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 to ensure safety, preventing deadlocks in a decentralized fashion with global consensus 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 \emph{social mini-games}. Our approach to ensuring liveness rests on two novel insights: $(i)$ there exists a mixed-strategy Nash equilibrium that allows decentralized robots to perturb their state onto \textit{liveness sets} i.e. states where robots are deadlock-free and $(ii)$ forward invariance of liveness sets can be achieved identical to how control barrier functions (CBFs) guarantee forward invariance of safety sets. 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 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（包括门道和交叉路口）中运行的分散式多机器人系统的安全与无死锁导航。尽管已有许多保障安全性的方案被提出，但在缺乏全局共识的分散式框架下预防死锁仍是一个未解决的问题。我们首先将目标形式化为一个在受限空间中存在多个冲突智能体的非合作、非通信、部分可观测的多机器人导航问题，并将其定义为“社交小游戏”。我们的活跃性保障方法基于两个新见解：（i）存在混合策略纳什均衡，允许分散式机器人将其状态扰动至“活跃性集合”——即机器人处于无死锁状态；（ii）活跃性集合的前向不变性可通过与控制障碍函数（CBF）保障安全集合前向不变性相同的方式实现。我们在仿真及实体机器人上评估了该方法，使用了F1/10机器人、Clearpath Jackal以及Boston Dynamics Spot，在门道和走廊交叉场景中展开测试。与具有和不具有死锁解决能力的完全分散式及集中式方法相比，我们通过成功率、碰撞率、停止时间、速度变化、路径偏移、到达目标时间和流量率等综合指标证明，本方法能够实现更安全、更高效、更平滑的导航。