Abstract
The levels of agility and flight or swimming performance demonstrated by insects, birds, fish, and even some aquatic invertebrates, are often vastly superior to what even the most advanced human-engineered vehicles operating in the same regimes are capable of. Key to this superior locomotion is the animal’s manipulation of the generation and shedding of vortices through optimal control of their motion kinematics. Many research efforts related to biological and bio-inspired propulsion focus on understanding the influence of the motion kinematics on the propulsion performance and on optimising the kinematics to improve efficiency or manoeuvrability. One of the first challenges to tackle when conducting a numerical or experimental optimisation of motion kinematics of objects moving through a fluid is the parameterisation of the motion kinematics. In this paper, we present three different approaches to parameterise kinematics, using a set of control points that are connected by a spline interpolation, a finite Fourier series, and a reduced-order modal reconstruction based on a proper orthogonal decomposition of a set of random walk trajectories. We compare the results and performance of the different parameterisations for the example of an experimental multi-objective optimisation of the pitching kinematics of a robotic flapping wing device. The optimisation was conducted using a genetic algorithm with the objective to maximise stroke average lift and efficiency. The performance is evaluated with regard to the diversity of the randomly created initial populations, the convergence behaviour of the optimisation, and the final Pareto fronts with their corresponding fitness values. The suggested approaches perform equally well and yield fitness values that are in close proximity for the different kinematic functions and different number of input parameters. The main differences are concerned with the implementation of experimental constraints and minor variations in the shape of the Pareto optimal motions are observed. Dedicated applications for each approach are suggested.
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Acknowledgements
The authors thank Guillaume de Guyon-Crozier for the help in implementing the fifth-degree spline kinematic function. Funding has been provided by the Swiss National Science Foundation under Grant Number 200021_175792.
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Busch, C., Gehrke, A. & Mulleners, K. On the parametrisation of motion kinematics for experimental aerodynamic optimisation. Exp Fluids 63, 10 (2022). https://doi.org/10.1007/s00348-021-03367-5
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DOI: https://doi.org/10.1007/s00348-021-03367-5