2022 Fiscal Year Annual Research Report
Mathematical control theory for microrobot and cell locomotion
| Project/Area Number |
22F22023
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| Allocation Type | Single-year Grants |
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| Research Institution | Kyoto University |
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Principal Investigator |
石本 健太 京都大学, 数理解析研究所, 准教授 (00741141)
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| Co-Investigator(Kenkyū-buntansha) |
MOREAU CLEMENT 京都大学, 数理解析研究所, 外国人特別研究員
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| Project Period (FY) |
2022-04-22 – 2024-03-31
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| Keywords | control theory / microswimming / fluid mechanics / mathematical modelling / shape optimisation |
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| Outline of Annual Research Achievements |
The research plan for the Fellowship comprises three axes.
First axis: Fundamental tools in controllability and control theory. In this line of research, we have finalised a version of [1], with major results in controllability of systems with a drift, which got accepted for publication in 2023. Second axis: Improve microswimmer efficiency and design. In this line of research, we have considerably developed the project around shape optimisation for fluid dynamics at microscopic scale. A first manuscript was completed and submitted in summer 2022. Subsequent refinements of the numerical framework and several research visits were conducted to extend the project in new directions: optimal shapes with friction and dynamical optimisation with links to optimal control. Our work on multi scale modelling for microswimmer description, in collaboration with researchers in the UK, led to important results disseminated in several papers (one published [2] and two submitted) Finally, control of micro robots is investigated through a collaboration initiated with a robotics team in the UK: establishment of a model and optimal swimming strokes. Third axis: new means of microswimmer propulsion. In this line of research, our paper on the control of multiple swimmers was published in Journal of Fluid Mechanics in July 2022 [3]. Our new research on odd elasticity as a model for internal activity (with a first publication in July 2022 [4]) now constitutes the main perspective of this axis, with the hope of using it as a basis for smart robot / self-propelled design.
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| Current Status of Research Progress |
Current Status of Research Progress
1: Research has progressed more than it was originally planned.
Reason
Significant progress has been made in each of the three axes of the initial research plan. Overall, we can say the current status is more than planned. The research in the first axis is going as planned. Further investigation of systems with drift and constraints will go on during the second year, backed by collaborations in France.
The research in the second axis has been considerably fruitful, more than initially planned, with ramifications within each subsection developing into full-size research projects: multiscale analysis and influence of shape on microswimmer dynamics ; theoretical and numerical questions investigated on shape optimisation at low-Reynolds number regime ; modelling and control of multiflagellated robots. The research in the third axis has gone further than planned. The preliminary investigation on fluctuation-driven swimmers has led to analysis of noisy swimming cycles and constitutes a line of research in the internal activity modelling through odd elasticity.
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| Strategy for Future Research Activity |
The plan for the research in the second year of the Fellowship is five-fold.
1- Control-affine systems with drift: Investigate the Chen-Fliess series in the case of several controls. 2- State-constrained control systems: Explore the properties of simple systems with numerical simulations. Links to stabilization problems. Collaboration with researchers in France. 3- Hydrodynamic shape optimisation: Numerical simulations and FEM method for Navier conditions. Implement constraints in minimizers. State existence of minimizers in dynamic shape optimisation case. 4- Control and propulsion: Controllability and optimal control of multi flagellated robot, in collaboration with robotics team in the UK. Optimal control of variable Jeffery equation. 5- Modeling microswimmers: Investigate odd filaments, odd rings and interacting filaments.
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