Sunday December 15th
9:00-9:15
Organizers
Morning session: Foundations of bifurcation theory for control
9:15-10:00
Naomi Ehrich Leonard
I will present fundamentals of local bifurcation theory and discuss its utility in studying and designing decision-making dynamics and control. A local bifurcation of a nonlinear dynamical system refers to a change in the number and/or stability of equilibrium solutions as a system parameter or environmental input varies. I will show how to analyze local bifurcations and derive results that can be used to understand and design dynamics for robustness to perturbation and adaptability to change.
References:
N.E. Leonard, A. Bizyaeva, A. Franci, “Fast and flexible multiagent decision-making”, Annual Review of Control, Robotics, and Autonomous Systems, 7, 2024
N.E. Leonard, “Multi-agent system dynamics: Bifurcation and behavior of animal groups,” Annual Reviews in Control, 38:2, 171-183, 2014
Coffee Break 10:00 - 10:30
10:30-11:15
Rodolphe Sepulchre
An excitable behavior is best characterized by its threshold. But what is the threshold of an excitable behavior? This talk will review the history of that basic question in neuronal circuits and highlights the difficulty of defining a mathematical concept of threshold with the classical state-space representation of dynamical system theory. Those limitations motivate a novel modeling framework, based on a kernel representation of the circuit elements. The kernel representation comes with a scale parameter, that provides a model representation "at scale”. The scale parameter is the bifurcation parameter of the excitability analysis: an excitable system is bistable at fine scale and monostable at coarse scale. We define the threshold as the intermediate value of the scale parameter at which the system is singular. We illustrate this definition on classical models of excitability, showing that it is a constitutive property of any mixed feedback motif.
11:15 - 12:00
Fernando Castaños
The concept of structural stability endows bifurcation theory with the distinctive feature of having a qualitative nature while simultaneously being completely rigorous, an essential feature for the analysis and design of complex systems. In turn, structural stability rests upon a given topological equivalence relation among systems’ flows, with each given equivalence relation yielding a particular bifurcation theory. We are interested in equivalence relations suitable for nonsmooth systems. Specifically, we focus on systems modeled by linear complementarity problems, a class broad enough to exhibit complex nonlinear behaviors while remaining analytically tractable. We propose an equivalence relation for this class of systems and demonstrate that the resulting bifurcation theory aligns with its smooth system counterparts.
Lunch Break 12:00 - 13:00
13:00 - 13:30
Shinkyu Park
In this presentation, we explore the application of the nonlinear opinion dynamics model to facilitate spatial navigation for multiple mobile robots, particularly in settings prone to deadlock situations, such as narrow corridors. Utilizing the model's inherent capability to break deadlocks, we have developed a decentralized navigation algorithm for multi-robot systems. This algorithm enables each robot to independently assess and select navigation strategies, guaranteeing deadlock-free navigation. These strategies are informed by observing the movements of surrounding robots, ensuring each robot can reach its destination without the need for explicit coordination with others. Moreover, to address the challenge of scalability, we propose an approach to reduce the computational demands, facilitating the efficient implementation of the algorithm for a large number of robots.
13:30-14:00
Charlotte Cathcart
This presentation explores Excitable Nonlinear Opinion Dynamics (E-NOD) as a system to balance robust and agile decision-making. E-NOD builds on the foundation of Nonlinear Opinion Dynamics (NOD) by introducing a negative feedback term to generate solutions that “spike” between strong values and an ultrasensitive singularity, inspired by the behavior of excitable systems. We examine the parameter regimes where NOD may lose its decision-making flexibility and demonstrate how E-NOD can restore it through the emergence of homoclinic limit cycles. E-NOD as a control is applied to social robots, enabling them to navigate dynamic environments with increased agility. E-NOD fosters real-time cooperative behavior, even for sequential decision-making scenarios, enhancing robots' ability to proactively interact with oncoming humans.
References:
Cathcart et al. "Proactive opinion-driven robot navigation around human movers." IROS, 2023.
Cathcart et al. "Excitable Nonlinear Opinion Dynamics (E-NOD) for Agile Decision-Making." arXiv, 2024.
14:00-14:30
Andreagiovanni Reina
How can large groups of simple robots running decentralised minimalistic algorithms reach a consensus? Simple robots can be useful in nanorobotics and in scenarios with low-cost requirements. I show that through decentralised voting algorithms, swarms of minimalistic robots can make best-of-n decisions. My research shows that by using a biologically-inspired voting model based on inhibitory signals, the swarm can collectively perform better and be more robust against a minority of malfunctioning robots than in models without inhibition. I explain these phenomena through a combination of bifurcation analysis of nonlinear models and large-scale robot experiments.
References:
A. Reina, R. Zakir, G. De Masi, E. Ferrante. "Cross-inhibition leads to group consensus despite the presence of strongly opinionated minorities and asocial behaviour". Nature Communications Physics, 6, 236, 2023
14:30-15:00
Nak-Seung Patrick Hyun
In nature, different species of smaller animals produce ultra-fast movements to aid in their locomotion or protect themselves against predators. These ultra-fast impulsive motions are possible, as often times, there exist a small latch in the organism that could hold the potential energy of the system, and once released, generate an impulsive motion. These types of systems are classified as Latch Mediated Spring Actuated (LaMSA) systems, a multi-dimensional, multi-mode hybrid system that switches between a latched and an unlatched state. The LaMSA mechanism has been studied extensively in the field of biology and is observed in a wide range of animal species, such as the mantis shrimp, grasshoppers, and trap-jaw ants. In recent years, research has been done in mathematically modeling the LaMSA behavior with physical implementations of the mechanism. A significant focus is given to mimicking the physiological behavior of the species and following an end-to-end trajectory of impulsive motion. This talk introduces a foundational analysis of the theoretical dynamics of the contact latch-based LaMSA mechanism. The speaker answers the question on what makes these small-scale systems impulsive, with a focus on the intrinsic properties of the system using bifurcations. Necessary and sufficient conditions are derived for the existence of the saddle fixed points. The speaker proposes a mathematical explanation for mediating the latch when a saddle node exists, and the impulsive behavior after the bifurcation happens.
References:
Paper: V. Srinivasan, N.P. Hyun, “Bifurcations in Latch-Mediated Spring Actuation (LaMSA) Systems”, MTNS 2024
Paper: E. Steinhardt, N.P. Hyun, et al., “A physical model of mantis shrimp for exploring the dynamics of ultrafast systems”, PNAS 118, 2021
Paper: M. Iton, et al., “The principles of cascading power limits in small, fast biological and engineered systems”. Science 360, 2018
Paper: N.P. Hyun, et al., ” Spring and latch dynamics can act as control pathways in ultrafast systems” , Bioinspir. Biomim. 18, 2023
Coffee Break 15:00-15:30
15:30-16:00
Juncal Arbelaiz
In this talk, I will propose and analyze the suitability of a spiking controller to engineer the locomotion of a single-segmented soft robotic crawler. Inspired by the FitzHugh-Nagumo model of neural excitability, a bistable dynamic controller is designed, capable of generating spikes on-demand when coupled to the passive crawler mechanics. A proprioceptive sensory strain signal from the crawler mechanics turns bistability of the controller into a rhythmic spiking. The output voltage, in turn, activates the crawler’s actuators to generate crawling movement through peristaltic waves.
Dimensional analysis provides insights on the characteristic scales in the crawler’s mechanical and electrical dynamics, and how they determine the crawling gait. In the singularly perturbed limit, geometric analysis is used to show that this control strategy achieves endogenous crawling. I will also analyze how bifurcations in the closed-loop excitable crawler organize different regimes and illustrate how the design of the crawling gait can be simply achieved by modulation of a small number of system parameters. Time permitting, extensions of this control approach to adaptive crawling gaits and spatially distributed multi-segmented soft crawling robots will be discussed.
References:
J. Arbelaiz, A. Franci, N.E. Leonard, R. Sepulchre, B. Bamieh. "Excitable crawling", arXiv, 2024
Y. Shen, N.E. Leonard, B. Bamieh, J. Arbelaiz. "Optimal gait design for nonlinear soft robotic crawlers", arXiv, 2024
16:00-16:30
Guillaume Drion
Artificial intelligence (AI) has made huge progress in recent years, especially in the field of machine learning. Among AI methods, recurrent neural networks (RNNs) provide state-of-the-art performances in a wide variety of tasks that require memory. Training RNNs is however known to be difficult when time series and underlying temporal dependencies become long. Using a dynamical systems approach, we will show that learning of long temporal dependencies is possible when RNNs exhibit multiple stable equilibria; a property known as multistability. Most standard RNN cells only have one stable equilibrium at initialization for stability reasons, and multistability is often not easily attained by initially monostable networks through gradient descent, making learning of long time dependencies between inputs and outputs difficult. Following this insight, we will embed RNNs with long-lasting memory at the cellular level by introducing bistability in classical recurrent cell, which will be shown to strongly improve RNN performance on time-series which require very long memory. We will then generalize this result to all RNNs cells by designing of a novel way to initialize any recurrent cell connectivity that maximizes multistability through a procedure called ‘‘warmup’’ to improve its capability to learn arbitrarily long time dependencies.
16:30-17:00
Thiago Burghi
Biological neurons are capable of sustaining endogenous oscillations whose onsets have traditionally been studied using bifurcation theory. Recently, transitions between neural rhythms have been analyzed through the same framework , providing significant physiological insights into how neuronal behavior is disrupted by global perturbations such as temperature and pH. However, the simplified models used in rigorous mathematical treatments lack the expressiveness needed to quantitatively capture the dynamics and predict the bifurcations of living neurons during electrophysiology experiments. In this talk, I will first review how data-driven models of neuronal behavior address this limitation by rapidly learning single-neuron dynamics and predicting the bifurcations that lead to the onset of spiking and bursting oscillations. Next, I will introduce a new class of models that incorporate the effects of global biophysical perturbations on neural dynamics in a data-driven yet principled manner. Our main results demonstrate that these models can predict high-temperature crashes in the bursting activity of neurons from the Stomatogastric Ganglion (STG), a well-known central pattern generator. I will conclude by discussing how the speed of these predictions enables the use of closed-loop control strategies in real experimental settings to detect and reverse rhythmic switches in neuronal dynamics, such as those observed in neurons from the STG. In the long run, this approach could pave the way for designing effective closed-loop interventions for neurological applications.
References:
Burghi, Thiago B., Maarten Schoukens, and Rodolphe Sepulchre. “System Identification of Biophysical Neuronal Models.” In Proceedings of the 59th IEEE Conference on Decision and Control, 6180–85. Jeju Island, Republic of Korea, 2020.
Franci, A., G. Drion, and R. Sepulchre. “Modeling the Modulation of Neuronal Bursting: A Singularity Theory Approach.” SIAM Journal on Applied Dynamical Systems 13, no. 2 (January 1, 2014): 798–829.
Izhikevich, Eugene M. Dynamical Systems in Neuroscience. Cambridge, MA: MIT Press, 2007.
Ratliff, Jacob, Alessio Franci, Eve Marder, and Timothy O’Leary. “Neuronal Oscillator Robustness to Multiple Global Perturbations.” Biophysical Journal 120, no. 8 (April 2021): 1454–68.
17:00-17:30
Haimin Hu
Non-cooperative interactions commonly occur in multi-agent decision-making such as car racing, where an ego vehicle must decide within a split-second whether to overtake a rival or stay behind until a safe overtaking “corridor” opens. The recently developed nonlinear opinion dynamics (NOD) show promise in enabling such split-second decisions and avoiding safety-critical deadlocks. However, automatically selecting appropriate model parameters in general multi-agent settings remains a challenge. In this talk, we will present our recent progress in studying the synergy between dynamic game theory and NOD. We will begin by introducing a procedure for automatically synthesizing NOD based on the value functions of dynamic games, conditioned on agents’ intents. Building on this game-induced NOD, we propose a game-theoretic trajectory optimization algorithm that swiftly resolves ambiguities in multi-agent interactions. We then generalize this approach with a deep learning pipeline that synthesizes a neural NOD model from expert demonstrations, given as a dataset containing partially observed state and action data of interacting agents. Finally, we will showcase the practicality of these algorithms within a human-aware safety filter framework, applied to safety-critical human-robot interaction scenarios, including vehicle coordination at highway toll stations and autonomous car racing.
References:
Emergent coordination through game-induced nonlinear opinion dynamics (CDC'23)
Think Deep and Fast: Learning Neural Nonlinear Opinion Dynamics from Inverse Dynamic Games for Split-Second Interactions (WAFR'24 submission)
The safety filter: A unified view of safety-critical control in autonomous systems (ARCRAS)
17:30-17:45
Organizers