Distributed event-triggered control strategies for multi-agent formation stabilization and tracking

Abstract

This paper addresses the problem of formation control and tracking a of desired trajectory by an Euler-Lagrange multi-agent systems. It is inspired by recent results by Qingkai et al. and adopts an event-triggered control strategy to reduce the number of communications between agents. For that purpose, to evaluate its control input, each agent maintains estimators of the states of its neighbour agents. Communication is triggered when the discrepancy between the actual state of an agent and the corresponding estimate reaches some threshold. The impact of additive state perturbations on the formation control is studied. A condition for the convergence of the multi-agent system to a stable formation is studied. The time interval between two consecutive communications by the same agent is shown to be strictly positive. Simulations show the effectiveness of the proposed approach.Distributed cooperative control of a multi-agent system (MAS) usually requires significant exchange of information between agents. In early contributions, see, e.g., [25,39], communication was considered permanent. Recently, more practical approaches have been proposed. For example, in [40,41,42], communication is intermittent, alternating phases of permanent communication and of absence of communication. Alternatively, communication may only occur at discrete time instants, either periodically as in [13], or triggered by some event, as in [9,11,46,37]. This paper proposes a strategy to reduce the number of communications for displacement-based formation control while following a desired reference trajectory. Agent dynamics are described by Euler-Lagrange models and include perturbations. This work extends results presented in [44] by introducing an event-triggered strategy, and results of [19,33,34] by addressing systems with more complex dynamics than a simple integrator. To obtain efficient distributed control laws, each agent uses an estimator of the state of the other agents. The proposed distributed communication triggering condition (CTC) involves the inter-agent displacements and the relative discrepancy between actual and estimated agent states. A single a priori trajectory has to be evaluated to follow the desired path. Effect of state perturbations on the formation and on the communications are analyzed. Conditions for the Lyapunov stability of the MAS have been introduced. The time interval between two consecutive communications by the same agent is shown to be strictly positive.This paper is organized as follows. Related work is detailed in Section 2. Some assumptions are introduced in Section 3 and the formation parametrization is described in Section 4. As the problem considered here is to drive a formation of agents along a desired reference trajectory, the designed distributed control law consists of two parts. The first part (see Section 4) drives the agents to some target formation and maintains the formation, despite the presence of perturbations. It is based on estimates of the states of the agents described in Section 5.1...

Distributed event-triggered formation control for multi-agent systems in presence of packet losses

“…As soon as a function of the error between this estimate and xi reaches some threshold, Agent i triggers a communication to allow its neighbors to refresh their estimate of xi. The main difficulty, compared to [19,21], lies in the fact that estimators have to account for packet losses. In the solution proposed here, each Agent maintains several estimates of its own state accounting for different packet loss hypotheses, and an estimate of the state of its neighbors with the last information received.…”

“…The estimate qj i of the state of Agent i, evaluated by Agent j, only depends on the information provided by Agent i. The estimate qj i is reset to qi as soon as a message sent by Agent i is received by Agent j, see (21). Consequently, when Agent i has sent ki messages, and wants to evaluate an image of its own state as computed by one of its neighbors, ki different hypotheses have to be considered, each of which is associated to a different estimator of qi at time t ∈ [t i,k i , t i,k i +1 [:…”

“…An analysis of the impact of the values of the parameters on the reduction of communications has been presented in [21] in absence of packet losses. These results can be extended to the case with packet losses.…”

“…This paper addresses the distributed formation control of a MAS consisting of agents with nonlinear Euler-Lagrange dynamics, affected by state perturbations, and communications with losses. An event-triggered control strategy is proposed extending that presented in [21] to account for packet losses. Each agent maintains several estimators of its own state to mimic the estimators of its state maintained by its neighbors.…”

“…This reduces the amount of estimators of its own state maintained by each agent. The CTC proposed in [21] is then updated to explicitly account for the potential loss of transmitted packets. The asymptotic convergence of the MAS to the target formation, as well as the absence of Zeno behavior have been proved.…”