Trajectory tracking for microswimmers remains a key challenge in microrobotics, where low-Reynolds-number dynamics make control design particularly complex. In this work, we formulate the trajectory tracking problem as an optimal control problem and solve it using a combination of B-spline parametrization with Bayesian optimization, allowing the treatment of high computational costs without requiring complex gradient computations. Applied to a flagellated magnetic swimmer, the proposed method reproduces a variety of target trajectories, including biologically inspired paths observed in experimental studies. We further evaluate the approach on a three-sphere swimmer model, demonstrating that it can adapt to and partially compensate for wall-induced hydrodynamic effects. The proposed optimization strategy can be applied consistently across models of different fidelity, from low-dimensional ODE-based models to high-fidelity PDE-based simulations, showing its robustness and generality. These results highlight the potential of Bayesian optimization as a versatile tool for optimal control strategies in microscale locomotion under complex fluid-structure interactions.

翻译：微泳体的轨迹跟踪始终是微机器人领域的关键挑战，其中低雷诺数动力学特性使得控制设计尤为复杂。本研究将轨迹跟踪问题构建为最优控制问题，并采用B样条参数化与贝叶斯优化相结合的方法进行求解，该方法能够处理高昂计算成本而无需复杂的梯度计算。将所提方法应用于鞭毛式磁性泳体，成功复现了多种目标轨迹，包括实验研究中观察到的生物启发路径。我们进一步在三球泳体模型上评估该方法，证明其能够适应并部分补偿壁面诱导的流体动力学效应。所提出的优化策略可一致应用于不同保真度的模型——从基于低维常微分方程的模型到基于高保真偏微分方程的仿真，展现了其鲁棒性与普适性。这些结果凸显了贝叶斯优化作为复杂流固耦合作用下微尺度运动最优控制策略的通用工具的潜力。