On the parametrisation of motion kinematics for experimental aerodynamic optimisation

TL;DR

This paper compares three methods for parameterizing motion kinematics in fluid-structure interaction experiments, aiming to optimize robotic wing motion for lift and efficiency using genetic algorithms.

Contribution

It introduces and evaluates three novel kinematic parameterization approaches for optimizing bio-inspired propulsion systems.

Findings

Fourier series and modal reconstruction outperform spline interpolation in convergence.

Parameterization impacts the diversity and quality of optimization results.

All methods successfully optimize lift and efficiency, with trade-offs in convergence speed.

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.