Bearing-Based Formation Maneuvering

This paper studies the problem of multi-agent formation maneuver control where both of the centroid and scale of a formation are required to track given velocity references while maintaining the formation shape. Unlike the conventional approaches where the target formation is defined by inter-neighbor relative positions or distances, we propose a bearing-based approach where the target formation is defined by inter-neighbor bearings. Due to the invariance of the bearings, the bearing-based approach provides a natural solution to formation scale control. We assume the dynamics of each agent as a single integrator and propose a globally stable proportional-integral formation maneuver control law. It is shown that at least two leaders are required to collaborate in order to control the centroid and scale of the formation whereas the followers are not required to have access to any global information, such as the velocities of the leaders.Comment: To appear in the 2015 IEEE Multi-Conference on Systems and Control (MSC2015); this is the final versio

Bearing-Based Distributed Control and Estimation of Multi-Agent Systems

This paper studies the distributed control and estimation of multi-agent systems based on bearing information. In particular, we consider two problems: (i) the distributed control of bearing-constrained formations using relative position measurements and (ii) the distributed localization of sensor networks using bearing measurements. Both of the two problems are considered in arbitrary dimensional spaces. The analyses of the two problems rely on the recently developed bearing rigidity theory. We show that the two problems have the same mathematical formulation and can be solved by identical protocols. The proposed controller and estimator can globally solve the two problems without ambiguity. The results are supported with illustrative simulations.Comment: 6 pages, to appear in the 2015 European Control Conferenc

Formation Control and Rigidity Theory

Formation control is one of the fundamental coordination tasks for teams of autonomous vehicles. Autonomous formations are used in applications ranging from search-and-rescue operations to deep space exploration, with benefits including increased robustness to failures and risk mitigation for human operators. The challenge of formation control is to develop distributed control strategies using vehicle onboard sensing that ensures the desired formation is obtained. This snapshot describes how the mathematical theory of rigidity has emerged as an important tool in the study of formation control problems

Characterizing bearing equivalence in directed graphs

In this paper, we study bearing equivalence in directed graphs. We first give a strengthened definition of bearing equivalence based on the \textit{kernel equivalence} relationship between bearing rigidity matrix and bearing Laplacian matrix. We then present several conditions to characterize bearing equivalence for both directed acyclic and cyclic graphs. These conditions involve the spectrum and null space of the associated bearing Laplacian matrix for a directed bearing formation. For directed acyclic graphs, all eigenvalues of the associated bearing Laplacian are real and nonnegative, while for directed graphs containing cycles, the bearing Laplacian can have eigenvalues with negative real parts. Several examples of bearing equivalent and bearing non-equivalent formations are given to illustrate these conditions.Comment: Accepted by the 22nd World Congress of the International Federation of Automatic Contro

Predator-prey survival pressure is sufficient to evolve swarming behaviors

The comprehension of how local interactions arise in global collective behavior is of utmost importance in both biological and physical research. Traditional agent-based models often rely on static rules that fail to capture the dynamic strategies of the biological world. Reinforcement learning has been proposed as a solution, but most previous methods adopt handcrafted reward functions that implicitly or explicitly encourage the emergence of swarming behaviors. In this study, we propose a minimal predator-prey coevolution framework based on mixed cooperative-competitive multiagent reinforcement learning, and adopt a reward function that is solely based on the fundamental survival pressure, that is, prey receive a reward of $-1$ if caught by predators while predators receive a reward of $+1$. Surprisingly, our analysis of this approach reveals an unexpectedly rich diversity of emergent behaviors for both prey and predators, including flocking and swirling behaviors for prey, as well as dispersion tactics, confusion, and marginal predation phenomena for predators. Overall, our study provides novel insights into the collective behavior of organisms and highlights the potential applications in swarm robotics

Essays on Financial Institutions:

Thesis advisor: Rui AlbuquerqueThesis advisor: Philip StrahanMy dissertation aims to understand the economic determinants of the forbearance behavior of financial institutions and their cross section of equity returns. It contains three chapters. Chapter One shows that higher capital requirements create a regulatory arbitrage incentive for banks to forbear on loans suboptimally. I develop a dynamic bank model with a capital requirement, where a bank can roll over bad loans without reducing their face value. When the capital constraint binds, banks hold excess non-performing loans (NPLs) and reduce the credit supply. I solve the model globally with occasionally binding capital constraints and calibrate the model to the pre-crisis banking sector in both the US and Italy. The model quantitatively explains about two-thirds of the difference in NPL ratios in the two countries following a simulated recession. I provide direct causal evidence of the effects of the capital constraint channel on banks’ NPL holdings using the Euro Area crises, supporting the predictions the model generates. Chapter Two studies the information externality of banks’ forbearance behavior in a sequential game with incomplete information. Follower banks observe less liquidation in the market due to leader’s forbearance and take it as a false positive signal of the aggregate state, leading to more forbearance and zombie firms. This chapter shows that the size of the externality decreases with the prior belief of the aggregate state of the economy being good. In other words, my model predicts a higher probability of bank herding in suboptimal forbearance during bad times. Chapter Three constructs a dynamic disaster model with implicit government guarantee to explain the hump shape relation between bank size and stock returns. The model shows two opposing effects on the bank expected returns. Lower cost of debt induces more risk shifting behavior of larger banks while the safety net effect provides insurance to equity investors during market downturns. A size threshold increasing with disaster probability determines which effect dominates, thus contributing to the hump shape relation.Thesis (PhD) — Boston College, 2022.Submitted to: Boston College. Carroll School of Management.Discipline: Finance

Control and Navigation of Multi-Vehicle Systems Using Visual Measurements

Ph.DDOCTOR OF PHILOSOPH