A standing challenge in multirobot systems is to realize safe and efficient motion planning and coordination methods that are capable of accounting for uncertainties and contingencies. The challenge is rendered harder by the fact that robots may be heterogeneous and that their plans may be posted asynchronously. Most existing approaches require constraints on the infrastructureor unrealistic assumptions on robot models. In this article, we propose a centralized, loosely-coupled supervisory controller that overcomes these limitations. The approach responds to newly posed constraints and uncertainties during trajectory execution, ensuring at all times that planned robot trajectories remain kinodynamically feasible, that the fleet is in a safe state, and that there are no deadlocks or livelocks. This is achieved without the need for hand-coded rules, fixed robot priorities, or environment modification. We formally state all relevant properties of robot behavior in the most general terms possible, without assuming particular robot models or environments, and provide both formal and empirical proof that the proposed fleet control algorithms guarantee safety and liveness.