Modelling and Simulation of the Nonlinear Dynamics of Arrays of Coupled Filaments for Robot Walkers
This thesis project centers on modelling and simulation of the nonlinear dynamics of systems of filaments attached to a solid substrate that couples their motion. The geometry of the system is inspired by ubiquitous structures found in small organisms. These structures, called cilia, exhibit different types of organized coordinated patterns used for locomotion, among other functions. One notable type of coordination is called metachronal, which manifests through wave propagation across the filaments, and it is inherently related to motility and locomotion. The same type of wave phenomena are observed in larger organisms such as centipedes and millipedes, which use it for terrestrial locomotion. While there are many studies on cilia-inspired robot locomotion, they often focus on hydrodynamic coupling or magnetic actuation. This thesis introduces a model with mechanical coupling. The main objective of the thesis is to derive a mechanical model and to simulate it, creating the foundation for the systematic prediction of the emergence of coordinated patterns of the system. The ultimate goal for future work is to use the predictions to design controls for terrestrial locomotion systems for mobile autonomous robots capable of navigating across various terrains. The system we simulate consists of arrays of rigid filaments that are coupled through visco-elastic lumped elements at the base. These filaments emulate hair-like structures idealized as inverted pendulums, capturing certain characteristics of cilia-like structures that are relevant for the locomotion. Mechanical coupling is achieved through elastic springs and linear viscous dampers, creating a lumped-parameter model of the coupling base. The governing equations for the system are derived using Euler-Lagrange's formalism. In simulations, our primary objective is to examine coordinated patterns under diverse initial conditions. The evolution of the simulated system demonstrates a convergence towards a synchronized state. The study contributes to the exploration of bio-inspired approaches for developing robust terrestrial robot walkers capable of adaptive and efficient movement.
metachronal Wave, synchronization, basal coupling, visco-elastic properties, lumped-parameter model, Euler-Lagrange equation
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