Distributed safe planning for satisfying minimal temporal relaxations of TWTL specifications

Abstract

We investigate a multi-agent planning problem, where each agent aims to achieve an individual task while avoiding collisions with other agents. Each agent’s task is expressed as a Time-Window Temporal Logic (TWTL) specification defined over a discretized environment. We propose a distributed receding horizon algorithm for online planning of agent trajectories. We show that under mild assumptions on the environment, the resulting trajectories are always safe (collision-free) and lead to the satisfaction of the TWTL specifications or a finite temporal relaxation. Accordingly, each agent is guaranteed to safely achieve its task, possibly with some minimal finite delay. Performance of the proposed algorithm is demonstrated via numerical simulations and experiments with quadrotors.