Decentralized Multi-Robot Social Navigation in Constrained Environments via Game-Theoretic Control Barrier Functions

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)$^{-1}$.