Performance study of propulsion of N-link artificial Eukaryotic flagellum swimming microrobot within a fractional order approach: From simulations to hardware-in-the-loop experiments

Abstract The understanding of how bioinspired artificial microrobot 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 (PDμ) 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 fractional proposed approach.