Date of Award
Doctor of Philosophy (PhD)
Remotely actuated microscale swimming robots have the potential to revolutionize many aspects of biomedicine. However, for the longterm goals of this field of research to be achievable, it is necessary to develop modelling, simulation, and control strategies which effectively and efficiently account for not only the motion of individual swimmers, but also the complex interactions of such swimmers with their environment including other nearby swimmers, boundaries, other cargo and passive particles, and the fluid medium itself. The aim of this thesis is to study these problems in simulation from the perspective of controls and dynamical systems, with a particular focus on problems involving not just the control of a single swimming robot, but those which require coordinated interaction between multiple swimmers, between a swimmer and a boundary, between swimmers and passive particles, or for the manipulation of the fluid itself. While the scope of this thesis remains centered on problems in this application area, many of the methods implemented and developed herein have broader applications in other areas of applied dynamical systems, control theory, and uncertainty quantification, among others.
The first part of this thesis is concerned primarily with the development and implementation in simulation of an efficient numerical model for the motion of magnetically actuated microswimming robots composed of three rigidly connected spheres. We then use this method to study the dynamics of groups of such microswimming robots, which are driven by a torque induced through a uniform, rotating magnetic field. We show that the swimmer motion produces a rotational fluid velocity field in the plane orthogonal to the direction of the magnetic field's rotation, which causes interacting swimmers to move in circular or helical trajectories around a common center. We use this modelling method to develop control strategies for individual swimmers, as well as for swimmers interacting with passive particles of finite size. We show that such microswimmers can be utilized as contactless mobile manipulators of microparticles in a fluid, effectively manipulating a payload that does not have to be physically bound to the swimmer, but may be instead manipulated by the microrobot through hydrodynamic interaction.
In the second part of this thesis, our focus shifts to the problem of controlling the transport of probability density functions evolving under the action of a controlled dynamical system. This problem is motivated by the interpretation of such probability density functions as characterizing concentrations of a passive substance injected into a fluid, such as one which must be manipulated by a microswimming robot. The controlled transport of groups or ensembles of states of a dynamical system has many engineering applications, including motion planning and robot navigation in uncertain environments, mixing and manipulation of fluid particles, control of multi-agent systems, and uncertainty quantification in complex systems. We consider the problem of transporting a density of states from an initial state distribution to a desired final distribution through a dynamical system with actuation. We consider two models of the density transport dynamics: (1) a data-driven method based on finite-dimensional approximations of the Perron-Frobenius operators associated with the drift and control vector fields of the system and (2) a method based on polynomial chaos expansions, where the system dynamics are expanded in orthogonal polynomials of the uncertain quantities. Using these approximations, the density transport problem can be expressed as an optimal control problem in a higher dimensional, lifted state, which we solve using differential dynamic programming, an iterative trajectory optimization scheme. We apply these methods to the problem of steering distributions of fluid particles in a Stokes flow to a desired final distribution in a fixed, finite time by controlling the torques of a group of micro-rotors in the flow. We study cases of fixed rotors, where only the rotor strengths are controlled, as well as cases with moving rotors where both the strengths and translational velocities of the rotors are controlled. We analyze the benefits of using multiple rotors as well as the flow structures associated with the flow field generated by the optimal control.
Buzhardt, Jake, "Controlled Manipulation and Transport by Microswimmers in Stokes Flows" (2023). All Dissertations. 3531.
Author ORCID Identifier
Acoustics, Dynamics, and Controls Commons, Biomedical Engineering and Bioengineering Commons, Controls and Control Theory Commons, Control Theory Commons, Dynamic Systems Commons, Fluid Dynamics Commons, Navigation, Guidance, Control and Dynamics Commons, Navigation, Guidance, Control, and Dynamics Commons, Non-linear Dynamics Commons, Numerical Analysis and Computation Commons, Ordinary Differential Equations and Applied Dynamics Commons