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.




  • 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] [PDF] [DOI]
    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 = {},
    volume = {12},
    year = {2017}

  • 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] [PDF] [DOI]
    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 = {},
    year = {2017}

  • 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] [PDF] [DOI]
    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 = {},
    volume = {108},
    year = {2017}


  • 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] [Abstract] [PDF] [DOI]

    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.

    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 = {},
    volume = {722},
    year = {2013}


  • 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] [Abstract] [PDF] [DOI]

    We investigate the C-start escape response of larval fish by combining flow simulations using remeshed vortex methods with an evolutionary optimization. We test the hypothesis of the optimality of C-start of larval fish by simulations of larval-shaped, two- and three-dimensional self-propelled swimmers. We optimize for the distance travelled by the swimmer during its initial bout, bounding the shape deformation based on the larval mid-line curvature values observed experimentally. The best motions identified within these bounds are in good agreement with in vivo experiments and show that C-starts do indeed maximize escape distances. Furthermore we found that motions with curvatures beyond the ones experimentally observed for larval fish may result in even larger escape distances. We analyse the flow field and find that the effectiveness of the C-start escape relies on the ability of pronounced C-bent body configurations to trap and accelerate large volumes of fluid, which in turn correlates with large accelerations of the swimmer.

    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 = {},
    volume = {698},
    year = {2012}


  • 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] [Abstract] [PDF] [DOI]

    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.

    author = {Mattia Gazzola and Philippe Chatelain and Wim M. van Rees and Petros Koumoutsakos},
    doi = {10.1016/},
    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 = {},
    volume = {230},
    year = {2011}


  • 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] [Abstract] [PDF] [DOI]

    We present a novel particle method, combining remeshed Smoothed Particle Hydrodynamics with Immersed Boundary and Level Set techniques for the simulation of flows past complex deforming geometries. The present method retains the Lagrangian adaptivity of particle methods and relies on the remeshing of particle locations in order to ensure the accuracy of the method. In fact this remeshing step enables the introduction of Immersed Boundary Techniques used in grid based methods. The method is applied to simulations of flows of isothermal and compressible fluids past steady and unsteady solid boundaries that are described using a particle Level Set formulation. The method is validated with two and three-dimensional benchmark problems of flows past cylinders and spheres and it is shown to be well suited to simulations of large scale simulations using tens of millions of particles, on flow-structure interaction problems as they pertain to self-propelled anguilliform swimmers.

    author = {S.E. Hieber and P. Koumoutsakos},
    doi = {10.1016/},
    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 = {},
    volume = {227},
    year = {2008}


  • S. Kern, P. Koumoutsakos, and K. Eschler, “Optimization of anguilliform swimming,” Phys. Fluids, vol. 19, iss. 9, p. 91102, 2007.
    [BibTeX] [PDF] [DOI]
    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 = {},
    volume = {19},
    year = {2007}


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

    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.

    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 = {},
    volume = {209},
    year = {2006}