Bio-Inspired Flying and Swimming Devices

We study archetypal types of flyers and swimmers found in nature ranging from the microscale (pollen and bacteria) to the macroscale level (birds and eels). These forms serve for inspiration of engineering devices that can be in turn optimized using bioinspired algorithms.

To school, or not to school…

There has been a long-standing debate as to whether schooling fish reduce energy expenditure by adapting their swimming response to unsteady flow. This question has profound evolutionary significance, since any behavior that may lead to energy-savings can give a species an undeniable advantage over others that do not exploit this mechanism.

With the help of unsupervised machine learning algorithms, we have demonstrated that it is feasible to teach an artificial agent (a self-propelled fish-like swimmer) the capability to take adaptive decisions autonomously, so as to exploit energy deposited in the flow by an upstream swimmer. The ‘smart’ agent is able to minimize its own energy expenditure by interacting judiciously with the unsteady wake, while having no a-priori knowledge regarding details of the complex fluid phenomena involved.

Moreover, the agent explicitly chooses to pursue in the leader’s wake while attempting to maximize swimming-efficiency, although it is given no direct incentive to do so. This suggests that large groups of fish may indeed resort to schooling as a means of energy-saving. The results lay the groundwork for future robotic applications, where groups of robotic swimmers may attempt to maximize range and endurance by swimming in a coordinated manner, without having to depend upon complex (and potentially sub-optimal) hand-crafted rules.

Discovering the benefits of unsteady swimming

Steady, continuous swimming is rarely observed in most fish species. A large number adopt an intermittent form of locomotion referred to as `burst-and-coast’ swimming, where a few quick flicks of the tail are followed by a prolonged unpowered glide. This behavior is believed to confer energetic benefits, in addition to stabilizing the sensory field, and diminishing the wake-signature for predator-avoidance.

Unfortunately, these advantages may be offset by a reduction in average speed. We have coupled high-fidelity simulations with evolutionary-optimization algorithms to discover a range of intermittent-swimming patterns, the most efficient of which resemble the swimming-behavior of live fish. Importantly, the use of multi-objective optimization reveals locomotion patterns that strike the perfect balance between both speed and efficiency. Some of these patterns do not generally occur in nature, but can be invaluable for use in robotic applications. The resulting increase in range, endurance, and average speed can greatly enhance the mission capability of robotic swimmers.

Publications

2017

  • G. Novati, S. Verma, D. Alexeev, D. Rossinelli, W. M. van Rees, and P. Koumoutsakos, “Synchronisation through learning for two self-propelled swimmers,” Bioinspir. Biomim., vol. 12, iss. 3, p. 36001, 2017.

BibTeX

@article{novati2017a,
author = {Guido Novati and Siddhartha Verma and Dmitry Alexeev and Diego Rossinelli and Wim M van Rees and Petros Koumoutsakos},
doi = {10.1088/1748-3190/aa6311},
journal = {{Bioinspir. Biomim.}},
month = {mar},
number = {3},
pages = {036001},
publisher = {{IOP} Publishing},
title = {Synchronisation through learning for two self-propelled swimmers},
url = {https://cse-lab.seas.harvard.edu/files/cse-lab/files/novati2017a.pdf},
volume = {12},
year = {2017}
}

Abstract

The coordinated motion by multiple swimmers is a fundamental component in fish schooling. The flow field induced by the motion of each self-propelled swimmer implies non-linear hydrodynamic interactions among the members of a group. How do swimmers compensate for such hydrodynamic interactions in coordinated patterns? We provide an answer to this riddle though simulations of two, self-propelled, fish-like bodies that employ a learning algorithm to synchronise their swimming patterns. We distinguish between learned motion patterns and the commonly used a-priori specified movements, that are imposed on the swimmers without feedback from their hydrodynamic interactions. First, we demonstrate that two rigid bodies executing pre-specified motions, with an alternating leader and follower, can result in substantial drag-reduction and intermittent thrust generation. In turn, we study two self-propelled swimmers arranged in a leader-follower configuration, with a-priori specified body-deformations. These two self-propelled swimmers do not sustain their tandem configuration. The follower experiences either an increase or decrease in swimming speed, depending on the initial conditions, while the swimming of the leader remains largely unaffected. This indicates that a-priori specified patterns are not sufficient to sustain synchronised swimming. We then examine a tandem of swimmers where the leader has a steady gait and the follower learns to synchronize its motion, to overcome the forces induced by the leader’s vortex wake. The follower employs reinforcement learning to adapt its swimming-kinematics so as to minimize its lateral deviations from the leader’s path. Swimming in such a sustained synchronised tandem yields up to 30% reduction in energy expenditure for the follower, in addition to a 20% increase in its swimming-efficiency. The present results show that two self-propelled swimmers can be synchronised by adapting their motion patterns to compensate for flow-structure interactions. Moreover, swimmers can exploit the vortical structures of their flow field so that synchronised swimming is energetically beneficial.
  • S. Verma, P. Hadjidoukas, P. Wirth, and P. Koumoutsakos, “Multi-objective optimization of artificial swimmers,” in 2017 IEEE congress on evolutionary computation (CEC), 2017, p. 1037–1046.

BibTeX

@inproceedings{verma2017b,
author = {Siddhartha Verma and Panagiotis Hadjidoukas and Philipp Wirth and Petros Koumoutsakos},
booktitle = {2017 {IEEE} Congress on Evolutionary Computation ({CEC})},
doi = {10.1109/cec.2017.7969422},
month = {jun},
pages = {1037--1046},
publisher = {IEEE},
title = {Multi-objective optimization of artificial swimmers},
url = {https://cse-lab.seas.harvard.edu/files/cse-lab/files/verma2017b.pdf},
year = {2017}
}

Abstract

A fundamental understanding of how various biological traits and features provide organisms with a com- petitive advantage can help us improve the design of several mechanical systems. Numerical optimization can be invaluable for this purpose, by allowing us to scrutinize the evolution of specific biological adaptations. Importantly, the use of numeri- cal optimization can help us overcome limiting constraints that restrict the evolutionary capability of biological species. Thus, we couple high-fidelity simulations of self-propelled swimmers with evolutionary optimization algorithms, to examine peculiar swimming patterns observed in a number of fish species. More specifically, we investigate the intermittent form of locomotion referred to as ‘burst-and-coast’ swimming, which involves a few quick flicks of the fish’s tail followed by a prolonged unpowered glide. This mode of swimming is believed to confer energetic benefits, in addition to several other advantages. We discover a range of intermittent-swimming patterns, the most efficient of which resembles the swimming-behaviour observed in live fish. We also discover patterns which lead to a marked increase in swimming-speed, albeit with a significant increase in energy expenditure. Notably, the use of multi- objective optimization reveals locomotion patterns that strike the perfect balance between speed and efficiency, which can be invaluable for use in robotic applications. The analyses presented may also be extended for optimal design and control of airborne vehicles. As an additional goal of the paper, we highlight the ease with which disparate codes can be coupled via the software framework used, without encumbering the user with the details of efficient parallelization.
  • S. Verma, G. Novati, F. Noca, and P. Koumoutsakos, “Fast motion of heaving airfoils,” in Procedia computer science – ICCS 2017, 2017, p. 235–244.

BibTeX

@inproceedings{verma2017d,
author = {Siddhartha Verma and Guido Novati and Flavio Noca and Petros Koumoutsakos},
booktitle = {Procedia Computer Science – {ICCS} 2017},
doi = {10.1016/j.procs.2017.05.166},
note = {International Conference on Computational Science, ICCS 2017, 12-14 June 2017, Zurich, Switzerland},
pages = {235--244},
publisher = {Elsevier {BV}},
title = {Fast Motion of Heaving Airfoils},
url = {https://cse-lab.seas.harvard.edu/files/cse-lab/files/verma2017d.pdf},
volume = {108},
year = {2017}
}

Abstract

Heaving airfoils can provide invaluable physical insight regarding the flapping flight of birds and insects. We examine the thrust-generation mechanism of oscillating foils, by coupling two-dimensional simulations with multi-objective optimization algorithms. We show that the majority of the thrust originates from the creation of low pressure regions near the leading edge of the airfoil. We optimize the motion of symmetric airfoils exploiting the Knoller-Betz-Katzmayr effect, to attain high speed and lower energy expenditure. The results of the optimization indicate an inverse correlation between energy-efficiency, and the heaving-frequency and amplitude for a purely-heaving airfoil.

2013

  • W. M. van Rees, M. Gazzola, and P. Koumoutsakos, “Optimal shapes for anguilliform swimmers at intermediate Reynolds numbers,” J. Fluid Mech., vol. 722, 2013.

BibTeX

@article{rees2013a,
author = {Wim M. van Rees and Mattia Gazzola and Petros Koumoutsakos},
doi = {10.1017/jfm.2013.157},
journal = {{J. Fluid Mech.}},
month = {apr},
publisher = {Cambridge University Press ({CUP})},
title = {Optimal shapes for anguilliform swimmers at intermediate {R}eynolds numbers},
url = {https://cse-lab.seas.harvard.edu/files/cse-lab/files/rees2013a.pdf},
volume = {722},
year = {2013}
}

Abstract

We investigate the optimal morphologies for fast and efficient anguilliform swimmers at intermediate Reynolds numbers, by combining an evolution strategy with three-dimensional viscous vortex methods. We show that anguilliform swimmer shapes enable the trapping and subsequent acceleration of regions of fluid transported along the entire body by the midline travelling wave. A sensitivity analysis of the optimal morphological traits identifies that the width thickness in the anterior of the body and the height of the caudal fin are critical factors for both speed and efficiency. The fastest swimmer without a caudal fin, however, still retains 80 % of its speed, showing that the entire body is used to generate thrust. The optimal shapes share several features with naturally occurring morphologies, but their overall appearances differ. This demonstrates that engineered swimmers can outperform biomimetic swimmers for the criteria considered here.

2012

  • M. Gazzola, V. W. M. Rees, and P. Koumoutsakos, “C-start: optimal start of larval fish,” J. Fluid Mech., vol. 698, p. 5–18, 2012.

BibTeX

@article{gazzola2012a,
author = {M. Gazzola and W. M. Van Rees and P. Koumoutsakos},
doi = {10.1017/jfm.2011.558},
journal = {{J. Fluid Mech.}},
month = {feb},
pages = {5--18},
publisher = {Cambridge University Press ({CUP})},
title = {C-start: optimal start of larval fish},
url = {https://cse-lab.seas.harvard.edu/files/cse-lab/files/gazzola2012a.pdf},
volume = {698},
year = {2012}
}

2011

  • M. Gazzola, P. Chatelain, W. M. van Rees, and P. Koumoutsakos, “Simulations of single and multiple swimmers with non-divergence free deforming geometries,” J. Comput. Phys., vol. 230, iss. 19, p. 7093–7114, 2011.

BibTeX

@article{gazzola2011b,
author = {Mattia Gazzola and Philippe Chatelain and Wim M. van Rees and Petros Koumoutsakos},
doi = {10.1016/j.jcp.2011.04.025},
journal = {{J. Comput. Phys.}},
month = {aug},
number = {19},
pages = {7093--7114},
publisher = {Elsevier {BV}},
title = {Simulations of single and multiple swimmers with non-divergence free deforming geometries},
url = {https://cse-lab.seas.harvard.edu/files/cse-lab/files/gazzola2011b.pdf},
volume = {230},
year = {2011}
}

Abstract

We present a vortex particle method coupled with a penalization technique to simulate single and multiple swimmers in an incompressible, viscous flow in two and three dimensions. The proposed algorithm can handle arbitrarily deforming bodies and their corresponding non-divergence free deformation velocity fields. The method is validated on a number of benchmark problems with stationary and moving boundaries. Results include flows of tumbling objects and single and multiple self-propelled swimmers.

2008

  • S. E. Hieber and P. Koumoutsakos, “An immersed boundary method for smoothed particle hydrodynamics of self-propelled swimmers,” J. Comput. Phys., vol. 227, iss. 19, p. 8636–8654, 2008.

BibTeX

@article{hieber2008a,
author = {S.E. Hieber and P. Koumoutsakos},
doi = {10.1016/j.jcp.2008.06.017},
journal = {{J. Comput. Phys.}},
month = {oct},
number = {19},
pages = {8636--8654},
publisher = {Elsevier {BV}},
title = {An immersed boundary method for smoothed particle hydrodynamics of self-propelled swimmers},
url = {https://cse-lab.seas.harvard.edu/files/cse-lab/files/hieber2008a.pdf},
volume = {227},
year = {2008}
}

2007

  • S. Kern, P. Koumoutsakos, and K. Eschler, “Optimization of anguilliform swimming,” Phys. Fluids, vol. 19, iss. 9, p. 91102, 2007.

BibTeX

@article{kern2007a,
author = {S. Kern and P. Koumoutsakos and Kristina Eschler},
doi = {10.1063/1.2774981},
journal = {{Phys. Fluids}},
month = {sep},
number = {9},
pages = {091102},
publisher = {{AIP} Publishing},
title = {Optimization of anguilliform swimming},
url = {https://cse-lab.seas.harvard.edu/files/cse-lab/files/kern2007a.pdf},
volume = {19},
year = {2007}
}

Abstract

The European eel Anguilla anguilla migrates from the coasts of Europe to its spawning grounds in the Sargasso Sea. As the eels cover this 6000 km distance without feeding, anguilliform swimming has been regarded as a prime example of highly efficient aquatic propulsion.1 We investigate the hydrodynamics of anguilliform swimming motions using three-dimensional simulations of the fluid flow past a self-propelled body. An evolutionary optimization algorithm2 is used to determine the motion of the body for different objectives, linking swimming motion and biological function in a systematic fashion. The objectives are the swimming efficiency and the burst swimming speed of the swimmer as they pertain to migration and hunt/escape behavior, respectively. The kinematics of burst swimming is characterized by the large amplitude undulations of the tail and the straightness of the anterior part of the body. In contrast, during efficient swimming, significant lateral undulations are present along the entire length of the body. In burst swimming, the majority of the thrust is generated at the tail, whereas in efficient swimming, in addition to the tail, the central part of the body contributes significantly to the thrust.3 The wake, for both swimming modes, consists largely of a double row of vortex rings and corresponding lateral jets with an axis aligned with the swimming direction Fig. 1 and is consistent with experimental results.4

2006

  • S. Kern and P. Koumoutsakos, “Simulations of optimized anguilliform swimming,” J. Exp. Biol., vol. 209, iss. 24, p. 4841–4857, 2006.

BibTeX

@article{kern2006b,
author = {S. Kern and P. Koumoutsakos},
doi = {10.1242/jeb.02526},
journal = {{J. Exp. Biol.}},
month = {dec},
number = {24},
pages = {4841--4857},
publisher = {The Company of Biologists},
title = {Simulations of optimized anguilliform swimming},
url = {https://cse-lab.seas.harvard.edu/files/cse-lab/files/kern2006b.pdf},
volume = {209},
year = {2006}
}

Abstract

The hydrodynamics of anguilliform swimming motions was investigated using three-dimensional simulations of the fluid flow past a self-propelled body. The motion of the body is not specified a priori, but is instead obtained through an evolutionary algorithm used to optimize the swimming efficiency and the burst swimming speed. The results of the present simulations support the hypothesis that anguilliform swimmers modify their kinematics according to different objectives and provide a quantitative analysis of the swimming motion and the forces experienced by the body. The kinematics of burst swimming is characterized by the large amplitude of the tail undulations while the anterior part of the body remains straight. In contrast, during efficient swimming behavior significant lateral undulation occurs along the entire length of the body. In turn, during burst swimming, the majority of the thrust is generated at the tail, whereas in the efficient swimming mode, in addition to the tail, the middle of the body contributes significantly to the thrust. The burst swimming velocity is 42% higher and the propulsive efficiency is 15% lower than the respective values during efficient swimming. The wake, for both swimming modes, consists largely of a double row of vortex rings with an axis aligned with the swimming direction. The vortex rings are responsible for producing lateral jets of fluid, which has been documented in prior experimental studies. We note that the primary wake vortices are qualitatively similar in both swimming modes except that the wake vortex rings are stronger and relatively more elongated in the fast swimming mode. The present results provide quantitative information of three-dimensional fluid-body interactions that may complement related experimental studies. In addition they enable a detailed quantitative analysis, which may be difficult to obtain experimentally, of the different swimming modes linking the kinematics of the motion with the forces acting on the self-propelled body. Finally, the optimization procedure helps to identify, in a systematic fashion, links between swimming motion and biological function.