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 proposed game-theoretic navigation algorithm 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, corridor intersection, roundabout, and hallway scenario. We show that $(i)$ our approach results in safer and more efficient navigation compared to local planners based on geometrical constraints, optimization, multi-agent reinforcement learning, and auctions, $(ii)$ our deadlock resolution strategy is the smoothest in terms of smallest average change in velocity and path deviation, and most efficient in terms of makespan $(iii)$ our approach yields a flow rate of $2.8 - 3.3$ (ms)$^{-1}$ which is comparable to flow rate in human navigation at $4$ (ms)$^{-1}$.

翻译：我们提出了一种方法，以确保在受限环境（包括门道和交叉口）中运行的分散式多机器人系统实现安全且无死锁的导航。尽管已有许多解决方案确保安全性，但在分散式框架下通过全局共识防止死锁仍是一个开放问题。我们首先将目标形式化为受约束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，并将其称为"社交小游戏"。我们的存活保障方法基于两个关键洞见：（i）存在一种混合策略纳什均衡，使分散式机器人能够将其状态扰动至"存活集"——即机器人无死锁的状态；（ii）存活集的前向不变性可通过类似控制障碍函数（CBF）保证安全集前向不变性的方式实现。我们在仿真以及物理机器人（使用F$1/10$机器人、Clearpath Jackal和波士顿动力Spot）上评估了所提出的博弈论导航算法，场景包括门道、走廊交叉口、环岛和走廊。实验表明：（i）与基于几何约束、优化、多智能体强化学习和拍卖的局部规划器相比，我们的方法导航更安全、更高效；（ii）我们的死锁解决策略在速度平均变化及路径偏差最小化方面最为平滑，同时在完工时间指标上效率最高；（iii）我们的方法实现了$2.8 - 3.3$ (ms)$^{-1}$的流量率，与人类导航中$4$ (ms)$^{-1}$的流量率相当。