Mathematical control theory for mirorobot and cell locomotion

该研究会的研究计划包括三个轴：第一个轴：可控性和控制理论的基本工具。在这方面的研究中，我们已经完成了[1]的一个版本，其主要结果是具有漂移的系统的可控性，该版本于2023年被接受出版。第二个轴：提高微泳者的效率和设计。在这方面的研究中，我们围绕微观尺度的流体动力学形状优化进行了相当大的发展。第一份手稿于2022年夏天完成并提交。随后对数值框架进行了改进，并进行了几次研究访问，以将该项目扩展到新的方向：具有摩擦的最佳形状和与最佳控制相联系的动态优化。我们与英国的研究人员合作，在描述微泳者的多尺度建模方面的工作，导致了几篇论文(一篇发表[2]，两篇提交)中传播的重要结果。最后，通过与英国机器人团队发起的合作研究微型机器人的控制：建立模型和最佳游泳姿势。第三轴：微泳者推进的新手段。在这方面的研究中，我们关于控制多名游泳者的论文发表在2022年7月的《流体力学杂志》上[3]。我们对奇数弹性作为内部活动模型的新研究(2022年7月首次发表[4])现在构成了这一轴的主要视角，希望将其用作智能机器人/自行式设计的基础。

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.