A Distributed Algorithm for the Assignment of the Laplacian Spectrum for Path Graphs

In this paper, we bring forward a distributed algorithm for the assignment of a prescribed Laplacian spectrum for path graphs by means of asymmetric weight assignment. We first describe the meaningfulness and the relevance of this mathematical setting in modern technological applications, and some examples are reported, revealing its practical usefulness in a variety of applications. Then, the solution is derived both theoretically and through an algorithm. Special attention is devoted to a distributed implementation of the main algorithm, which is a valuable feature for several modern applications. Finally, the positivity is discussed, which is revealed to be a consequence of the strict interlacing property

On thruster allocation, fault detection and accomodation issues for underwater robotic vehicles

The use of mono-directional thrusters on under- water vehicle poses interesting issues on actuator allocation, fault detection and accommodation. Preliminary results relative to the horizontal motion of an unhabited underwater vehicle (UUV) are presented

On Planning Smooth Paths for Marine Vehicles

The issue of designing smooth planar paths with maximum curvature and curvature derivative constraints is addressed. The proposed solution can be used to build C^infty class reference paths for marine vehicles linking a set of via points while guaranteeing bounded curvature and curvature derivative

Observability and reachability of grid graphs via reduction and symmetries

In this paper we investigate the observability and reachability properties of a network system, running a Laplacian based average consensus algorithm, when the communication graph is a grid. More in detail, we characterize the structure of the grid eigenvectors by means of suitable decompositions of the graph. For each eigenvalue, based on its multiplicity and on suitable symmetries of the corresponding eigenvectors, we provide necessary and suf\ufb01cient conditions to characterize all and only the nodes from which the network system is observable (reachable). We discuss the proposed criteria and show, through suitable examples, how such criteria reduce the complexity of the observability (respectively reachability) analysis of the grid

Observability and Reachability of Simple Grid and Torus Graphs

In this paper we investigate the observability and reachability properties of a network system, running a Laplacian based average consensus algorithm, when the communication graph is a grid or a torus. More in detail, under suitable conditions on the eigenvalue multiplicity, we provide necessary and sufficient conditions, based on simple algebraic rules from number theory, to characterize all and only the nodes from which the network system is observable (reachable). For any set of observation (leader) nodes, we provide a closed form expression for the unobservable (unreachable) eigenvalues and for the eigenvectors of the unobservable (unreachable) subsystem