This thesis studies the effects of morphological factors of hexapod robots on their locomotion stability. In particular, an offset model for such robots is proposed. The stability margin as well as the error margin are used to indicate the stability of the hexapod robot, as it walks with different gaits in arbitrary directions. Two hexapod gaits are compared, which are the symmetric gait and the metachronal gait. The former is an artificial gait and the latter, on the contrary, is a natural gait which can be observed in many multiped animals. As we investigate advantages and disadvantages of the two gaits, we find that the stability of a hexapod robot can be enhanced by increasing the offset value. This is particularly true for a robot moving in the X and oblique directions with a symmetrical gait. However, altering the offset is less useful for metachronal gaits. In general, a hexapod robot moves most stably in the Y direction with a symmetrical gait, whereas it is most stable in the X direction with a metachronal gait.

Locomotion is a key characteristic of almost all forms of life and is often accomplished, whether on land, in water, or in the air, by reciprocal motion of two or more appendages. Among the zooplankton, many species propel themselves by rhythmically beating multiple pairs of closely spaced leg-like appendages in a back-to-front (metachronal) pattern. The focus of this study is to understand the mechanical design, kinematic operation, and hydrodynamic result of metachrony in the zooplankton. In the first part of this study, Antarctic krill (Euphausia superba) are investigated as an ecologically important model species that metachronally beats its swimming legs (pleopods) to perform drag-based propulsion. Based on high speed videos of freely swimming Antarctic krill, hovering, fast forward swimming, and upside down swimming are identified as three distinct swimming modes with significantly different stroke amplitudes and beat frequencies. When transitioning between hovering and fast forward swimming, Antarctic krill first increase beat amplitude and secondarily increase beat frequency. In considering the design components that contribute to metachrony being a successful swimming technique, a comparison among many different species shows that the ratio between the appendage separation distance and appendage length is limited to a narrow range of values (i.e. 0.2 - 0.65). In the second part of this study, metachrony is examined at smaller length and time scales by examining the impulsive escape jump of a calanoid copepod (Calanus finmarchicus). The wake generated by the copepod's metachronally beating swimming legs is experimentally measured using a novel (and newly developed) tomographic particle image velocimetry (PIV) system capable of making volumetric 3D velocity measurements with high temporal and spatial resolution using IR illumination. The flow generated by the escaping copepod consisted of a stronger posterior vortex ring generated by the metachronally stroking swimming legs and a weaker one generated anteriorly around the body by the impulsive start of the escape, both of which decayed over time. The experiments also revealed azimuthal asymmetry in the vortices caused by body yawing and the action of the swimming legs, flow features not considered in previous axisymmetric computational and theoretical models of copepod jumps. While not accounting for this asymmetry, an impulsive stresslet is nonetheless useful in modeling the flow created by the escaping copepod and represents the flow more accurately than an impulsive Stokeslet. In the final part of this study, the flow associated with metachronal hovering in Antarctic krill is experimentally and theoretically investigated in regards to the energy requirements of the pelagic lifestyle. Volumetric flow measurements of a hovering Antarctic krill show that each stroking pleopod drags flow behind it such that a downward stream develops medially. The lateral exopodites induce tip vortices which add to the lift force on each appendage. Furthermore, the flow beneath the hovering krill develops into a pulsed jet with a Strouhal number in the 'high-efficiency zone' of 0.2 < St < 0.4. Actuator disk theory is used to make theoretical estimates of the induced power necessary to hover, the results of which match induced power values calculated from measured flow gradients contributing to viscous energy dissipation.

Eukaryotic organisms rely on the coordinated beating of motile cilia for a multitude of fundamental reasons. In smaller organisms, such as Paramecium and the single cell alga Chlamydomonas reinhardtii, it is a matter of propulsion, to swim towards a higher concentration of nutrients or away from damaging environments. Larger organisms use instead the coordinated motion of cilia to push fluid along an epithelium: examples common to mammals are the circulation of cerebrospinal fluid in the brain, the transport of ovules in the fallopian tubes, and breaking the left/right symmetry in the embryo. Another notable example, and one that is central to this thesis, is mucociliary clearance in human airways: A carpet of motile cilia helps keeping the cell surface free from pathogens and foreign particles by constantly evacuating from lungs, bronchi, and trachea a barrier of mucus. The question of how motile cilia interact with one another to beat in a coordinated fashion is an open and pressing one, with immediate implications for the medical community. In order for the fluid propulsion to be effective, the motion of cilia needs to be phase-locked across significant distances, in the form of travelling waves (``metachronal waves''). It is still not known how this long-range coordination emerges from local rules, as there is no central node regulating the coordination among cilia. In the first part of this thesis I will focus on studying the coordination in carpets of cilia with a top-down approach, by proposing, implementing, and applying a new method of analysing microscope videos of ciliated epithelia. Chapter 1 provides the reader with an introduction on motile cilia and flagella, treating their structure and motion and reporting the different open questions currently tackled by the scientific community, with particular interest in the coordination mechanisms of cilia and the mucociliary clearance apparatus. Chapter 2 introduces Differential Dynamic Microscopy (DDM), a powerful and versatile image analysis tool that bridges the gap between spectroscopy and microscopy by allowing to perform scattering experiments on a microscope. The most interesting aspects of DDM for this work are that it can be applied to microscope videos where it is not possible to resolve individual objects in the field of view, and it requires no user input. These two characteristics make DDM a perfect candidate for analysing several hundred microscope videos of weakly scattering filaments such as cilia. In Chapter 3 I will present how it is possible to employ DDM to extract a wealth of often-overlooked information from videos of ciliated epithelia: DDM can successfully probe the ciliary beat frequency (CBF) in a sample, measure the direction of beating of the cilia, and detect metachronal waves and read their direction and wavelength. In vitro ciliated epithelia however often do not show perfect coordination or alignment among cilia. For the analysis of these samples, where the metachronal coordination might not be evident, we developed a new approach, called multiscale DDM (multiDDM), to measure a coordination length scale, a characteristic length of the system over which the coordination between cilia is lost. The new technique of multiDDM is employed in Chapter 4 to study how the coordination among cilia changes as a response to changes in the rheology of the mucous layer. In particular, we show that cilia beating under a thick, gel-like mucus layer show a larger coordination length scale, as if the mucus acted as an elastic raft effectively coupling cilia over long distances. This is corroborated by the coordination length scale being larger in samples from patients affected by Cystic Fibrosis than in healthy samples, and much shorter when the mucus layer is washed and cilia therefore beat in a near-Newtonian fluid. We then show how it is possible to employ multiDDM to measure the effectiveness of drugs in recovering, in CF samples, a coordination length scale typical of a healthy phenotype. In the second part I will focus instead on the single cilium scale, showing how we can attempt to link the beating pattern of cilia to numerical simulations studying synchronisation in a model system. In particular in Chapter 5 I will describe our approach to quantitatively describe the beating pattern of single cilia obtained from human airway cells of either healthy individuals or patients affected by Primary Ciliary Dyskinesia. Our description of the beating pattern, and the selection of a few meaningful, summary parameters, are then shown to be accurate enough to discriminate between different mutations within Primary Ciliary Dyskinesia. In Chapter 6 instead I report the results obtained by coarse-graining the ciliary beat pattern into a model system consisting of two ``rotors''. The rotors are simulated colloidal particles driven along closed trajectories while leaving their phase free. In my study, the trajectories followed by the rotors are analytical fits of experimental trajectories of the centre of drag of real cilia. The rotors, that are coupled only via hydrodynamics interactions, are seen to phase-lock, and the shape of the trajectory they are driven along is seen to influence the steady state of the system.

La clairance mucociliaire est un processus physico-chimique qui sert à transporter et éliminer le mucus bronchique. Pour cela, des milliards d'appendices de taille micrométrique, que l'on nomme cils, recouvrent l'épithélium respiratoire. Ces cils propulsent le mucus en suivant un motif périodique comprenant une phase de poussée où leur pointe peut pénétrer dans le mucus, et une phase de récupération où ils sont totalement immergés dans le fluide périciliaire. Un dysfonctionnement de ce processus peut engendrer de nombreux problèmes de santé. Il a été observé expérimentalement que les cils ne battent pas aléatoirement, mais synchronisent leurs battements avec leurs voisins, formant ainsi des ondes métachronales. Toutefois, les observations in vivo sont extrêmement difficiles à réaliser, et les propriétés de ces ondes restent mal connues. Dans cette thèse, nous utilisons un solveur Lattice Boltzmann - Frontière Immergée afin de reproduire un épithélium bronchique et étudier l'émergence, ainsi que les capacités de transports et de mélanges, de ces ondes / The mucociliary clearance process is a physico-chemical process which aims is to transport and eliminate bronchial mucus. To do so, billions of micro-sized appendages, called cilia, cover the respiratory epithelium. These cilia propel the mucus by performing a periodical pattern composed of a stroke phase where their tips can enter the mucus layer, and a recovery phase where the cilia are completely immersed in the periciliary liquid layer. A failure of this process may induce numerous health problems. It has been experimentally observed that cilia do not beat randomly, but instead adapt their beatings accordingly to their neighbours, forming metachronal waves. However, in vivo observations are extremely difficult to perfom, and the properties of these waves remain poorly understood. In this thesis, we use a Lattice Boltzmann - Immersed Boundary solver to reproduce a bronchial epithelium and study the emergence, as well as the transport and mixing capacities, of these waves