Biswadip Dey

Truong X. Nghiem, Ján Drgoňa, Colin Jones et al.

Physics-informed machine learning (PIML) is a set of methods and tools that systematically integrate machine learning (ML) algorithms with physical constraints and abstract mathematical models developed in scientific and engineering domains. As opposed to purely data-driven methods, PIML models can be trained from additional information obtained by enforcing physical laws such as energy and mass conservation. More broadly, PIML models can include abstract properties and conditions such as stability, convexity, or invariance. The basic premise of PIML is that the integration of ML and physics can yield more effective, physically consistent, and data-efficient models. This paper aims to provide a tutorial-like overview of the recent advances in PIML for dynamical system modeling and control. Specifically, the paper covers an overview of the theory, fundamental concepts and methods, tools, and applications on topics of: 1) physics-informed learning for system identification; 2) physics-informed learning for control; 3) analysis and verification of PIML models; and 4) physics-informed digital twins. The paper is concluded with a perspective on open challenges and future research opportunities.

Kayhan Ozcimder, Biswadip Dey, Alessio Franci et al.

We studied social decision-making in the rule-based improvisational dance $There$ $Might$ $Be$ $Others$, where dancers make in-the-moment compositional choices. Rehearsals provided a natural test-bed with communication restricted to non-verbal cues. We observed a key artistic explore-exploit tension in which the dancers switched between exploitation of existing artistic opportunities and riskier exploration of new ones. We investigated how the rules influenced the dynamics using rehearsals together with a model generalized from evolutionary dynamics. We tuned the rules to heighten the tension and modeled nonlinear fitness and feedback dynamics for mutation rate to capture the observed temporal phasing of the dancers' exploration-versus-exploitation. Using bifurcation analysis, we identified key controls of the tension and showed how they could shape the decision-making dynamics of the model much like turning a "dial" in the instructions to the dancers could shape the dance. The investigation became an integral part of the development of the dance.

Daniel Rho, Jun Myeong Choi, Matthew Thornton et al.

Existing inverse physics methods recover physical parameters from multi-view videos, where geometric constraints across views resolve scale and 3D structure. In monocular settings, however, such constraints are absent, leading to severe scale ambiguity, inaccurate geometry, and weak coupling between appearance optimization and physical simulation. We propose MonoPhysics, a framework for monocular inverse physics estimation of deformable objects using differentiable MPM simulation and 3D Gaussian Splatting, which jointly optimizes geometry, appearance, and physical parameters from a single camera view. We address these challenges through three visual-physical bridges: global scale alignment, physics-aware geometry refinement, and a differentiable position map, which together enable accurate optimization from monocular observations alone. We evaluate on Vid2Sim and our new dataset of elastic and plastic objects, showing that MonoPhysics outperforms existing baselines in monocular settings and achieves performance comparable to multi-view baselines using only a single camera. Our project page is available at https://daniel03c1.github.io/MonoPhysics/

Haoran Su, Yaofeng D. Zhong, Joseph Y. J. Chow et al.

Emergency vehicles (EMVs) play a crucial role in responding to time-critical calls such as medical emergencies and fire outbreaks in urban areas. Existing methods for EMV dispatch typically optimize routes based on historical traffic-flow data and design traffic signal pre-emption accordingly; however, we still lack a systematic methodology to address the coupling between EMV routing and traffic signal control. In this paper, we propose EMVLight, a decentralized reinforcement learning (RL) framework for joint dynamic EMV routing and traffic signal pre-emption. We adopt the multi-agent advantage actor-critic method with policy sharing and spatial discounted factor. This framework addresses the coupling between EMV navigation and traffic signal control via an innovative design of multi-class RL agents and a novel pressure-based reward function. The proposed methodology enables EMVLight to learn network-level cooperative traffic signal phasing strategies that not only reduce EMV travel time but also shortens the travel time of non-EMVs. Simulation-based experiments indicate that EMVLight enables up to a $42.6\%$ reduction in EMV travel time as well as an $23.5\%$ shorter average travel time compared with existing approaches.

Yaofeng Desmond Zhong, Jiequn Han, Biswadip Dey et al.

Differentiable simulation enables gradients to be back-propagated through physics simulations. In this way, one can learn the dynamics and properties of a physics system by gradient-based optimization or embed the whole differentiable simulation as a layer in a deep learning model for downstream tasks, such as planning and control. However, differentiable simulation at its current stage is not perfect and might provide wrong gradients that deteriorate its performance in learning tasks. In this paper, we study differentiable rigid-body simulation with contacts. We find that existing differentiable simulation methods provide inaccurate gradients when the contact normal direction is not fixed - a general situation when the contacts are between two moving objects. We propose to improve gradient computation by continuous collision detection and leverage the time-of-impact (TOI) to calculate the post-collision velocities. We demonstrate our proposed method, referred to as TOI-Velocity, on two optimal control problems. We show that with TOI-Velocity, we are able to learn an optimal control sequence that matches the analytical solution, while without TOI-Velocity, existing differentiable simulation methods fail to do so.

Yaofeng Desmond Zhong, Tongtao Zhang, Amit Chakraborty et al.

Transformer layers, which use an alternating pattern of multi-head attention and multi-layer perceptron (MLP) layers, provide an effective tool for a variety of machine learning problems. As the transformer layers use residual connections to avoid the problem of vanishing gradients, they can be viewed as the numerical integration of a differential equation. In this extended abstract, we build upon this connection and propose a modification of the internal architecture of a transformer layer. The proposed model places the multi-head attention sublayer and the MLP sublayer parallel to each other. Our experiments show that this simple modification improves the performance of transformer networks in multiple tasks. Moreover, for the image classification task, we show that using neural ODE solvers with a sophisticated integration scheme further improves performance.

Shinjan Ghosh, Amit Chakraborty, Georgia Olympia Brikis et al.

Physics-informed neural networks (PINNs) provide a framework to build surrogate models for dynamical systems governed by differential equations. During the learning process, PINNs incorporate a physics-based regularization term within the loss function to enhance generalization performance. Since simulating dynamics controlled by partial differential equations (PDEs) can be computationally expensive, PINNs have gained popularity in learning parametric surrogates for fluid flow problems governed by Navier-Stokes equations. In this work, we introduce RANS-PINN, a modified PINN framework, to predict flow fields (i.e., velocity and pressure) in high Reynolds number turbulent flow regimes. To account for the additional complexity introduced by turbulence, RANS-PINN employs a 2-equation eddy viscosity model based on a Reynolds-averaged Navier-Stokes (RANS) formulation. Furthermore, we adopt a novel training approach that ensures effective initialization and balance among the various components of the loss function. The effectiveness of the RANS-PINN framework is then demonstrated using a parametric PINN.

Tongtao Zhang, Biswadip Dey, Krishna Veeraraghavan et al.

Computational fluid dynamics (CFD) simulations, a critical tool in various engineering applications, often require significant time and compute power to predict flow properties. The high computational cost associated with CFD simulations significantly restricts the scope of design space exploration and limits their use in planning and operational control. To address this issue, machine learning (ML) based surrogate models have been proposed as a computationally efficient tool to accelerate CFD simulations. However, a lack of clarity about CFD data requirements often challenges the widespread adoption of ML-based surrogates among design engineers and CFD practitioners. In this work, we propose an ML-based surrogate model to predict the temperature distribution inside the cabin of a passenger vehicle under various operating conditions and use it to demonstrate the trade-off between prediction performance and training dataset size. Our results show that the prediction accuracy is high and stable even when the training size is gradually reduced from 2000 to 200. The ML-based surrogates also reduce the compute time from ~30 minutes to around ~9 milliseconds. Moreover, even when only 50 CFD simulations are used for training, the temperature trend (e.g., locations of hot/cold regions) predicted by the ML-surrogate matches quite well with the results from CFD simulations.

Ankur Kamboj, Biswadip Dey, Vaibhav Srivastava

We develop a physics-informed learning framework for energy-shaping control of port-Hamiltonian (pH) systems from trajectory data. The proposed approach {co-learns} a pH system model and an optimal energy-balancing passivity-based controller (EB-PBC) through alternating optimization with policy-aware data collection. At each iteration, the system model is refined using trajectory data collected under the current control policy, and the controller is re-optimized on the updated model. Both components are parameterized by neural networks that embed the pH {dynamics} and EB-PBC structure, ensuring interpretability in terms of energy {interactions}. The learned controller renders the closed-loop system inherently passive and provably stable, and exploits passive plant dynamics without canceling the natural potential. A dissipation regularization enforces strict energy decay during training, thereby enhancing robustness to sim-to-real gaps. The proposed framework is validated on state-regulation and swing-up tasks for planar and torsional pendulum systems.

Shinjan Ghosh, Julian Busch, Georgia Olympia Brikis et al.

Design exploration or optimization using computational fluid dynamics (CFD) is commonly used in the industry. Geometric variation is a key component of such design problems, especially in turbulent flow scenarios, which involves running costly simulations at every design iteration. While parametric RANS-PINN type approaches have been proven to make effective turbulent surrogates, as a means of predicting unknown Reynolds number flows for a given geometry at near real-time, geometry aware physics informed surrogates with the ability to predict varying geometries are a relatively less studied topic. A novel geometry aware parametric PINN surrogate model has been created, which can predict flow fields for NACA 4 digit airfoils in turbulent conditions, for unseen shapes as well as inlet flow conditions. A local+global approach for embedding has been proposed, where known global design parameters for an airfoil as well as local SDF values can be used as inputs to the model along with velocity inlet/Reynolds number ($\mathcal{R}_e$) to predict the flow fields. A RANS formulation of the Navier-Stokes equations with a 2-equation k-epsilon turbulence model has been used for the PDE losses, in addition to limited CFD data from 8 different NACA airfoils for training. The models have then been validated with unknown NACA airfoils at unseen Reynolds numbers.

Shinjan Ghosh, Amit Chakraborty, Georgia Olympia Brikis et al.

Computational fluid dynamics (CFD) solvers employing two-equation eddy viscosity models are the industry standard for simulating turbulent flows using the Reynolds-averaged Navier-Stokes (RANS) formulation. While these methods are computationally less expensive than direct numerical simulations, they can still incur significant computational costs to achieve the desired accuracy. In this context, physics-informed neural networks (PINNs) offer a promising approach for developing parametric surrogate models that leverage both existing, but limited CFD solutions and the governing differential equations to predict simulation outcomes in a computationally efficient, differentiable, and near real-time manner. In this work, we build upon the previously proposed RANS-PINN framework, which only focused on predicting flow over a cylinder. To investigate the efficacy of RANS-PINN as a viable approach to building parametric surrogate models, we investigate its accuracy in predicting relevant turbulent flow variables for both internal and external flows. To ensure training convergence with a more complex loss function, we adopt a novel sampling approach that exploits the domain geometry to ensure a proper balance among the contributions from various regions within the solution domain. The effectiveness of this framework is then demonstrated for two scenarios that represent a broad class of internal and external flow problems.

Daniel Rho, Jun Myeong Choi, Biswadip Dey et al.

Neural rendering has made significant strides in 3D reconstruction and novel view synthesis. With the integration with physics, it opens up new applications. The inverse problem of estimating physics from visual data, however, still remains challenging, limiting its effectiveness for applications like physically accurate digital twin creation in robotics and XR. Existing methods that incorporate physics into neural rendering frameworks typically require dense multi-view videos as input, making them impractical for scalable, real-world use. When presented with sparse multi-view videos, the sequential optimization strategy used by existing approaches introduces significant error accumulation, e.g., poor initial 3D reconstruction leads to bad material parameter estimation in subsequent stages. Instead of sequential optimization, directly optimizing all parameters at the same time also fails due to the highly non-convex and often non-differentiable nature of the problem. We propose ProJo4D, a progressive joint optimization framework that gradually increases the set of jointly optimized parameters guided by their sensitivity, leading to fully joint optimization over geometry, appearance, physical state, and material property. Evaluations on PAC-NeRF and Spring-Gaus datasets show that ProJo4D outperforms prior work in 4D future state prediction, novel view rendering of future state, and material parameter estimation, demonstrating its effectiveness in physically grounded 4D scene understanding. For demos, please visit the project webpage: https://daniel03c1.github.io/ProJo4D/

Rajat Arora, Pratik Kakkar, Biswadip Dey et al.

This work presents a physics-informed neural network (PINN) based framework to model the strain-rate and temperature dependence of the deformation fields in elastic-viscoplastic solids. To avoid unbalanced back-propagated gradients during training, the proposed framework uses a simple strategy with no added computational complexity for selecting scalar weights that balance the interplay between different terms in the physics-based loss function. In addition, we highlight a fundamental challenge involving the selection of appropriate model outputs so that the mechanical problem can be faithfully solved using a PINN-based approach. We demonstrate the effectiveness of this approach by studying two test problems modeling the elastic-viscoplastic deformation in solids at different strain rates and temperatures, respectively. Our results show that the proposed PINN-based approach can accurately predict the spatio-temporal evolution of deformation in elastic-viscoplastic materials.

Haoran Su, Yaofeng Desmond Zhong, Biswadip Dey et al.

Emergency vehicles (EMVs) play a critical role in a city's response to time-critical events such as medical emergencies and fire outbreaks. The existing approaches to reduce EMV travel time employ route optimization and traffic signal pre-emption without accounting for the coupling between route these two subproblems. As a result, the planned route often becomes suboptimal. In addition, these approaches also do not focus on minimizing disruption to the overall traffic flow. To address these issues, we introduce EMVLight in this paper. This is a decentralized reinforcement learning (RL) framework for simultaneous dynamic routing and traffic signal control. EMVLight extends Dijkstra's algorithm to efficiently update the optimal route for an EMV in real-time as it travels through the traffic network. Consequently, the decentralized RL agents learn network-level cooperative traffic signal phase strategies that reduce EMV travel time and the average travel time of non-EMVs in the network. We have carried out comprehensive experiments with synthetic and real-world maps to demonstrate this benefit. Our results show that EMVLight outperforms benchmark transportation engineering techniques as well as existing RL-based traffic signal control methods.

Haoran Su, Yaofeng Desmond Zhong, Biswadip Dey et al.

Emergency vehicles (EMVs) play a crucial role in responding to time-critical events such as medical emergencies and fire outbreaks in an urban area. The less time EMVs spend traveling through the traffic, the more likely it would help save people's lives and reduce property loss. To reduce the travel time of EMVs, prior work has used route optimization based on historical traffic-flow data and traffic signal pre-emption based on the optimal route. However, traffic signal pre-emption dynamically changes the traffic flow which, in turn, modifies the optimal route of an EMV. In addition, traffic signal pre-emption practices usually lead to significant disturbances in traffic flow and subsequently increase the travel time for non-EMVs. In this paper, we propose EMVLight, a decentralized reinforcement learning (RL) framework for simultaneous dynamic routing and traffic signal control. EMVLight extends Dijkstra's algorithm to efficiently update the optimal route for the EMVs in real time as it travels through the traffic network. The decentralized RL agents learn network-level cooperative traffic signal phase strategies that not only reduce EMV travel time but also reduce the average travel time of non-EMVs in the network. This benefit has been demonstrated through comprehensive experiments with synthetic and real-world maps. These experiments show that EMVLight outperforms benchmark transportation engineering techniques and existing RL-based signal control methods.

Yaofeng Desmond Zhong, Biswadip Dey, Amit Chakraborty

The incorporation of appropriate inductive bias plays a critical role in learning dynamics from data. A growing body of work has been exploring ways to enforce energy conservation in the learned dynamics by encoding Lagrangian or Hamiltonian dynamics into the neural network architecture. These existing approaches are based on differential equations, which do not allow discontinuity in the states and thereby limit the class of systems one can learn. However, in reality, most physical systems, such as legged robots and robotic manipulators, involve contacts and collisions, which introduce discontinuities in the states. In this paper, we introduce a differentiable contact model, which can capture contact mechanics: frictionless/frictional, as well as elastic/inelastic. This model can also accommodate inequality constraints, such as limits on the joint angles. The proposed contact model extends the scope of Lagrangian and Hamiltonian neural networks by allowing simultaneous learning of contact and system properties. We demonstrate this framework on a series of challenging 2D and 3D physical systems with different coefficients of restitution and friction. The learned dynamics can be used as a differentiable physics simulator for downstream gradient-based optimization tasks, such as planning and control.

Yaofeng Desmond Zhong, Biswadip Dey, Amit Chakraborty

The last few years have witnessed an increased interest in incorporating physics-informed inductive bias in deep learning frameworks. In particular, a growing volume of literature has been exploring ways to enforce energy conservation while using neural networks for learning dynamics from observed time-series data. In this work, we survey ten recently proposed energy-conserving neural network models, including HNN, LNN, DeLaN, SymODEN, CHNN, CLNN and their variants. We provide a compact derivation of the theory behind these models and explain their similarities and differences. Their performance are compared in 4 physical systems. We point out the possibility of leveraging some of these energy-conserving models to design energy-based controllers.

Udari Madhushani, Biswadip Dey, Naomi Ehrich Leonard et al.

Value function based reinforcement learning (RL) algorithms, for example, $Q$-learning, learn optimal policies from datasets of actions, rewards, and state transitions. However, when the underlying state transition dynamics are stochastic and evolve on a high-dimensional space, generating independent and identically distributed (IID) data samples for creating these datasets poses a significant challenge due to the intractability of the associated normalizing integral. In these scenarios, Hamiltonian Monte Carlo (HMC) sampling offers a computationally tractable way to generate data for training RL algorithms. In this paper, we introduce a framework, called \textit{Hamiltonian $Q$-Learning}, that demonstrates, both theoretically and empirically, that $Q$ values can be learned from a dataset generated by HMC samples of actions, rewards, and state transitions. Furthermore, to exploit the underlying low-rank structure of the $Q$ function, Hamiltonian $Q$-Learning uses a matrix completion algorithm for reconstructing the updated $Q$ function from $Q$ value updates over a much smaller subset of state-action pairs. Thus, by providing an efficient way to apply $Q$-learning in stochastic, high-dimensional settings, the proposed approach broadens the scope of RL algorithms for real-world applications.

Tongtao Zhang, Biswadip Dey, Pratik Kakkar et al.

Incompressible fluid flow around a cylinder is one of the classical problems in fluid-dynamics with strong relevance with many real-world engineering problems, for example, design of offshore structures or design of a pin-fin heat exchanger. Thus learning a high-accuracy surrogate for this problem can demonstrate the efficacy of a novel machine learning approach. In this work, we propose a physics-informed neural network (PINN) architecture for learning the relationship between simulation output and the underlying geometry and boundary conditions. In addition to using a physics-based regularization term, the proposed approach also exploits the underlying physics to learn a set of Fourier features, i.e. frequency and phase offset parameters, and then use them for predicting flow velocity and pressure over the spatio-temporal domain. We demonstrate this approach by predicting simulation results over out of range time interval and for novel design conditions. Our results show that incorporation of Fourier features improves the generalization performance over both temporal domain and design space.

Yaofeng Desmond Zhong, Biswadip Dey, Amit Chakraborty

In this work, we introduce Dissipative SymODEN, a deep learning architecture which can infer the dynamics of a physical system with dissipation from observed state trajectories. To improve prediction accuracy while reducing network size, Dissipative SymODEN encodes the port-Hamiltonian dynamics with energy dissipation and external input into the design of its computation graph and learns the dynamics in a structured way. The learned model, by revealing key aspects of the system, such as the inertia, dissipation, and potential energy, paves the way for energy-based controllers.

Kevin S. Galloway, Biswadip Dey

Motivated by real-world applications of unmanned aerial vehicles, this paper introduces a decentralized control mechanism to guide steering control of autonomous agents maneuvering in the vicinity of multiple moving entities (e.g. other autonomous agents) and stationary entities (e.g. fixed beacons or points of references) in a three-dimensional environment. The proposed control law, which can be perceived as a modification of the three-dimensional constant bearing (CB) pursuit law, provides a means to allocate simultaneous attention to multiple entities. We investigate the behavior of the closed-loop dynamics for a system with one agent referencing two beacons, as well as a two-agent mutual pursuit system wherein each agent employs the beacon-referenced CB pursuit law with regards to the other agent and a stationary beacon. Under certain assumptions on the associated control parameters, we demonstrate that this problem admits circling equilibria with agents moving on circular orbits with a common radius, in planes perpendicular to a common axis passing through the beacons. As the common radius and distances from the beacon are determined by the choice of parameters in the pursuit law, this approach provides a means to engineer desired formations in a 3-dimensional setting.

Akshay Iyer, Biswadip Dey, Arindam Dasgupta et al.

Microstructures of a material form the bridge linking processing conditions - which can be controlled, to the material property - which is the primary interest in engineering applications. Thus a critical task in material design is establishing the processing-structure relationship, which requires domain expertise and techniques that can model the high-dimensional material microstructure. This work proposes a deep learning based approach that models the processing-structure relationship as a conditional image synthesis problem. In particular, we develop an auxiliary classifier Wasserstein GAN with gradient penalty (ACWGAN-GP) to synthesize microstructures under a given processing condition. This approach is free of feature engineering, requires modest domain knowledge and is applicable to a wide range of material systems. We demonstrate this approach using the ultra high carbon steel (UHCS) database, where each microstructure is annotated with a label describing the cooling method it was subjected to. Our results show that ACWGAN-GP can synthesize high-quality multiphase microstructures for a given cooling method.

Yaofeng Desmond Zhong, Biswadip Dey, Amit Chakraborty

In this paper, we introduce Symplectic ODE-Net (SymODEN), a deep learning framework which can infer the dynamics of a physical system, given by an ordinary differential equation (ODE), from observed state trajectories. To achieve better generalization with fewer training samples, SymODEN incorporates appropriate inductive bias by designing the associated computation graph in a physics-informed manner. In particular, we enforce Hamiltonian dynamics with control to learn the underlying dynamics in a transparent way, which can then be leveraged to draw insight about relevant physical aspects of the system, such as mass and potential energy. In addition, we propose a parametrization which can enforce this Hamiltonian formalism even when the generalized coordinate data is embedded in a high-dimensional space or we can only access velocity data instead of generalized momentum. This framework, by offering interpretable, physically-consistent models for physical systems, opens up new possibilities for synthesizing model-based control strategies.

Kevin S. Galloway, Biswadip Dey

Motivated by station-keeping applications in various unmanned settings, this paper introduces a steering control law for a pair of agents operating in the vicinity of a fixed beacon in a three-dimensional environment. This feedback law is a modification of the previously studied three-dimensional constant bearing (CB) pursuit law, in the sense that it incorporates an additional term to allocate attention to the beacon. We investigate the behavior of the closed-loop dynamics for a two agent mutual pursuit system in which each agent employs the beacon-referenced CB pursuit law with regards to the other agent and a stationary beacon. Under certain assumptions on the associated control parameters, we demonstrate that this problem admits circling equilibria wherein the agents move on circular orbits with a common radius, in planes perpendicular to a common axis passing through the beacon. As the common radius and distances from the beacon are determined by choice of parameters in the feedback law, this approach provides a means to engineer desired formations in a three-dimensional setting.

Kevin S. Galloway, Biswadip Dey

Cyclic pursuit frameworks provide an efficient way to create useful global behaviors out of pairwise interactions in a collective of autonomous robots. Earlier work studied cyclic pursuit with a constant bearing (CB) pursuit law, and has demonstrated the existence of a variety of interesting behaviors for the corresponding dynamics. In this work, by attaching multiple branches to a single cycle, we introduce a modified version of this framework which allows us to consider any weakly connected pursuit graph where each node has an outdegree of 1. This provides a further generalization of the cyclic pursuit setting. Then, after showing existence of relative equilibria (rectilinear or circling motion), pure shape equilibria (spiraling motion) and periodic orbits, we also derive necessary conditions for stability of a 3-agent collective. By paving a way for individual agents to join or leave a collective without perturbing the motion of others, our approach leads to improved reliability of the overall system.

Zahra Aminzare, Biswadip Dey, Elizabeth N. Davison et al.

Finding the conditions that foster synchronization in networked oscillatory systems is critical to understanding a wide range of biological and mechanical systems. However, the conditions proved in the literature for synchronization in nonlinear systems with linear coupling, such as has been used to model neuronal networks, are in general not strict enough to accurately determine the system behavior. We leverage contraction theory to derive new sufficient conditions for cluster synchronization in terms of the network structure, for a network where the intrinsic nonlinear dynamics of each node may differ. Our result requires that network connections satisfy a cluster-input-equivalence condition, and we explore the influence of this requirement on network dynamics. For application to networks of nodes with neuronal spiking dynamics, we show that our new sufficient condition is tighter than those found in previous analyses which used nonsmooth Lyapunov functions. Improving the analytical conditions for when cluster synchronization will occur based on network configuration is a significant step toward facilitating understanding and control of complex oscillatory systems.

Kevin S. Galloway, Biswadip Dey

Cyclic pursuit frameworks, which are built upon pursuit interactions between neighboring agents in a cycle graph, provide an efficient way to create useful global behaviors in a collective of autonomous robots. Previous work had considered cyclic pursuit with a constant bearing (CB) pursuit law, and demonstrated the existence of circling equilibria for the corresponding dynamics. In this work, we propose a beacon-referenced version of the CB pursuit law, wherein a stationary beacon provides an additional reference for the individual agents in a collective. When implemented in a cyclic framework, we show that the resulting dynamics admit relative equilibria corresponding to a circling orbit around the beacon, with the circling radius and the distribution of agents along the orbit determined by parameters of the proposed pursuit law. We also derive necessary conditions for stability of the circling equilibria, which provides a guide for parameter selection. Finally, by introducing a change of variables, we demonstrate the existence of a family of invariant manifolds related to spiraling motions around the beacon which preserve the "pure shape" of the collective, and study the reduced dynamics on a representative manifold.

Udit Halder, Biswadip Dey

Drawing inspiration from flight behavior in biological settings (e.g. territorial battles in dragonflies, and flocking in starlings), this paper demonstrates two strategies for coverage and flocking. Using earlier theoretical studies on mutual motion camouflage, an appropriate steering control law for area coverage has been implemented in a laboratory test-bed equipped with wheeled mobile robots and a Vicon high speed motion capture system. The same test-bed is also used to demonstrate another strategy (based on local information), termed topological velocity alignment, which serves to make agents move in the same direction. The present work illustrates the applicability of biological inspiration in the design of multi-agent robotic collectives.

Kevin S. Galloway, Biswadip Dey

This paper investigates a modification of cyclic constant bearing (CB) pursuit in a multi-agent system in which each agent pays attention to a neighbor and a beacon. The problem admits shape equilibria with collective circling about the beacon, with the circling radius and angular separation of agents determined by choice of parameters in the feedback law. Stability of circling shape equilibria is shown for a 2-agent system, and the results are demonstrated on a collective of mobile robots tracked by a motion capture system.