טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentWiezel Oren
SubjectOptimal Control, Optimization and Asymptotic Analysis of
Simple Microswimmer Models
DepartmentDepartment of Mechanical Engineering
Supervisor Professor Yizhar Or
Full Thesis textFull thesis text - English Version


Abstract

Recent advances in micro- and nano-technologies have accelerated the possibility of creating microscopic swimming devices for medical applications. Such robotic swimmers can be used for targeted drug delivery, tumor detection, assisting sperm motility and more. Importantly, the nature of fluid-swimmer interaction in microscopic scale, where inertial forces are negligible and viscous effect are dominant, calls for methods of propulsion, actuation and control that are drastically different from the conventional ones normally used for the design of large-scale swimming devices. Theoretical analysis of the dynamics and control of microswimmers using simplified mathematical models provides a way of optimizing swimmer's geometries and actuations that lead to more efficient swimming.


Our research in this collection of published papers begins with studying a simple mathematical model of microswimmer, namely, Purcell's three-link swimmer. First, we employ asymptotic analysis in order to derive approximate expressions for the swimmer's displacement as well as energy expenditure and efficiency. This allows us to obtain optimal stroke amplitudes and optimal designs of the swimmer geometry.

In the second paper, we utilize variational methods of optimal control (Pontryagin's maximum principle) in order to obtain optimal stroke patterns for maximal displacement for Purcell's swimmer.


The third paper presents a collaborative work with research groups from France and Italy, in which we investigated energetically optimal gaits in leading order of an $N$-link microswimmer model. Using a constrained variational formulation, we found that the energy-optimal small-amplitude gaits are ellipses lying in a two-dimensional plane embedded within the N - 1 dimensional space of shape variables.


Another system with a similar structure is the high Reynolds "perfect fluid" swimmer. This swimmer, governed by inertia and with negligible viscosity, has dynamics with a structure very similar to the low-Re swimmers. In the fourth paper, we employ the methods of asymptotic analysis and optimal control in order to optimize gaits for this swimmer as well.


Some of the theoretical results are demonstrated experimentally using a macro-scale robotic prototype of the three-link swimmer in viscous silicone fluid, presented as ``unpublished results''.


Finally, we review a geometric method for analysis of gaits and compare the results from this method to our results We use these results to explain cases where the variational method failed to find the optimal gaits.