This article presents a new form of robust distributed model predictive control (MPC) for multiple dynamically decoupled subsystems, in which distributed control agents exchange plans to achieve satisfaction of coupling constraints. The new method offers greater flexibility in communications than existing robust methods, and relaxes restrictions on the order in which distributed computations are performed. The local controllers use the concept of tube MPC - in which an optimisation designs a tube for the system to follow rather than a trajectory - to achieve robust feasibility and stability despite the presence of persistent, bounded disturbances. A methodical exploration of the trades between performance and communication is provided by numerical simulations of an example scenario. It is shown that at low levels of inter-agent communication, distributed MPC can obtain a lower closed-loop cost than that obtained by a centralised implementation. A further example shows that the flexibility in communications means the new algorithm has a relatively low susceptibility to the adverse effects of delays in computation and communication.