We present an approach to ensure safe and deadlock-free navigation for decentralized multi-robot systems operating in constrained environments, including doorways and intersections. Although many solutions have been proposed that ensure safety and resolve deadlocks, optimally preventing deadlocks in a minimally invasive and decentralized fashion remains an open problem. We first formalize the objective as a non-cooperative, non-communicative, partially observable multi-robot navigation problem in constrained spaces with multiple conflicting agents, which we term as social mini-games. Formally, we solve a discrete-time optimal receding horizon control problem leveraging control barrier functions for safe long-horizon planning. Our approach to ensuring liveness rests on the insight that \textit{there exists barrier certificates that allow each robot to preemptively perturb their state in a minimally-invasive fashion onto liveness sets i.e. states where robots are deadlock-free}. We evaluate our approach in simulation as well on physical robots using F$1/10$ robots, a Clearpath Jackal, as well as a Boston Dynamics Spot in a doorway, hallway, and corridor intersection scenario. Compared to both fully decentralized and centralized approaches with and without deadlock resolution capabilities, we demonstrate that our approach results in safer, more efficient, and smoother navigation, based on a comprehensive set of metrics including success rate, collision rate, stop time, change in velocity, path deviation, time-to-goal, and flow rate.

翻译：我们提出了一种方法，用于确保在受限环境（包括门口和交叉口）中运行的去中心化多机器人系统实现安全且无死锁的导航。尽管已有许多方案被提出以确保安全并解决死锁问题，但以最小侵入性和去中心化的方式最优地预防死锁仍然是一个开放性问题。我们首先将该目标形式化为一个在具有多个冲突智能体的受限空间中的非合作、非通信、部分可观测的多机器人导航问题，我们称之为社交微博弈。形式上，我们通过利用控制屏障函数解决一个离散时间最优滚动时域控制问题，以实现安全的长时域规划。我们确保活性（liveness）的方法基于以下洞见：\textit{存在允许每个机器人以最小侵入方式抢先扰动其状态至活性集（即机器人处于无死锁状态的状态集合）的屏障证书}。我们在仿真中以及使用F$1/10$机器人、Clearpath Jackal以及波士顿动力Spot机器人，在门口、走廊和通道交叉口场景下对我们的方法进行了物理评估。与具备或不具备死锁解决能力的完全去中心化及集中式方法相比，我们基于一套全面的指标（包括成功率、碰撞率、停止时间、速度变化、路径偏差、到达目标时间和流率）证明，我们的方法能实现更安全、更高效且更平滑的导航。