Multi-Goal Multi-Agent Path Finding via Decoupled and Integrated Goal Vertex Ordering

Abstract

We introduce multi-goal multi agent path finding (MG-MAPF) which generalizes the standard discrete multi-agent path finding (MAPF) problem. While the task in MAPF is to navigate agents in an undirected graph from their starting vertices to one individual goal vertex per agent, MG-MAPF assigns each agent multiple goal vertices and the task is to visit each of them at least once. Solving MG-MAPF not only requires finding collision free paths for individual agents but also determining the order of visiting agent's goal vertices so that common objectives like the sum-of-costs are optimized. We suggest two novel algorithms using different paradigms to address MG-MAPF: a heuristic search-based algorithm called Hamiltonian-CBS (HCBS) and a compilation-based algorithm built using the satisfiability modulo theories (SMT), called SMT-Hamiltonian-CBS (SMT-HCBS).

Optimal and Bounded-Suboptimal Multi-Goal Task Assignment and Path Finding

“…Recent research has developed several improved versions of CBS [21]- [24]. An extended version of CBS has been developed for the case where each agent has multiple pre-assigned goal locations [25]. However, the MAPF problem is insufficient for modelling real-world settings where goal locations are not pre-assigned to agents.…”

Multi-Goal Multi-Agent Pickup and Delivery

“…In LNS-PBS and LNS-wPBS, each agent maintains (1) a dummy endpoint, i.e., an endpoint that it can move to and stay indefinitely at without collisions (initially, this dummy endpoint is its start location), (2) a task sequence, that consists of the uncompleted tasks that it has to execute, (3) a corresponding goal sequence, that consists of all goal locations of the tasks in its task sequence plus its dummy endpoint at the end, and (4) a path, that moves the agent from its current location through all locations in its goal sequence without collisions. Algorithm 1 without the blue parts (i.e., Lines [6][7][8]) shows how LNS-PBS works. Many of its steps (not shown in the pseudo-code but introduced later), including the use of dummy endpoints, the strategy of which unexecuted tasks can be assigned to agents, and the modification of PBS, are designed to ensure its completeness.…”

“…We will explain Lines [3], [4], and [5] in Sections IV-A, IV-B, and IV-C, respectively. We will prove the completeness of LNS-PBS for well-formed MG-MAPD instances in Section IV-D and finally introduce LNS-wPBS (i.e., Lines [6][7][8]) in Section IV-E.…”

“…In addition, there is some work that focuses only on the path-finding part of the MAPD problem. For instance, Surynek [6] proposes the optimal Multi-Goal MAPF algorithms HCBS and SMT-HCBS for planning collision-free paths for a set of goal locations (where the ordering of the goal locations is not specified). However, these algorithms solve only one-shot problems where each agent has only one task, and their scalability is limited.…”

“…tasks) (seq. goals) (well-formed) CENTRAL [1] TA-Hybrid [4] HBH+MLA* [3] RMCA [5] (SMT-)HCBS [6] N/A RHCR [7] LNS-PBS LNS-wPBS window for the windowed MAPF algorithm. Empirically, LNS-PBS and LNS-wPBS often yield smaller service times than state-of-the-art MAPD algorithms, and LNS-wPBS scales to thousands of agents and thousands of tasks in a large warehouse.…”