Radhika Nagpal’s research while affiliated with Princeton University and other places

The schooling behavior of fish is hypothesized to confer many survival benefits, including foraging success, safety from predators, and energy savings through hydrodynamic interactions when swimming in formation. Underwater robot collectives may be able to achieve similar benefits in future applications, e.g. using formation control to achieve efficient spatial sampling for environmental monitoring. Although many theoretical algorithms exist for multi-robot formation control, they have not been tested in the underwater domain due to the fundamental challenges in underwater communication. Here we introduce a leader-follower strategy for underwater formation control that allows us to realize complex 3D formations, using purely vision-based perception and a reactive control algorithm that is low computation. We use a physical platform, BlueSwarm, to demonstrate for the first time an experimental realization of inline, side-by-side, and staggered swimming 3D formations. More complex formations are studied in a physics-based simulator, providing new insights into the convergence and stability of formations given underwater inertial/drag conditions. Our findings lay the groundwork for future applications of underwater robot swarms in aquatic environments with minimal communication.

The coordinated movement of fish schools has long captivated researchers studying animal collective behavior. Classical literature from Weihs and Lighthill suggests that fish schools should favor planar diamond formations to increase hydrodynamic efficiency, inspiring a large body of work ranging from fluid simulations to hydrofoil experiments. However, whether fish schools actually adopt and maintain this idealized formation remains debated and unresolved. When fish schools are free to self-organize in three dimensions, what formations do they prefer? By tracking polarized schools of giant danios (Devario aequipinnatus) swimming continuously for ten hours, we demonstrate that fish rarely stay in a horizontal plane, and even more rarely, in the classical diamond formation. Of all fish pairs within four body-lengths from each other, only 25.2% are in the same plane. Of these, 54.6% are inline, 30.0% are staggered, and 15.4% are side-by-side. The diamond formation was observed in less than 0.1% of all frames. Notably, a "ladder formation" emerged as the most probable formation for schooling giant danios, appearing in 79% of all fish pairs and fish schools elongate at higher swimming speeds. These findings highlight the dynamic and three-dimensional nature of fish schools and suggest that hydrodynamic benefits may be obtained without requiring fixed positions. This research provides a foundation for future studies that examine the hydrodynamics and control of underwater collectives in 3D formations.

In this work computational models of Bluebots, bio-inspired swimming robots that demonstrate 3D maneuverability and collective behaviors, are developed. Flexibility is prescribed to the caudal fins (CF) using a virtual skeleton. The hydrodynamic interactions occurring within in-line arrangements of these Bluebots is investigated by altering the flexion angle of the leader Bluebot caudal fin and a balance between optimizing leader Bluebot (LB) performance and follower Bluebot (FB) wake interaction is identified. Compared to the rigid CF baseline, optimal CF flexion for the thrust of LB leads to higher negative pressure within generated vortex structures and narrowing of the thrust jet which impinges along the entire body of the FB. Further increase of the LB flexion creates even stronger negative pressure regions while widening the thrust jet behind the leader. These flow conditions are more favorable for the FB as the accelerated flow only interacts with the anterior of the robot body and the stronger negative pressure supplies stronger anterior suction. The ability of the FB to sense these flow changes is also important, and the pressure sensor data on the FB exhibits differences between the cases. Near the anterior surface, the sensor pressure data provides insight to the varying vortex ring strengths for higher LB CF flexion, meanwhile, such differences are not as obvious when examining probe data further downstream on the FB.

Collective behaviour defines the lives of many animal species on the Earth. Underwater swarms span several orders of magnitude in size, from coral larvae and krill to tunas and dolphins. Agent-based algorithms have modelled collective movements of animal groups by use of social forces , which approximate the behaviour of individual animals. But details of how swarming individuals interact with the fluid environment are often under-examined. How do fluid forces shape aquatic swarms? How do fish use their flow-sensing capabilities to coordinate with their schooling mates? We propose viewing underwater collective behaviour from the framework of fluid stigmergy , which considers both physical interactions and information transfer in fluid environments. Understanding the role of hydrodynamics in aquatic collectives requires multi-disciplinary efforts across fluid mechanics, biology and biomimetic robotics. To facilitate future collaborations, we synthesize key studies in these fields.

Fish benefit energetically when swimming in groups, which is reflected in lower tail-beat frequencies for maintaining a given speed. Recent studies further show that fish save the most energy when swimming behind their neighbor such that both the leader and the follower benefit. However, the mechanisms underlying such hydrodynamic advantages have thus far not been established conclusively. The long-standing drafting hypothesis—reduction of drag forces by judicious positioning in regions of reduced oncoming flow–fails to explain advantages of in-line schooling described in this work. We present an alternate hypothesis for the hydrodynamic benefits of in-line swimming based on enhancement of propulsive thrust. Specifically, we show that an idealized school consisting of in-line pitching foils gains hydrodynamic benefits via two mechanisms that are rooted in the undulatory jet leaving the leading foil and impinging on the trailing foil: (i) leading-edge suction on the trailer foil, and (ii) added-mass push on the leader foil. Our results demonstrate that the savings in power can reach as high as 70% for a school swimming in a compact arrangement. Informed by these findings, we designed a modification of the tail propulsor that yielded power savings of up to 56% in a self-propelled autonomous swimming robot. Our findings provide insights into hydrodynamic advantages of fish schooling, and also enable bioinspired designs for significantly more efficient propulsion systems that can harvest some of their energy left in the flow.

Fish migrate across considerable distances and exhibit remarkable agility to avoid predators and feed. Fish swimming performance and maneuverability remain unparalleled when compared to robotic systems, partly because previous work has focused on robots and flapping foil systems that are either big and complex, or tethered to external actuators and power sources. By contrast, we present a robot—the Finbot—that combines high degrees of autonomy, maneuverability, and biomimicry with miniature size (160 cm³). Thus, it is well-suited for controlled three-dimensional experiments on fish swimming in confined laboratory test beds. Finbot uses four independently controllable fins and sensory feedback for precise closed-loop underwater locomotion. Different caudal fins can be attached magnetically to reconfigure Finbot for swimming at top speed (122 mm s⁻¹ ≡ 1 BL s⁻¹) or minimal cost of transport (CoT = 8.2) at Strouhal numbers as low as 0.53. We conducted more than 150 experiments with 12 different caudal fins to measure three key characteristics of swimming fish: (i) linear speed-frequency relationships, (ii) U-shaped CoT, and (iii) reverse Kármán wakes (visualized with particle image velocimetry). More fish-like wakes appeared where the CoT was low. By replicating autonomous multi-fin fish-like swimming, Finbot narrows the gap between fish and fish-like robots and can address open questions in aquatic locomotion, such as optimized propulsion for new fish robots, or the hydrodynamic principles governing the energy savings in fish schools.

Many fish species gather by the thousands and swim in harmony with seemingly no effort. Large schools display a range of impressive collective behaviors, from simple shoaling to collective migration and from basic predator evasion to dynamic maneuvers such as bait balls and flash expansion. A wealth of experimental and theoretical work has shown that these complex three-dimensional (3D) behaviors can arise from visual observations of nearby neighbors, without explicit communication. By contrast, most underwater robot collectives rely on centralized, above-water, explicit communication and, as a result, exhibit limited coordination complexity. Here, we demonstrate 3D collective behaviors with a swarm of fish-inspired miniature underwater robots that use only implicit communication mediated through the production and sensing of blue light. We show that complex and dynamic 3D collective behaviors—synchrony, dispersion/aggregation, dynamic circle formation, and search-capture—can be achieved by sensing minimal, noisy impressions of neighbors, without any centralized intervention. Our results provide insights into the power of implicit coordination and are of interest for future underwater robots that display collective capabilities on par with fish schools for applications such as environmental monitoring and search in coral reefs and coastal environments.