Mathematical control theory for mirorobot and cell locomotion

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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.