Recherches et rapports sur les mathématiques

Assessment of Geometry and Gaits for Optimal Displacement and Efficiency

Siddik Shaik

This paper studies the displacement and efficiency of a Purcell’s three-link microswimmer in low Reynolds number regime, capable of moving by the implementation of a motion primitive or gait. An optimization is accomplished getting to the geometry of the swimmer and therefore the motion primitives, considering the form of the gait and its amplitude. the target is to seek out the geometry of the swimmer, amplitude and shape of the gaits which make optimal the displacement and efficiency, in both a private way and combined (the last case are going to be mentioned as multiobjective optimization). Three traditional gaits are compared with two primitives proposed by the authors and other three gaits recently defined within the literature. Results demonstrate that the very best displacement is obtained by the Tam and Hosoi optimal velocity gait, which also achieves the simplest efficiency in terms of energy consumption. The rectilinear and Tam and Hosoi optimal efficiency gaits are the second optimum primitives. Regarding the multiobjective optimization and considering the 2 criteria with an equivalent weight, the optimum gaits end up to be the rectilinear and Tam and Hosoi optimal efficiency gaits. Thus, the conclusions of this study can help designers to pick , on the one hand, the simplest swimmer geometry for a desired motion primitive and, on the opposite , the optimal method of motion for trajectory tracking for such a sort of Purcell’s swimmers counting on the specified control objective.