This thesis addresses a multi-agent planning problem, where each agent aims to achieve an individual task while avoiding collisions with other agents in the environment. It is assumed that each agent's task is expressed as a Time-Window Temporal Logic (TWTL) specification defined over a 3D environment. A distributed receding horizon algorithm is introduced for online planning of trajectories. Under mild assumptions on the environment topology, the resulting agent trajectories are always safe (collision-free) and lead to the satisfaction of the TWTL specifications or their finite temporal relaxations. Accordingly, each agent is guaranteed to safely achieve its task while avoiding deadlocks. Performance of the proposed algorithm is demonstrated via numerical simulations and through experiments with quadrotors.