This paper presents a cooperative form of distributed robust model predictive control that is used for multi-vehicle trajectory optimization. The overall goal is to develop an approach that solves small subproblems but minimizes a fleet-level objective. In this new algorithm, vehicles solve their subproblems in sequence, while simultaneously generating feasible perturbations to the decisions of the other vehicles. In order to avoid reproducing the global optimization, the decisions of other vehicles are parameterized using a much smaller number of variables than in the centralized formulation. The resulting algorithm is shown to be robustly feasible under the action of unknown but bounded disturbances and monotonically decreases the fleet objective while cycling through the vehicles in the fleet and over the time. Simulation results demonstrate the proposed algorithm can improve the fleet objective by temporarily sacrificing on the individual objective.