Multi-Agent Pathfinding with Non-Unit Integer Edge Costs via Enhanced Conflict-Based Search and Graph Discretization

Multi-Agent Path Finding (MAPF) seeks collision-free paths for multiple agents from their respective start locations to their respective goal locations while minimizing path costs. Most existing MAPF algorithms rely on a common assumption of synchronized actions, where the actions of all agents start at the same time and always take a time unit, which may limit the use of MAPF planners in practice. To get rid of this assumption, Continuous-time Conflict-Based Search (CCBS) is a popular approach that can find optimal solutions for MAPF with asynchronous actions (MAPF-AA). However, CCBS has recently been identified to be incomplete due to an uncountably infinite state space created by continuous wait durations. This paper proposes a new method, Conflict-Based Search with Asynchronous Actions (CBS-AA), which bypasses this theoretical issue and can solve MAPF-AA with completeness and solution optimality guarantees. Based on CBS-AA, we also develop conflict resolution techniques to improve the scalability of CBS-AA further. Our test results show that our method can reduce the number of branches by up to 90%.

Multi-Agent Path Finding (MAPF) is the problem of planning conflict-free paths for multiple agents in a shared space, each from its start to its goal. Classical MAPF has been the dominant formulation for many years, with its assumptions of discrete time and graph-based conflicts presumably easing the search for solutions. These assumptions limit the physical environments and agents for which a solution is truly collision-free, and also place an upper bound on solution quality that no algorithmic improvements can lift. This work investigates how much solution quality, and in what contexts, the classical MAPF formulation forfeits. Continuous-time MAPF (MAPF$_R$) relaxes these assumptions, making it a natural counter-formulation to compare against across various agent counts and sizes, and graph connectedness, topologies, and resolutions. We find that continuous time and agent shape consideration are worth relatively little on their own; their value comes from enabling an expanded range of move actions, on average improving solution quality by at least $5\%$ on narrow and constrained maps and $17\%$ on maps with open spaces. In some cases, the improvements exceed $20\%$. Doubling the map resolution with classical MAPF recovers less than $3\%$, meaning that little of what is forfeited can be bought back through more compute. This work therefore provides insight on when classical MAPF is a reasonable simplification, and when MAPF$_R$ unlocks significantly higher-quality solutions.

Many research fields share a common structure: a set of agents, each pursuing its own goal, whose actions must be coordinated so that no two of them conflict. Multi-Agent Path Finding (MAPF) is a concrete instance of this structure, with applications from warehouses to road traffic and airports. Much of MAPF research assumes discrete time, circular agents sharing one spatial graph, a single goal per agent, and that an agent must remain at its goal once reached, precluding heterogeneous fleets, non-geometric conflicts, task sequences, and agents that move on after completing them. We generalise the MAPF formulation to lift these assumptions, and present Anytime-Optimal Continuous-time Conflict-Based Search (AOC-CBS), an exact and solution-complete solver for it. AOC-CBS guarantees the eventual return of an optimal solution, while reporting an incumbent with a known optimality gap upper bound throughout its runtime; it is configurable with a portfolio of repair functions, one of which we introduce (Tier-Prioritized Safe Interval Path Planning), and can exploit multiple processor cores. We demonstrate AOC-CBS on a mixed fleet of non-convex agents moving along smooth, kinodynamically feasible trajectories. Preliminary experiments against the exact solver OC-CBS, on well-known benchmarks and roadmaps we sample from them, show AOC-CBS is comparable at finding optimal solutions while extending scalability from the tens to the hundreds of agents when a bounded optimality gap is accepted.