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In cooperative multi-agent robotic systems, coordination is necessary inorder to complete a given task. Important examples include search and rescue,operations in hazardous environments, and environmental monitoring.Coordination, in turn, requires simultaneous satisfaction of safety criticalconstraints, in the form of state and input constraints, and a connectivityconstraint, in order to ensure that at every time instant there exists acommunication path between every pair of agents in the network. In this work,we present a model predictive controller that tackles the problem of performingmulti-agent coordination while simultaneously satisfying safety critical andconnectivity constraints. The former is formulated in the form of state andinput constraints and the latter as a constraint on the second smallesteigenvalue of the associated communication graph Laplacian matrix, also knownas Fiedler eigenvalue, which enforces the connectivity of the communicationnetwork. We propose a sequential quadratic programming formulation to solve theassociated optimization problem that is amenable to distributed optimization,making the proposed solution suitable for control of multi-agent roboticssystems relying on local computation. Finally, the effectiveness of thealgorithm is highlighted with a numerical simulation.

Multi-agent Distributed Model Predictive Control with Connectivity Constraint