  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.
