The paper considers the problem of formation path-following of multiple vehicles and proposes a solution based on combining distributed model predictive control with parametrizations of the trajectories of the vehicles using polynomial splines. Introducing such parametrization leads indeed to two potential benefits: a) reducing the number of optimization variables, and b) enabling enforcing constraints on the vehicles in a computationally efficient way. Moreover, the proposed solution formulates the formation path-following problem as a distributed optimization problem that may then be solved using the alternating direction method of multipliers (ADMM). The paper then analyzes the effectiveness of the proposed method via numerical simulations with surface vehicles and differential drive robots
