Bearing rigidity theory and its applications for control and estimation of network systems: Life beyond distance rigidity

Distributed control and location estimation of multiagent systems have received tremendous research attention in recent years because of their potential across many application domains [1], [2]. The term agent can represent a sensor, autonomous vehicle, or any general dynamical system. Multiagent systems are attractive because of their robustness against system failure, ability to adapt to dynamic and uncertain environments, and economic advantages compared to the implementation of more expensive monolithic systems

Distance-based Control of Kn Formations in General Space with Almost Global Convergence

In this paper, we propose a distance-based formation control strategy for a group of mobile agents to achieve almost global convergence to a target formation shape provided that the formation is represented by a complete graph, and each agent is governed by a single-integrator model. The undamental idea of achieving almost global convergence is to use a virtual formation of which the dimension is augmented with some virtual coordinates. We define a cost function associated with the virtual formation and apply the gradient-descent algorithm to the cost function so that the function has a global minimum at the target formation shape. We show that all agents finally achieve the target formation shape for almost all initial conditions under the proposed control law.This work was supported in part by the Australian Research Council under Grants DP130103610 and DP160104500, and in part by the National Research Foundation of Korea under Grant NRF-2017R1A2B3007034. The work of Z. Sun was supported by the Prime Minister’s Australia Asia Incoming Endeavour Postgraduate Award

Angle rigidity and its usage to stabilize multi-agent formations in 2D

Motivated by the challenging formation stabilization problem for mobile robotic teams wherein no distance or relative position measurements are available but each robot can only measure some of relative angles with respect to its neighbors in its local coordinate frame, we develop the notion of "angle rigidity" for a multi-point framework, named "angularity", consisting of a set of nodes embedded in a Euclidean space and a set of angle constraints among them. Different from bearings or angles defined in a global frame, the angles we use do not rely on the knowledge of a global frame and are signed according to the counter-clockwise direction. Here angle rigidity refers to the property specifying that under proper angle constraints, the angularity can only translate, rotate or scale as a whole when one or more of its nodes are perturbed locally. We first demonstrate that this angle rigidity property, in sharp comparison to bearing rigidity or other reported rigidity related to angles of frameworks in the literature, is not a global property since an angle rigid angularity may allow flex ambiguity. We then construct necessary and sufficient condit

Bearing-only Formation Control of multiple UAVs with an NMPC approach: architectures and methodologies

openUno dei maggior campi di sviluppo e d’innovazione nel nostro secolo riguarda l’ambito della robotica mobile in particolare lo studio del coordinamento di sistemi multi agenti. Questo tipo di tecnologia permette di essere impiegata in ambiti di calamità naturali o situazioni critiche dove i sistemi multi agenti posso operare missioni di search and rescue o monitoraggio ambientale. In campo vengono impiegati veicoli terrestri autonomi UGV (Unmanned Ground Vehicle) e veicoli aerei autonomi UAV(Unmanned Aerial Vehicle) che possono cooperare tra di loro. Gli ambienti esterni presentano diverse problematiche e una di queste può essere la mancanza di accesso alla rete GPS. Per tale motivo si studiano leggi di controllo che non impiegano questo tipo di informazioni come bearing-only formation control dove gli agenti rilevano tra di loro solo angoli relativi, i quali possono essere calcolati tramite una semplice camera 2D. Questo lavoro di tesi ha lo scopo di esplorare la teoria della bearing rigidity applicata a formazioni di agenti omogenei nello specifico quadricotteri sfruttando la tecnologia NMPC con MATMPC. La tesi va ad esplorare le differenze delle diverse architetture in particolare va ad implementare una architettura centralizzata e mette giù le basi per un possibile sviluppo di un’architettura decentralizzata. Il lavoro mostra come è creare il modello per NMPC con diverse varianti del modello dell’agente (come è stato modellizzato), diversi funzionali di costo e diverse formazioni. Per l’implementazione viene usato ROS2 per lo sviluppo dell’intero ecosistema di controllo e viene usata la piattaforma PX4 che mette a disposizione un ottima architettura di controllo a basso livello per la gestione del singolo quadricottero. Inoltre la tesi usa il sistema SITL(Software In The Loop) di PX4 per rendere le simulazioni di Gazebo il più vicine alla realtà.One of the major fields of development and innovation in our century concerns mobile robotics, particularly the study of multi-agent system coordination. This type of technol- ogy can be employed in natural disaster scenarios or critical situations where multi-agent systems can perform search and rescue missions or environmental monitoring. In this field, autonomous ground vehicles (UGVs) and unmanned aerial vehicles (UAVs) are used, which can cooperate with each other. Outdoor environments pose various challenges, and one of these challenges can be the lack of access to GPS network. For this reason, control laws that do not rely on GPS information are studied, such as ”bearing-only formation control,” where agents only perceive relative angles between each other, which can be calculated using a simple 2D camera. The purpose of this thesis work is to explore the theory of bearing rigidity applied to forma- tions of homogeneous agents, specifically quadcopters, using Nonlinear Model Predictive Control (NMPC) with MATMPC. The thesis aims to explore the differences between dif- ferent architectures, particularly by implementing a centralized architecture and laying the groundwork for a possible development of a decentralized architecture. The work demon- strates how to create the model for NMPC with various agent model variants,different cost functions, and different formations. ROS2 is used for the implementation of the entire control ecosystem, and the PX4 platform is used, which provides an excellent low-level control architecture for managing individual quadcopters. Additionally, the thesis utilizes the PX4 Software In The Loop (SITL) system to make Gazebo simulations as close to reality as possible

Dual gauge field theory of quantum liquid crystals in two dimensions

We present a self-contained review of the theory of dislocation-mediated quantum melting at zero temperature in two spatial dimensions. The theory describes the liquid-crystalline phases with spatial symmetries in between a quantum crystalline solid and an isotropic superfluid: quantum nematics and smectics. It is based on an Abelian-Higgs-type duality mapping of phonons onto gauge bosons ("stress photons"), which encode for the capacity of the crystal to propagate stresses. Dislocations and disclinations, the topological defects of the crystal, are sources for the gauge fields and the melting of the crystal can be understood as the proliferation (condensation) of these defects, giving rise to the Anderson-Higgs mechanism on the dual side. For the liquid crystal phases, the shear sector of the gauge bosons becomes massive signaling that shear rigidity is lost. Resting on symmetry principles, we derive the phenomenological imaginary time actions of quantum nematics and smectics and analyze the full spectrum of collective modes. The quantum nematic is a superfluid having a true rotational Goldstone mode due to rotational symmetry breaking, and the origin of this 'deconfined' mode is traced back to the crystalline phase. The two-dimensional quantum smectic turns out to be a dizzyingly anisotropic phase with the collective modes interpolating between the solid and nematic in a non-trivial way. We also consider electrically charged bosonic crystals and liquid crystals, and carefully analyze the electromagnetic response of the quantum liquid crystal phases. In particular, the quantum nematic is a real superconductor and shows the Meissner effect. Their special properties inherited from spatial symmetry breaking show up mostly at finite momentum, and should be accessible by momentum-sensitive spectroscopy.Comment: Review article, 137 pages, 32 figures. Accepted versio

Crystal gravity

We address a subject that could have been analyzed century ago: how does the universe of general relativity look like when it would have been filled with solid matter? Solids break spontaneously the translations and rotations of space itself. Only rather recently it was realized in various context that the order parameter of the solid has a relation to Einsteins dynamical space time which is similar to the role of a Higgs field in a Yang-Mills gauge theory. Such a "crystal gravity" is therefore like the Higgs phase of gravity. The usual Higgs phases are characterized by a special phenomenology. A case in point is superconductivity exhibiting phenomena like the Type II phase, characterized by the emergence of an Abrikosov lattice of quantized magnetic fluxes absorbing the external magnetic field. What to expect in the gravitational setting? The theory of elasticity is the universal effective field theory associated with the breaking of space translations and rotations having a similar status as the phase action describing a neutral superfluid. A geometrical formulation appeared in its long history, similar in structure to general relativity, which greatly facilitates the marriage of both theories. With as main limitation that we focus entirely on stationary circumstances -- the dynamical theory is greatly complicated by the lack of Lorentz invariance -- we will present a first exploration of a remarkably rich and often simple physics of "Higgsed gravity".Comment: 64 pages, 22 figures. The introduction has been revised compared to the first versio