In the near future mobile robots, such as personal robots or mobile manipulators, will share the workspace with other robots and humans. We present a method for mission and motion planning that applies to small teams of robots performing a task in an environment with moving obstacles, such as humans. Given a mission specification written in linear temporal logic, such as patrolling a set of rooms, we synthesize an automaton from which the robots can extract valid strategies. This centralized automaton is executed by the robots in the team at runtime, and in conjunction with a distributed motion planner that guarantees avoidance of moving obstacles. Our contribution is a correct-by-construction synthesis approach to multi-robot mission planning that guarantees collision avoidance with respect to moving obstacles, guarantees satisfaction of the mission specification and resolves encountered deadlocks, where a moving obstacle blocks the robot temporally. Our method provides conditions under which deadlock will be avoided by identifying environment behaviors that, when encountered at runtime, may prevent the robot team from achieving its goals. In particular, (1) it identifies deadlock conditions; (2) it is able to check whether they can be resolved; and (3) the robots implement the deadlock resolution policy locally in a distributed manner. The approach is capable of synthesizing and executing plans even with a high density of dynamic obstacles. In contrast to many existing approaches to mission and motion planning, it is scalable with the number of moving obstacles. We demonstrate the approach in physical experiments with walking humanoids moving in 2D environments and in simulation with aerial vehicles (quadrotors) navigating in 2D and 3D environments.@en