Information Flow and Cooperative Control of Vehicle Formations

Abstract

Abstract-We consider the problem of cooperation among a collection of vehicles performing a shared task using intervehicle communication to coordinate their actions. Tools from algebraic graph theory prove useful in modeling the communication network and relating its topology to formation stability. We prove a Nyquist criterion that uses the eigenvalues of the graph Laplacian matrix to determine the effect of the communication topology on formation stability. We also propose a method for decentralized information exchange between vehicles. This approach realizes a dynamical system that supplies each vehicle with a common reference to be used for cooperative motion. We prove a separation principle that decomposes formation stability into two components: Stability of the is achieved information flow for the given graph and stability of an individual vehicle for the given controller. The information flow can thus be rendered highly robust to changes in the graph, enabling tight formation control despite limitations in intervehicle communication capability.

Controlling the Dynamics and Stabilization of the Altitude and Attitude of An Underactuated Tri-rotor UAV

“…The tri-rotor UAV system is a combination of cascades and the complex dynamics of the underactuated system. Due to their complex coupling relationship exists in the system, the design and stability analysis of the vehicle is also quite complex [25]. Initially, the system model decoupled into fully actuated subsystem and an underactuated subsystem.…”

Distributed formation stabilization for mobile agents using virtual tensegrity structures

“…Towards this end, we convert our problem into the sparse null space problem first considered in [26], namely, given a m × n matrix A of rank r, (r ≤ m ≤ n), to find a sparse n × (n − r) matrix B such that B is full rank and its column span is null(A) [27]. We take the transpose of both sides of (6), yielding…”

“…Even though a wide range of issues have been studied, and hence several theoretical frameworks have been established to design control strategies, see, for example, [4] [5] establishing estimation strategy for Euler-Lagrange systems with partial states available, [6] [7] using matrix theory and graph theory, [8] based on gradient-descent control approach, graph rigidity theory [9][10], networked small-gain theory [11], sample-data for circle formation [12], to name a few, it should be noted that the desired formation shape can only be guaranteed to be locally stable in most of the research. In particular, based on the graph rigidity approach, it is challenging to coordinate a group of mobile robots globally converging to the prescribed formation [13].…”

Model reduction of linear multi-agent systems by clustering with $$\varvec{\mathcal {H}_2}$$ H 2 and $$\varvec{\mathcal {H}_\infty }$$ H ∞ error bounds

“…Widely studied topics in networked systems have been the problems of consensus and synchronization, see [19,20,27,30]. Other important subjects in the theory of networked systems are flocking, formation control, sensor placement, and controllability of networks, see, e.g., [8,9,11,12,24,29,34].…”