and Computer Engineering, University of Tehran, Tehran, Iran. (m.abedinzadeh; a.rouhollahi; mniliut.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.abedinzadehut.ac.ir Principle investigator; e-mail: mniliut.ac.ir All authors are with Cognitive Systems Lab., School of Electrical and Computer Engineering, University of Tehran, Tehran, Iran. (m.abedinzadeh; a.rouhollahi; mniliut.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) = 2t/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) = Asin(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) + 0t 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) = 2t + , 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.abedinzadehut.ac.ir Principle investigator; e-mail: mniliut.ac.ir All authors are with Cognitive Systems Lab., School of Electrical and Computer Engineering, University of Tehran, Tehran, Iran. (m.abedinzadeh; a.rouhollahi; mniliut.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.abedinzadehut.ac.ir Principle investigator; e-mail: mniliut.ac.ir All authors are with Cognitive Systems Lab., School of Electrical and Computer Engineering, University of Tehran, Tehran, Iran. (m.abedinzadeh; a.rouhollahi; mniliut.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.abedinzadehut.ac.ir Principle investigator; e-mail: mniliut.ac.ir All authors are with Cognitive Systems Lab., School of Electrical and Computer Engineering, University of Tehran, Tehran, Iran. (m.abedinzadeh; a.rouhollahi; mniliut.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.abedinzadehut.ac.ir Principle investigator; e-mail: mniliut.ac.ir All authors are with Cognitive Systems Lab., School of Electrical and Computer Engineering, University of Tehran, Tehran, Iran. (m.abedinzadeh; a.rouhollahi; mniliut.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.abedinzadehut.ac.ir Principle investigator; e-mail: mniliut.ac.ir All authors are with Cognitive Systems Lab., School of Electrical and Computer Engineering, University of Tehran, Tehran, Iran. (m.abedinzadeh; a.rouhollahi; mniliut.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 = FeV 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 TsAradlrad T | q|dtJ T 2dtN2m2 Uniform0.10.970.19-7e3(ref )3.2e2(ref )1.5e4(ref ) Non-uniform0.10.730.170.430.075.6e3(21%)4.8e2(47%)4.9e4(233%) Uniform0.20.440.18-3.1e2(ref )3.3e2(ref )1.4e3(ref ) Non-uniform0.20.550.220.430.091.8e2(39%)4.9e2(46%)2.1e3(46%) achieving different forward velocities (0.1,0.2m/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 c