Multi-Train Path Finding

Abstract

Multi-agent path finding (MAPF) is the problem of moving a set of agents from their individual start locations to their individual goal locations, without collisions. This problem has practical applications in video games, traffic control, robotics, and more. In MAPF we assume that agents occupy one location each time step. However, in real life some agents have different size or shape. Hence, a standard MAPF solution may be not suited in practice for some applications. In this paper, we describe a novel algorithm, based on the CBS algorithm, that finds a plan for moving a set of train-agents, i.e., agents that occupy a sequence of two or more locations, such as trains, buses, planes, or even snakes. We prove that our solution is optimal and show experimentally that indeed such a solution can be found. Finally, we explain how our solution can also apply to agents with any geometric shape.

Multi-Train Path Finding Revisited

“…We compare our approaches to MTPF with the original approach MT-CBS (Atzmon, Diei, and Rave 2019). We compare MT-CBS against three variants of LT-CBS, namely the basic variant LT-CBS defined in Algorithm 1, the strongest variant LT-CBSH-RCT, which uses admissible (H)euristics and symmetry reasoning for (R)ectangles, (C)orridors, and (T)arget conflicts, and a strawman variant LT-CBSH-RCT − , which resolves only ∆-delay conflicts (i.e., ignores occupation and self conflicts) and thus finds optimal kR-MAPF plans.…”

“…Compared to previous models for MTPF (Atzmon, Diei, and Rave 2019) and kR-MAPF (Atzmon et al 2018;Chen et al 2021), which assume that all agents have the same length and robustness guarantee (respectively), our approach allows each agent a i to have an individual value for k i . We also consider three variants of MTPF, each one of which corresponds to a different real-world scenario of different computational difficulty:…”

“…Multi-Train Conflict-Based Search (MT-CBS) (Atzmon, Diei, and Rave 2019) is an algorithm capable of computing optimal MTPF plans. It is a variant of the popular CBS algorithm (Sharon et al 2015) for optimal MAPF.…”

“…Multi-Train Path Finding (MTPF) (Atzmon, Diei, and Rave 2019) is an abstract model for solving these types of problems on a grid or, in general, graph. MTPF is Figure 1: A kR-MAPF plan with no collisions (left) and an MTPF plan with a collision at D at timestep t + 4 (right).…”

Generalized and Sub-Optimal Bipartite Constraints for Conflict-Based Search

“…Completeness is ensured only when the actions blocked by 𝐶 𝑖 are mutually conflicting with all actions blocked by 𝐶 𝑗 . This is known as the mutually disjunctive property [4,21] of constraint sets. Constraint sets are valid iff no solution exists when both agents 𝑖 and 𝑗 violate any constraints 𝑐 𝑖 ∈𝐶 𝑖 and 𝑐 𝑗 ∈𝐶 𝑗 , respectively, simultaneously.…”