Metachronal paddling is a swimming strategy in which an organism oscillates sets of adjacent limbs with a constant phase lag, propagating a metachronal wave through its limbs and propelling it forward. This limb coordination strategy is utilized by swimmers across a wide range of Reynolds numbers, which suggests that this metachronal rhythm was selected for its optimality of swimming performance. In this study, we apply reinforcement learning to a swimmer at zero Reynolds number and investigate whether the learning algorithm selects this metachronal rhythm, or if other coordination patterns emerge. We design the swimmer agent with an elongated body and pairs of straight, inflexible paddles placed along the body for various fixed paddle spacings. Based on paddle spacing, the swimmer agent learns qualitatively different coordination patterns. At tight spacings, a back-to-front metachronal wave-like stroke emerges which resembles the commonly observed biological rhythm, but at wide spacings, different limb coordinations are selected. Across all resulting strokes, the fastest stroke is dependent on the number of paddles, however, the most efficient stroke is a back-to-front wave-like stroke regardless of the number of paddles.

Motile microorganisms develop effective swimming gaits to adapt to complex biological environments. Translating this adaptability to smart microrobots presents significant challenges in motion planning and stroke design. In this work, we explore the use of reinforcement learning (RL) to develop stroke patterns for targeted navigation in a three-link swimmer model at low Reynolds numbers. Specifically, we design two RL-based strategies: one focusing on maximizing velocity (Velocity-Focused Strategy) and another balancing velocity with energy consumption (Energy-Aware Strategy). Our results demonstrate how the use of different reward functions influences the resulting stroke patterns developed via RL, which are compared with those obtained from traditional optimization methods. Furthermore, we showcase the capability of the RL-powered swimmer in adapting its stroke patterns in performing different navigation tasks, including tracing complex trajectories and pursuing moving targets. Taken together, this work highlights the potential of reinforcement learning as a versatile tool for designing efficient and adaptive microswimmers capable of sophisticated maneuvers in complex environments.

Microswimmers are sub-millimeter swimming microrobots that show potential as a platform for controllable locomotion in applications including targeted cargo delivery and minimally invasive surgery. To be viable for these target applications, microswimmers will eventually need to be able to navigate in environments with dynamic fluid flows and forces. Experimental studies with microswimmers towards this goal are currently rare because of the difficulty isolating intentional microswimmer motion from environment-induced motion. In this work, we present a method for measuring microswimmer locomotion within a complex flow environment using fiducial microspheres. By tracking the particle motion of ferromagnetic and non-magnetic polystyrene fiducial microspheres, we capture the effect of fluid flow and field gradients on microswimmer trajectories. We then determine the field-driven translation of these microswimmers relative to fluid flow and demonstrate the effectiveness of this method by illustrating the motion of multiple microswimmers through different flows.

This work introduces SwarmRL, a Python package designed to study intelligent active particles. SwarmRL provides an easy-to-use interface for developing models to control microscopic colloids using classical control and deep reinforcement learning approaches. These models may be deployed in simulations or real-world environments under a common framework. We explain the structure of the software and its key features and demonstrate how it can be used to accelerate research. With SwarmRL, we aim to streamline research into micro-robotic control while bridging the gap between experimental and simulation-driven sciences. SwarmRL is available open-source on GitHub at https://github.com/SwarmRL/SwarmRL.

Machine learning and artificial intelligence have recently represented a popular paradigm for designing and optimizing robotic systems across various scales. Recent studies have showcased the innovative application of large language models (LLMs) in industrial control [1] and in directing legged walking robots [2]. In this study, we utilize an LLM, GPT-4, to train two prototypical microrobots for swimming in viscous fluids. Adopting a few-shot learning approach, we develop a minimal, unified prompt composed of only five sentences. The same concise prompt successfully guides two distinct articulated microrobots -- the three-link swimmer and the three-sphere swimmer -- in mastering their signature strokes. These strokes, initially conceptualized by physicists, are now effectively interpreted and applied by the LLM, enabling the microrobots to circumvent the physical constraints inherent to micro-locomotion. Remarkably, our LLM-based decision-making strategy substantially surpasses a traditional reinforcement learning method in terms of training speed. We discuss the nuanced aspects of prompt design, particularly emphasizing the reduction of monetary expenses of using GPT-4.

Multi-Agent Reinforcement Learning (MARL) is a promising candidate for realizing efficient control of microscopic particles, of which micro-robots are a subset. However, the microscopic particles' environment presents unique challenges, such as Brownian motion at sufficiently small length-scales. In this work, we explore the role of temperature in the emergence and efficacy of strategies in MARL systems using particle-based Langevin molecular dynamics simulations as a realistic representation of micro-scale environments. To this end, we perform experiments on two different multi-agent tasks in microscopic environments at different temperatures, detecting the source of a concentration gradient and rotation of a rod. We find that at higher temperatures, the RL agents identify new strategies for achieving these tasks, highlighting the importance of understanding this regime and providing insight into optimal training strategies for bridging the generalization gap between simulation and reality. We also introduce a novel Python package for studying microscopic agents using reinforcement learning (RL) to accompany our results.

Many robotic systems locomote using gaits - periodic changes of internal shape, whose mechanical interaction with the robot's environment generate characteristic net displacements. Prominent examples with two shape variables are the low Reynolds number 3-link "Purcell swimmer" with inputs of 2 joint angles and the "ideal fluid" swimmer. Gait analysis of these systems allows for intelligent decisions to be made about the swimmer's locomotive properties, increasing the potential for robotic autonomy. In this work, we present comparative analysis of gait optimization using two different methods. The first method is variational approach of "Pontryagin's maximum principle" (PMP) from optimal control theory. We apply PMP for several variants of 3-link swimmers, with and without incorporation of bounds on joint angles. The second method is differential-geometric analysis of the gaits based on curvature (total Lie bracket) of the local connection for 3-link swimmers. Using optimized body-motion coordinates, contour plots of the curvature in shape space give visualization that enables identifying distance-optimal gaits as zero level sets. Combining and comparing results of the two methods enables better understanding of changes in existence, shape and topology of distance-optimal gait trajectories, depending on the swimmers' parameters.

The question of how "smart" active agents, like insects, microorganisms, or future colloidal robots need to steer to optimally reach or discover a target, such as an odor source, food, or a cancer cell in a complex environment has recently attracted great interest. Here, we provide an overview of recent developments, regarding such optimal navigation problems, from the micro- to the macroscale, and give a perspective by discussing some of the challenges which are ahead of us. Besides exemplifying an elementary approach to optimal navigation problems, the article focuses on works utilizing machine learning-based methods. Such learning-based approaches can uncover highly efficient navigation strategies even for problems that involve e.g. chaotic, high-dimensional, or unknown environments and are hardly solvable based on conventional analytical or simulation methods.

Artificial microswimmers that move similarly to naturally occurring swimming microorganisms have recently been the focus of some researchers. Microorganisms are all around us and are closely connected to how people live their daily lives. Microorganisms have piqued the interest of scientists ever since their discovery in the 19th century. They were cultivated for research purposes, but this process is costly and time-consuming. However, high-throughput sequencing technology cannot be developed at the same rate as the culture approach.

A team of researchers from Santa Clara University, New Jersey Institute of Technology, and the University of Hong Kong have successfully used deep reinforcement learning to teach microrobots how to swim. The new development is a major step forward in microswimming capabilities. Experts have been consistently focused on creating artificial microswimmers that can navigate similarly to naturally-occuring swimming microorganisms, such as bacteria. These microswimmers could be used for a variety of biomedical applications in the future, such as targeted drug delivery and microsurgery. Even with the focus on development, most of today's artificial microswimmers can only perform simple maneuvers with fixed locomotory gaits.