  This paper addresses the design of an optimization-based cooperative
path-following control law for multiple robotic vehicles that optimally
balances the transient trade-off between coordination and path-following
errors. To this end, we formulate a more general multi-agent framework where
each agent is associated with (i) a continuous-time dynamical model, which
governs the evolution of its state, and (ii) an output equation that is a
function of both the state of the agent and a coordination vector. According to
a given network topology, each agent can access its state and coordination
vector, as well as the coordination vectors of the neighboring agents. In this
setup, the goal is to design a distributed control law that steers the output
signals to the origin, while simultaneously driving the coordination vectors of
the agents of the network to consensus. To solve this, we propose a model
predictive control scheme that builds on a pre-existing auxiliary consensus
control law to design a performance index that combines the output regulation
objective with the consensus objective. Convergence guarantees under which one
can solve this coordinated output regulation problem are provided. Numerical
simulations display the effectiveness of the proposed scheme applied to a
cooperative path following control problem of a network of 3D nonholonomic
robotic vehicles.
