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Building an efficient and robust robot that does not use appendages for locomotion requires inspiration and a thorough understanding of the working principles of limbless animals’ locomotion. In these animals, the passive properties of their morphology and material allow them to dwell in complex terrains at different animals’ scales by using only a simple mode of locomotion, i.e., undulatory locomotion. A better understanding of these animals can inspire efficient locomotion strategies and lead to multi-gait terrain adaptation that exploits their physical intelligence. This study endeavors to model undulatory locomotion in various environments and study the effect of endogenous and exogenous dynamics in limbless bodies. First, undulatory locomotion is modeled analytically using the Lagrangian mechanics approach in a dry frictional environment. A discrete multi-bar system is set to get the propulsive force through frictional anisotropy. The system is then non-dimensionalized to determine the factors representing material and environmental properties. The principal components of the model are body stiffness, internal damping, moment of inertia, and frictional anisotropy. Simulations showed the interdependence of these quantities to achieve the desired speed. The results also highlighted the interdependence of endogenous and exogenous dynamics to achieve different locomotion gaits. Swimming, crawling, and polychaete-like locomotion are characterized based on stiffness factor, frictional factor, and frictional coefficient ratio. The model is validated by inputting the required parameters of the corn snake from the literature. Then undulatory locomotion is modeled in a viscous environment, and the results are compared with the dry environment. It is found that the optimum weight of dry and viscous frictional factors can be found in a hybrid environment to achieve better speed performance. Finally, the experimental validation is carried out in a dry friction environment. The results from experimental and physical models are compared. The physical robot is a wheel-based modular system with flexible joints moving on different substrates. The influence of the spatial distribution of the body stiffness on the speed performance is also explored. Findings suggest that the environment affects the performance of undulatory locomotion based on the body stiffness distribution. Although quantitatively the stiffness varies with the environment, we obtained a qualitative constitutive law for all environments. Specifically, we expect the stiffness distribution to exhibit either an ascending-descending or an ascending-plateau pattern along the length of the object, from head to tail. Furthermore, undulatory locomotion showed sensitivity to contact mechanics: solid-solid or solid-viscoelastic contact produced different locomotion dynamics. Our findings elucidate how terrestrial limbless animals achieve undulatory locomotion performance by exploiting the passive properties of the environment and the body. Application of the obtained results can lead to better-performing long-segmented robots exploiting the aptness of passive body dynamics and the characteristics of the environment where they need to move.

Biological systems offer novel and efficient solutions to many engineering applications, including marine propulsion. It is of interest to determine how fish interact with the water around them, and how best to utilize the potential their methods offer. A stingray-like fin was chosen for analysis due to the maneuverability and versatility of stingrays. The stingray fin was modeled in 2D as a sinusoidal wave with an amplitude increasing from zero at the leading edge to a maximum at the trailing edge. Using this model, a parametric study was performed to examine the effects of the fin on surrounding water in computational fluid dynamics (CFD) simulations. The results were analyzed both qualitatively, in terms of the pressure contours on the fin and vorticity in the trailing wake, and quantitatively, in terms of the resultant forces and the mechanical power requirements to actuate the desired fin motion. The average thrust was shown to depend primarily on the relationship between the swimming speed and the frequency and wavelength (which both are directly proportional to the wavespeed of the fin), although amplitude can be used to augment thrust production as well. However, acceleration was shown to significantly correlate with a large variation in lift and moment, as well as with greater power losses. Using results from the parametric study, the potential for power regeneration was also examined. Relationships between frequency, velocity, drag, and power input were determined using nonlinear regression that explained more than 99.8% of the data. The actuator for a fin was modeled as a single DC motor-shaft system, allowing the combination of the energetic effects of the motor with the fin-fluid system. When combined, even a non-ideal fin model was able to regenerate more power at a given flow speed than was required to swim at the same speed. Even in a more realistic setting, this high proportion of regenerative power suggests that regeneration and energy harvesting could be both feasible and useful in a mission setting. / Master of Science / Animals interact with the world much differently than engineered systems, and can offer new and efficient ways to solve engineering problems, including underwater vehicles. To learn how to move an underwater vehicle in an environmentally conscious way, it is useful to study how a fish’s movements affect the manner in which it moves through the water. Through careful study, the principles involved can be implemented for an efficient, low-disturbance underwater vehicle. The particular fish chosen for in-depth study was the stingray, due to its maneuverability and ability to travel close to the seafloor without disturbing the sediment and creatures around it. In this work, computational analysis was performed on a model of a single stingray fin to determine how the motion of the fin affects the water around it, and how the water affects the fin in turn. The results were analyzed both in terms of the wake behind the fin and in terms of how much power was required to make the fin move in a particular way. The speed of the fin motion was found to have the strongest effect in controlling swimming speed, although the lateral motion of the fin also helped with accelerating faster. Additionally, the potential for a robotic stingray fin to harness power from the water around it was examined. Based on results from simulations of the fin, a mathematical model was formulated to relate energy harvesting with the flow speed past the fin. This model was used to determine how worthwhile it was to use energy harvesting. Analysis of the model showed that harvesting energy from the water was quite efficient, and would likely be a worthwhile investment for an exploration mission.

Undulatory locomotion is a common and powerful strategy used in nature at different biological scales by a broad range of living organisms, from flagellated bacteria to prehistoric snakes, which have overcome the complexity of living in ”flowable” media. By taking inspiration from this evolution-induced strategy, we aim at modelling the locomotion in a granular and viscous environment with the objective to provide more insights for designing robots for soil-like media exploration. Moreover, in contrast to common types of movement, the granular locomotion is still not well understood and is an open and challenging field. We approached this phenomenon with several tools: (i.) numerically, via coupling the Finite Element Method (FEM) with the Discrete Element Method (DEM) using ABAQUS; (ii.) analytically, by employing the Lagrangian formalism to derive the equations of motion of a discrete and continuous system subject to non-conservative forces, and (iii.) experimentally, by creating an ad-hoc set up in order to observe the migration of microfibres used for the treatment of spinal cord injuries. The computational attempts to model the motion in a granular medium involved the simulation of the dynamics of an elastic beam (FEM) surrounded by rigid spherical particles (DEM). A propulsion mechanism was introduced by sinusoidally forcing the beam’s tip normally to the longitudinal axis, while the performance of the locomotion was evaluated by means of a parametric study. Depending on the parameters of the external excitation, after a transient phase, the slender body reached a steady-state with a constant translational velocity. In order to gain physical insights, we studied a simplified version of the previous continuous beam by introducing a discrete multi-bar system. The dynamics of the latter was analytically derived, by taking into account the forces exchanged between the locomotor and the environment, according to the Resistive Force Theory. By numerically solving the equations of motion and evaluating the input energy and dissipations, we were able to define the efficiency and thus provide an effective tool to optimise the locomotion. It is worth mentioning that the two approaches, despite the different physical hypothesis, show a qualitatively and quantitatively good accordance. The numerical and analytical models previously analysed have shown promising results for the interpretation of "ad-hoc" experiments that demonstrate the migration of a microfibre embedded in a spinal cord-like matrix. This migration needs to be avoided, once the regenerative microfibre is implanted in the lesioned spinal cord, for the sake of the patients health.