Second-order Consensus Protocols in Multiple Vehicle Systems with Local Interactions

Abstract

In this paper, a distributed coordination scheme with local interactions is studied for multiple vehicle systems. We introduce a second-order consensus protocol and derive necessary and/or sufficient conditions under which consensus can be reached in the context of uni-directional interaction topologies. The consensus protocol is then applied to achieve altitude alignment among a team of micro air vehicles as an illustrative example. Nomenclature h Altitude, m λ * Autopilot parameters κ * Autopilot parameters Subscript i Variable number Superscript c Command

Discrete double integrator consensus

“…This work is similar to [7], [10], [14] except here we use discrete time models and extensively use matrix spectral analysis. The paper is organized as follows.…”

“…Because, all the elements of P have a modulus less than one the matrix M 2 J 2 V 2 is (discrete-time) stable. [10]) Assuming the graph G n has a directed spanning tree and all elements of the set P have a modulus less than one, then the consensus protocol given in (3) will achieve consensus asymptotically.…”

“…If the agents communicate fast enough consensus can be approximated by continuous time models. For second order information states, the stability of continuous time consensus has recently been addressed [7]- [10].…”

Formation control of robotized aerial vehicles based on consensus-based algorithms

“…Consensus algorithms have recently been studied extensively in the context of cooperative control of multiple autonomous vehicles [3][4][5], while our attention is oriented toward consensus based formation control [6][7]. Notice that in the literature, most consensus algorithms consider the case where the communicating/cooperating vehicles come to consensus about the value of the consensus variable.…”

“…In this case, coefficient a ij can be omitted, because the coefficient is always equal to 1, except for the case when i = jcoefficient is 0. Similarly, second order consensus [3] (consensus by position and velocity of every quadrotor) is defined by the following equation:…”