Nonlinear dynamics and bifurcations of a planar undulating magnetic microswimmer

Swimming micro-organisms such as flagellated bacteria and sperm cells have fascinating locomotion capabilities. Inspired by their natural motion, there is an ongoing effort to develop artificial robotic nano-swimmers for potential in-body biomedical applications. A leading method for actuation of nano-swimmers is by applying a time-varying external magnetic field. Such systems have rich and nonlinear dynamics that calls for simple fundamental models. A previous work studied forward motion of a simple two-link model with passive elastic joint, assuming small-amplitude planar oscillations of the magnetic field about a constant direction. In this work, we found that there exists a faster, backward motion of the swimmer with very rich dynamics. By relaxing the small-amplitude assumption, we analyze the multiplicity of periodic solutions, as well as their bifurcations, symmetry breaking, and stability transitions. We have also found that the net displacement and/or mean swimming speed are maximized for optimal choices of various parameters. Asymptotic calculations are performed for the bifurcation condition and the swimmer's mean speed. The results may enable significantly improving the design aspects of magnetically-actuated robotic microswimmer.Comment: version 3, revised and resubmitted for review as journal publicatio

The role of functional surfaces in the locomotion of snakes

Snakes are one of the world’s most versatile organisms, at ease slithering through rubble or climbing vertical tree trunks. Their adaptations for conquering complex terrain thus serve naturally as inspirations for search and rescue robotics. In a combined experimental and theoretical investigation, we elucidate the propulsion mechanisms of snakes on both hard and granular substrates. The focus of this study is on physics of snake interactions with its environment. Snakes use one of several modes of locomotion, such as slithering on flat surfaces, sidewinding on sand, or accordion-like concertina and worm-like rectilinear motion to traverse crevices. We present a series of experiments and supporting mathematical models demonstrating how snakes optimize their speed and efficiency by adjusting their frictional properties as a function of position and time. Particular attention is paid to a novel paradigm in locomotion, a snake’s active control of its scales, which enables it to modify its frictional interactions with the ground. We use this discovery to build bio-inspired limbless robots that have improved sensitivity to the current state of the art: Scalybot has individually controlled sets of belly scales enabling it to climb slopes of 55 degrees. These findings will result in developing new functional materials and control algorithms that will guide roboticists as they endeavor towards building more effective all-terrain search and rescue robots.Ph.D

Design, Analysis, and Fabrication of a Snake-Inspired Robot with a Rectilinear Gait

Snake-inspired robots display promise in areas such as search, rescue and reconnaissance due to their ability to locomote through tight spaces. However, several specific issues regarding the design and analysis must be addressed in order to better design them. This thesis develops kinematic and dynamic models for a class of snake-inspired gait known as a rectilinear gait, where mechanism topology changes over the course of the gait. A model using an Eulerian framework and Coulomb friction yields torque expressions for the joints of the robot. B-spline curves are then used to generate a parametric optimization formulation for joint trajectory generation. Exact gradient computation of the torque functions is presented. A parametric model is used to describe the performance effects of changing system parameters such as mass, length, and motor speed. Finally, a snake-inspired robot is designed and fabricated in order to demonstrate both the vertical rectilinear gait and a modular, molded design aimed at reducing the cost of fabrication

Design, Analysis, and Fabrication of a Snake-Inspired Robot with a Rectilinear Gait

Snake-inspired robots display promise in areas such as search, rescue and reconnaissance due to their ability to locomote through tight spaces. However, several specific issues regarding the design and analysis must be addressed in order to better design them. This thesis develops kinematic and dynamic models for a class of snake-inspired gait known as a rectilinear gait, where mechanism topology changes over the course of the gait. A model using an Eulerian framework and Coulomb friction yields torque expressions for the joints of the robot. B-spline curves are then used to generate a parametric optimization formulation for joint trajectory generation. Exact gradient computation of the torque functions is presented. A parametric model is used to describe the performance effects of changing system parameters such as mass, length, and motor speed. Finally, a snake-inspired robot is designed and fabricated in order to demonstrate both the vertical rectilinear gait and a modular, molded design aimed at reducing the cost of fabrication