A Unified Dissertation on Bearing Rigidity Theory

This work focuses on the bearing rigidity theory, namely the branch of knowledge investigating the structural properties necessary for multi-element systems to preserve the inter-units bearings when exposed to deformations. The original contributions are twofold. The first one consists in the definition of a general framework for the statement of the principal definitions and results that are then particularized by evaluating the most studied metric spaces, providing a complete overview of the existing literature about the bearing rigidity theory. The second one rests on the determination of a necessary and sufficient condition guaranteeing the rigidity properties of a given multi-element system, independently of its metric space

On the estimation of atmospheric turbulence layers for AO systems

In current and next generation of ground telescopes, Adaptive Optics (AO) are employed to overcome the detrimental effects induced by the presence of atmospheric turbulence, that strongly affects the quality of data transmission and therefore limits the actual resolution of the overall system. The analysis as well as the prediction of the turbulent phase affecting the light wavefront is therefore of paramount impor- tance to guarantee the effective performance of the AO solution. In this work, a layered model of turbulence is proposed, based on the definition of a Markov-Random-Field whose parameters are determined according to the turbulence statistics. The problem of turbulence estimation is formalized within the stochastic framework and conditions for the identifiability of the turbulence structure (numbers of layers, energies and velocities) are stated. Finally, an algorithm to allow the layer detection and characterization from measurements is designed. Numerical simulations are used to assess the proposed procedure and validate the results, confirming the validity of the approach and the accuracy of the detection

Optimal Time-Invariant Distributed Formation Tracking for Second-Order Multi-Agent Systems

This paper addresses the optimal time-invariant formation tracking problem with the aim of providing a distributed solution for multi-agent systems with second-order integrator dynamics. In the literature, most of the results related to multi-agent formation tracking do not consider energy issues while investigating distributed feedback control laws. In order to account for this crucial design aspect, we contribute by formalizing and proposing a solution to an optimization problem that encapsulates trajectory tracking, distance-based formation control, and input energy minimization, through a specific and key choice of potential functions in the optimization cost. To this end, we show how to compute the inverse dynamics in a centralized fashion by means of the Projector-Operator-based Newton's method for Trajectory Optimization (PRONTO) and, more importantly, we exploit such an offline solution as a general reference to devise a novel online distributed control law. Finally, numerical examples involving a cubic formation following a straight path in the 3D space are provided to validate the proposed control strategies.Comment: 28 pages, 2 figures, submitted to the European Journal of Control on June 23rd, 2023 (version 1

Quaternion-based non-singular terminal sliding mode control for a satellite-mounted space manipulator

In this paper, a robust control solution for a satellite equipped with a robotic manipulator is presented. First, the dynamic model of the system is derived based on quaternions to describe the evolution of the attitude of the base satellite. Then, a non-singular terminal sliding mode controller that employs quaternions for attitude control, is proposed for concurrently handling all the degrees of freedom of the space manipulator. Moreover, an additional adaptive term is embedded in the controller to estimate the upper bounds of disturbances and uncertainties. The result is a resilient solution able to withstand unmodelled dynamics and interactions. Lyapunov theory is used to prove the stability of the controller and numerical simulations allow assessing performance and fuel efficiency

Newton-Raphson Consensus for Distributed Convex Optimization

We address the problem of distributed uncon- strained convex optimization under separability assumptions, i.e., the framework where each agent of a network is endowed with a local private multidimensional convex cost, is subject to communication constraints, and wants to collaborate to compute the minimizer of the sum of the local costs. We propose a design methodology that combines average consensus algorithms and separation of time-scales ideas. This strategy is proved, under suitable hypotheses, to be globally convergent to the true minimizer. Intuitively, the procedure lets the agents distributedly compute and sequentially update an approximated Newton- Raphson direction by means of suitable average consensus ratios. We show with numerical simulations that the speed of convergence of this strategy is comparable with alternative optimization strategies such as the Alternating Direction Method of Multipliers. Finally, we propose some alternative strategies which trade-off communication and computational requirements with convergence speed.Comment: 18 pages, preprint with proof

A Proximal Point Approach for Distributed System State Estimation

System state estimation constitutes a key problem in several applications involving multi-agent system architectures. This rests upon the estimation of the state of each agent in the group, which is supposed to access only relative measurements w.r.t. some neighbors state. Exploiting the standard least-squares paradigm, the system state estimation task is faced in this work by deriving a distributed Proximal Point-based iterative scheme. This solution entails the emergence of interesting connections between the structural properties of the stochastic matrices describing the system dynamics and the convergence behavior toward the optimal estimate. A deep analysis of such relations is provided, jointly with a further discussion on the penalty parameter that characterizes the Proximal Point approach.Comment: 6 pages, 2 figures, 1 table, manuscript n 3555, \c{opyright} 2020 the authors. This work has been accepted to IFAC for publication under a Creative Commons Licence CC-BY-NC-N

Adaptive Consensus-based Regulation of Open-Channel Networks

This paper deals with water management over open-channel networks subject to water height imbalance. Specifically, it is devised a fully distributed adaptive consensus-based algorithm within the discrete-time domain capable of (i) providing a suitable tracking reference that stabilizes the water increments over the underlying network at a common level; (ii) coping with general flow constraints related to each channel of the considered system. This iterative procedure is derived by solving a guidance problem that guarantees to steer the regulated network - represented as a closed-loop system - while satisfying requirements (i) and (ii), provided that a suitable design for the local feedback law controlling each channel flow is already available. The proposed solution converges exponentially fast towards the average consensus without violating the imposed constraints over time. In addition, numerical results are reported to support the theoretical findings, and the performance of the developed algorithm is discussed in the context of a realistic scenario.Comment: 13 pages, 5 figures, submitted to IEEE Access (version 1

Distributed Fault Detection in Sensor Networks via Clustering and Consensus

In this paper we address the average consensus problem in a Wireless Sensor-Actor Network with the particular focus on autonomous fault detection. To this aim, we design a distributed clustering procedure that partitions the network into clusters according to both similarity of measurements and communication connectivity. The exploitation of clustering techniques in consensus computation allows to obtain the detection and isolation of faulty nodes, thus assuring the convergence of the other nodes to the exact consensus value. More interestingly, the algorithm can be integrated into a Kalman filtering framework to perform distributed estimation of a dynamic quantity in presence of faults. The proposed approach is validated through numerical simulations and tests on a real world scenario dataset