  In cooperative multi-agent robotic systems, coordination is necessary in
order 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 critical
constraints, in the form of state and input constraints, and a connectivity
constraint, in order to ensure that at every time instant there exists a
communication path between every pair of agents in the network. In this work,
we present a model predictive controller that tackles the problem of performing
multi-agent coordination while simultaneously satisfying safety critical and
connectivity constraints. The former is formulated in the form of state and
input constraints and the latter as a constraint on the second smallest
eigenvalue of the associated communication graph Laplacian matrix, also known
as Fiedler eigenvalue, which enforces the connectivity of the communication
network. We propose a sequential quadratic programming formulation to solve the
associated optimization problem that is amenable to distributed optimization,
making the proposed solution suitable for control of multi-agent robotics
systems relying on local computation. Finally, the effectiveness of the
algorithm is highlighted with a numerical simulation.
