The understanding of how bioinspired artificial microrobots propel themselves by propagating a planar wave along their flagellum is crucial to improve their mechanical design, as well as their performance. Likewise, the implementation of such a planar wave motion in N-link swimming microrobots involves several challenges, among with the motion control of actuators can be highlighted, whose load (viscous drag forces) does not only depend on their own link and motion, but also on their position along the flagellum. This paper proposes an improved locomotion for an N-link artificial Eukaryotic flagellum (AEF) swimming microrobot taking into account a fractional order approach for both the waveform design for propulsion and the control of the flagellum distributed dynamics. On the one hand, the novel way of swimming, based on a fractional order power law for the amplitude modulation, allows to preserve the motion properties obtained applying classical traveling waveforms, but presenting some benefits in terms of propulsion. On the other, a robust fractional order proportional-derivative (PD^μ) controller is designed for the motion control of the microrobot. To demonstrate the advantages and validate both the waveform and the control strategy proposed, a hardware-in-the-loop (HIL) testbed for a 4-link robot is built. It consists of a microrobot simulator developed with the physical modeling tools in the MATLAB/Simulink environment and the embedded microcontroller Atmel ATmega32u4, where the control of the robot is programmed. The testbed, thanks to the simulator, allows to select different modes of swimming and geometry for the microrobot, as well as evaluating the performance of the locomotion in terms of propulsion, power efficiency or tracking. Experimental and simulation results are given to show that the best efficiency, with regard to both the way of swimming and the energy consumption with the control applied, is achieved with the proposed fractional approach.

了解生物启发的微型机器人如何通过沿鞭毛传播平面波来推动自身前进，这对于改善其机械设计和性能至关重要。同样，在N-link游泳微型机器人中实现这种平面波运动涉及多个挑战，其中可以突出显示执行器的运动控制，执行器的负载（粘滞阻力）不仅取决于其自身的链接和运动，而且在鞭毛上的位置。本文提出了一种改进的N链接人工真核鞭毛（AEF）游泳微型机器人运动，并考虑了分数阶方法来进行推进的波形设计和鞭毛分布动力学的控制。一方面，新颖的游泳方式 基于用于幅度调制的分数阶幂定律，可以保留使用经典行进波形获得的运动特性，但在推进方面有一些好处。另一方面，鲁棒的分数阶比例微分（PD^μ）控制器是为微型机器人的运动控制而设计的。为了展示其优势并验证所提出的波形和控制策略，为4链接机器人构建了硬件在环（HIL）测试平台。它由使用MATLAB / Simulink环境中的物理建模工具开发的微型机器人模拟器和嵌入式的微控制器Atmel ATmega32u4（在其中编程机器人的控制）组成。由于使用了模拟器，该测试台允许为微型机器人选择不同的游泳模式和几何形状，并可以根据推进力，功率效率或跟踪来评估运动性能。实验和仿真结果表明，在游泳方式和能量消耗（采用控制）方面，效率最高，