Generalized Target Assignment and Path Finding Using Answer Set Programming

Multi-Agent Path Finding (MAPF) deals with teams of agents that need to find collision-free paths from their respective starting locations to their respective goal locations on a graph. This model can be applied to a number of applications (e.g., autonomous warehouse systems (Wurman, D’Andrea, and Mountz 2008)). For example, in an autonomous warehouse system (illustrated by Figure 1), robots (in orange) navigate around a warehouse to pick up inventory pods from their storage locations (in green) and drop them off at designated inventory stations (in purple) in the warehouse. Several extensions of MAPF have been proposed (e.g., combined Target Assignment and Path Finding or TAPF). While TAPF better reflects real-world systems with homogeneous agents, such as our motivating application, it still has a key limitation: It assumes that the number of agents equals the number of tasks to be allocated. In our motivating application, there are typically more tasks than agents. As such, agents have to move towards a new task after completing their current task. Therefore, we propose Generalized TAPF (G-TAPF), a generalization of TAPF that allows the number of tasks to be greater than the number of agents. We also propose a new objective, which better captures more applications including our motivating warehouse application: Each task has an associated deadline that indicates the time at which it must be completed. We also propose use answer set programming (ASP) (Lifschitz 2002) as the general framework for solving the new G-TAPF problems.