Research
Current (or future) research topics
Self-organization-based phenomena are commonly observed in nature on various spatiotemporal scales. Typically, they exhibit macroscopic patterns arising from local interactions between individual components. In this context, I am attempting to understand the fundamental principles underlying such emergent phenomena based on simple mathematical models and develop “reasonable” control schemes for them. My field of research is interdisciplinary—at the crossroads between applied mathematics, mathematical biology, physics, control engineering, robotics, biology, medicine, social science, and sport science.
Decoding decentralized control mechanisms underlying animal locomotion
Animals exhibit astoundingly adaptive, robust, and versatile trends of locomotion in response to their environment. In this study, we focus on various model organisms such as snakes and brittle stars, and aim to uncover the autonomous decentralized control principles underlying their real-time adaptive locomotion through behavioral observation, mathematical modeling, and experiments with simulations or actual robotic systems. Furthermore, we explore strategies for driving uniquely structured robots—such as those equipped with tensegrity wheels—by applying the decentralized control principles we have identified.
Designing super-survival systems by studying collectives of living organisms that exhibit altruistic behaviors
Several living organisms are capable of surviving in harsh environments by forming swarms. In these systems,
individuals are often observed to exhibit altruistic behavior for the greater benefit of the overall swarm. For example, in bacterial biofilms, certain cells temporarily halt their uptake of nutrients to allow other starving cells to gain nourishment, which improves the survivability of the biofilm as a whole [1]. Further, while vampire bats cannot survive without food for more than three days, they often sustain themselves over several years by sharing food with each other in their community [2]. We aim to elucidate the control mechanisms underlying such altruistic behavior and design artificial agents with high survivability on this basis.
[1] J. Liu et al. Nature 523: 550-554 (2015)
[2] G.S. Wilkinson, Nature 308: 181 (1984)
Understanding mechanisms of “heterogeneous swarm intelligence”
Cells that make up living organisms are highly diverse, and even cells of the same type can exhibit differences in their properties. Cell populations leverage this individuality to form ordered structures in response to environmental cues, enabling collective movement and the emergence of macroscopic functions that a single cell could never achieve on its own. Similarly, in animal groups—such as flocks of crows or aggregations of tubifex worms—individual members possess unique traits, which appear to contribute to intelligent collective behaviors at the group level. We refer to this form of intelligence, arising from the collaboration of diverse individuals, as “heterogeneous swarm intelligence,” and aim to elucidate its mechanisms through mathematical modeling and simulation.
Understanding decentralized control mechanism in swarms of “soft” individuals
Most previous studies on swarms have modeled their constituent units as point masses or rigid bodies. In contrast, this research investigates the principles of collective intelligence that emerge when soft-bodied individuals physically interact with one another. In particular, we focus on the aquatic worm Tubifex, whose long, flexible bodies become entangled to form cohesive aggregates that change their shape depending on the situation while moving as a group. We aim to uncover the mechanisms by which these worm aggregates navigate and adapt to complex real-world environments—such as narrow spaces and uneven terrain—through behavioral experiments, mathematical modeling, and simulation. Additionally, we are investigating intriguing collective movements observed in swarms of jellyfish.
Decoding control and learning mechanisms underlying inter-personal sport activities
In activities related to inter-personal sports, certain skills are essential to communicate with others and develop oneself through friendly competition. However, control and learning mechanisms associated to these skills remain unclear. In this study, we investigate a variety of competitive activities—including player-versus-player e-sports—by integrating approaches from sports science, mathematical science, and robotics, with the aim of revealing these underlying principles.
Designing decentralized control schemes of transportation systems, robot swarms, and drones
This study aims to develop methods for appropriately controlling the flow of multiple self-propelled agents—such as vehicles, robots, and drones—in a manner that adapts to situational changes. For example, in the case of drones, the number of aerial units is expected to increase dramatically in the near future. Under such conditions, centralized control systems will face inherent limitations. To address this, we are working to design autonomous decentralized control rules that allow each unit to determine its own actions based on the surrounding environment, drawing inspiration from the behavioral principles of animals such as bats, sheep, and pedestrians.
Mathematical modeling of non-trivial social phenomena
In human society, emergent behaviors of the society as a whole, which are far beyond what could be imagined from the characteristics of its individual members, can sometimes occur. We aim to uncover the mechanisms behind these phenomena using agent-based models.
Research on non-reciprocal-interaction-based model inspired by the process of friendship formation
The non-reciprocal-interaction-based model is a simple mathematical model for collective behavior, inspired by the process of friendship formation in human society, proposed by us in a previous study. Although the original motivation behind its development was mere curiosity, our simulations revealed various interesting non-trivial patterns depending on the parameters (for further details, please consult the following link on YouTube: https://www.youtube.com/watch?v=1doJowB9yc0). In this study, we intend to identify prospective applications of this model.
Research
Previous research topics
Density oscillator (or Saline oscillator)
The density oscillator is a simple system that exhibits self-sustained oscillation. It alternately exhibits up- and down-flow through a pipe which connects two containers filled with fluids of different densities. However, the mechanism of the flow reversal has not yet been fully understood. From the detailed measurements, we have found that flow reversal begins with an intrusion of fluid, which is followed by rapid growth. This process is definitely sensitive to the viscosities of the fluids, and as a consequence, the critical heights leading to flow reversal are clearly viscosity-dependent. These experimental results are explained by a simple model, derived by considering forces acting on a unit volume element located at the tip of the intrusion. Using this model, we can successfully explain the mechanism of flow reversal, which is the most essential process in a density oscillator.
Control of coupled-oscillator systems based on multi-linear feedback
Methods to control the dynamics of coupled oscillators have been developed owing to various medical and technological demands. In this study, we develop a method to control coupled oscillators in which the coupling function expressed in a phase model is regulated by the multilinear feedback. The present method has wide applicability because we do not need to measure an individual output from each oscillator, but only measure the sum of the outputs from all the oscillators. Moreover, it allows us to easily control the coupling function up to higher harmonics. The validity of the present method is confirmed through a simulation.
Mathematical modeling of the relationship between the COVID-19 outbreak and economic activities
Acute respiratory syndrome caused by the coronavirus, COVID-19, is in the process of rapid transmission throughout the world, as of August, 2020. While avoiding close contact between humans is essential to mitigate the outbreak, such practice inevitably causes severe economic losses. This conundrum requires an urgent solution and the identification of strategies to mitigate outbreak while maintaining a basic level of economic activity is imperative. In this study, we aim to propose a mathematical model for the outbreak of COVID-19 by taking economic activities into account, with the intention of creating a platform to discuss solutions to the aforementioned dilemma.