Hybrid Framework for Consensus in Directed and Asynchronous Network of Non-Holonomic Agents

Abstract

Abstract-The paper presents a hybrid systems strategy for consensus (or formation realization) for a fleet of non-holonomic agents. In the proposed model, each agent has a smooth continuous-time dynamics and a piecewise constant impulsive reference. The jumps on the reference trajectory take place at some updating instants that are decided independently by each agent. The jumps computation is based on the relative distance with respect to some time-varying neighbors at the update instants. Between the updates of its reference each robot will track its own constant reference trajectory. Our results provide consensus (formation realization) as far as a minimum dwell-time condition between consecutive updates is satisfied. A numerical example illustrates the theoretical results.

Hybrid formalism for consensus of a general class of multi-agent systems with biased measurements

“…The decentralized strategy proposed in this work results in a hybrid closed-loop dynamics due to the jumping (nonsmooth) references that agents have to track. Basically, we generalize the results in [9], [10] considering a general class of non-linear systems, taking in account the sensor noise and developing a completely decentralised policy for the choice of the dwell-time between two consecutive communications. We also notice that a similar strategy has been used in [1] to solve the consensus problem for a general class of discretetime nonlinear dynamics.…”

“…This is the case if we consider dynamics (1) with r i = 0 and f i = ϕ i . It is also noteworthy that non-holonomic dynamics satisfy Assumptions 1-2 for what concerns the x−y 2D positioning errors as it has been studied in [10] and [9].…”

“…for the N interconnected hybrid systems (7)-(8) with the chosen decentralized control (9). The set in (10) requires that each agent reaches its own reference (e = 0) and that all the references achieve consensus over all the n components (∆ = 0).…”

“…We start by investigating the behavior of the discrete part of the hybrid system (8). Moreover, by rewriting the jump dynamics (9) in terms of r i and e i one obtains for t k ∈ T…”

Practical consensus tracking control of multiple nonholonomic wheeled mobile robots in polar coordinates

“…27,28 Due to the nonholonomic constraints, the design of cooperative tracking scheme for MNWMRs becomes more challenging than their single-robot counterparts in particular when the communication interactions among the networked robots are taken into account with an increase of group size. [29][30][31] However, the current research on consensus or formation tracking control for MNWMRs is mainly focused on designing kinematic controller, 32,33 and thus the existing analysis under Cartesian coordinate framework cannot be straightforwardly applied to such a collective motion case because of the complexity of multiple rotating deployment. For practical reasons, 27 it is necessary to develop a novel unified distributed algorithm for cooperative distributed consensus tracking of MNWMRs by systematically integrating both kinematic controller and dynamic controller.…”