# Dynamics and optimal actuation of a three-sphere low-Reynolds-number swimmer with muscle-like arms

## TL;DR

This paper models a three-sphere microswimmer with muscle-like arms, analyzing its dynamics, control strategies, and optimizing actuation for improved swimming performance at low Reynolds numbers.

## Contribution

It introduces a novel model of a microswimmer with muscle-inspired arms, deriving its equations, analyzing solutions, and exploring optimal actuation strategies.

## Key findings

- Analytical and numerical solutions of the swimmer's dynamics.
- Optimal actuation strategies for performance enhancement.
- Control-theoretic analysis of the swimmer's governing equations.

## Abstract

The three-sphere swimmer by Najafi and Golestanian is composed of three spheres connected by two arms. The case in which the swimmer can control the lengths of the two arms has been studied in detail. Here we study a variation of the model in which the swimmer's arms are constructed according to Hill's model of muscular contraction. The swimmer is able to control the tension developed in the active components of the arms. The two shape parameters and the tensions acting on the two arms are then obtained by solving a system of ordinary differential equations. We study the qualitative properties of the solutions, compute analytically their leading order approximation and compare them with numerical simulations. We also formulate and solve some optimisation problems, aimed at finding the actuation strategies maximising performance, for various performance measures. Finally, we discuss the structure of the governing equations of our microswimmers from the point of view of control theory. We show that our systems are control affine systems with drift.