Efficient Multi Agent Path Finding with Turn Actions

Q: What is the impact of redundant nodes in high-level search?

Redundant nodes in high-level search, such as N 1001 and N 101 in Figure 4, generate the same splitting constraints, leading to redundant exploration efforts. This redundancy can be eliminated by identifying subsuming nodes, where N 1 subsumes N 2 if N 2 is a sub-problem of N 1. By removing subsumed nodes, the number of expansions in target follow-up problems can be significantly reduced. The novel method presented in this section can be used in CBS and CBS T to prune high-level search nodes, enhancing the efficiency of the search process.

Q: How does pruning reduce CT tree size?

Pruning reduces CT tree size by creating nodes that can subsume or be subsumed by others. Current pruning relies on chance, but the proposed method prioritizes conflicts that have been resolved before, increasing the likelihood of subsumption. This prioritization is based on cardinality and previous conflict resolutions. By choosing conflicts more likely to lead to pruning, the CT tree size can be significantly reduced, improving runtime efficiency of the algorithm.

Q: What are the domains used in the experiments and how are the number of agents determined for each map?

The experiments were conducted on six different maps in different domains using grid-based MAPF benchmarks from Stern et al. (2019). The domains include random-32-32-20 (Random), warehouse-10-20-10-2-1 (Warehouse), empty-32-32 (Empty), room-64-64-16 (Room), Paris 1 256 (City), and den520d (Game). For each map, all 25 random scenario files from the benchmark sets were used. The number of agents started at 10 for the Room map, increasing by 1, and for the other 5 maps, it started at 10, increasing by 5. For each number of agents, all 25 instances were solved. The start and target direction were assigned to be North for each instance to ensure replicability.

Question

1. How can MAPF T be solved optimally?

2. What is the objective of MAPF T problem?

3. What is CBS in MAPF?

4. How does Multi-Valued Decision Diagrams (MDD) identify conflict types in CBS?

Accepted Answer

In this paper, we study optimal MAPF with Turn actions (MAPF T ), where we model turning as a separate unit-cost action. Although the problem has previously appeared in the literature, to the best of our knowledge, this is the first approach that solves it optimally. We adapt and generalize CBSH2-RTC (Li et al. 2021), a state-of-the-art optimal MAPF algorithm, to CBS T (CBS T ) to solve MAPF T. We show that MAPF T is substantially more challenging than MAPF. We then describe how to adapt a range of recent enhancements, originally developed for MAPF, to improve its performance. Finally, we show that CBS T can generate new types of redundant high-level nodes, ones that define sub-problems appearing elsewhere in the search tree. We introduce a novel pruning approach, based on logical subsumption, which detects and eliminates these nodes. Experimental results indicate this approach can avoid substantial amounts of duplicated work and we report convincing runtime improvements for CBS T.

Accepted Answer

The objective of MAPF T problem is to find a feasible solution with the minimal sum of individual costs of agents. This involves transiting the given set of agents from their start vertex, start orientation to goal vertex, goal orientation without any conflict. The solution aims to minimize the total time taken by all agents to reach their respective goal states, ensuring efficient navigation and coordination among the agents in the undirected gridmap environment.

Accepted Answer

CBS (Sharon et al. 2015) is a two-level search algorithm for optimal MAPF. At the low level, it invokes a single-agent search algorithm considering time and space dimensions to find optimal paths for each agent. At the high level, CBS performs best-first search on a constraint tree (CT) to maintain a priority queue of unexplored nodes. It selects nodes with the lowest cost to expand first. CBS generates the root node from the initial low-level search and resolves conflicts between agents by generating two successors, adding constraints, and replanning. It iteratively selects candidates, splits nodes, and inserts them into the priority queue until no conflicts are found. Adapting CBS to MAPF involves modifications to the state and graph expansions based on the MAPF action model. However, the size of the CT can be exponential in the depth of the optimal plan, affecting performance. Recent enhancements have been developed to improve CBS's performance.

Accepted Answer

Multi-Valued Decision Diagrams (MDD) in CBS identify conflict types by representing all optimal paths subject to constraints in a rooted directed graph. Each location reached at a timestep on an optimal path is represented by an MDD node at depth t. If a constraint prevents a node from being at a specific location, all current optimal paths become infeasible, resulting in a cost increase. MDDs in CBS work similarly to CBS, but with modifications such as paths from modified low-level search, recording state (v, t, th) in MDD nodes, and counting the number of MDD nodes at a given depth to identify cardinal conflicts. However, this method may fail to identify some cardinal conflicts.

Accepted Answer

Follow-up conflicts in target reasoning occur when new conflicts are found between the same pair of agents after applying constraints to resolve a conflict between two agents. Unlike in MAPF, target conflict resolution may not prevent follow-up conflicts at the target. In target reasoning, two disjoint length constraints are generated to resolve the target conflict. For example, if agent a j reaches its goal g j at timestep t j and stays there forever, while agent a i visits g j at timestep t i (t i >= t j), the usual constraints applied to resolve this conflict are (1) l j > t i and (2) l j <= t i. Figure 2 (a) illustrates a follow-up conflict in target reasoning. The target conflict occurs at vertex D2 at timestep t = 3. Resolving the target conflict requires more conflicts to be resolved, and if not careful, the conflict at D2 at time 3 may be resolved in the same way as before. This frequently happens when the shortest paths of two agents are in the same row. An initial constraint on root and running CBS T with target reasoning is given, and the branch with orange nodes leads to the optimal solution. The constraints shown in red illustrate that different nodes encounter the same sub-problem and generate the same constraints. This highlights the impact of follow-up problems on solving time and CT node expansions. In the CT tree, some constraints added in CT nodes may be redundant, leading to unexpected expansions in target follow-up conflicts. A pruning method is further developed to reduce redundant expansions.

Accepted Answer

Redundant nodes in high-level search, such as N 1001 and N 101 in Figure 4, generate the same splitting constraints, leading to redundant exploration efforts. This redundancy can be eliminated by identifying subsuming nodes, where N 1 subsumes N 2 if N 2 is a sub-problem of N 1. By removing subsumed nodes, the number of expansions in target follow-up problems can be significantly reduced. The novel method presented in this section can be used in CBS and CBS T to prune high-level search nodes, enhancing the efficiency of the search process.

Accepted Answer

Pruning reduces CT tree size by creating nodes that can subsume or be subsumed by others. Current pruning relies on chance, but the proposed method prioritizes conflicts that have been resolved before, increasing the likelihood of subsumption. This prioritization is based on cardinality and previous conflict resolutions. By choosing conflicts more likely to lead to pruning, the CT tree size can be significantly reduced, improving runtime efficiency of the algorithm.

Accepted Answer

The experiments were conducted on six different maps in different domains using grid-based MAPF benchmarks from Stern et al. (2019). The domains include random-32-32-20 (Random), warehouse-10-20-10-2-1 (Warehouse), empty-32-32 (Empty), room-64-64-16 (Room), Paris 1 256 (City), and den520d (Game). For each map, all 25 random scenario files from the benchmark sets were used. The number of agents started at 10 for the Room map, increasing by 1, and for the other 5 maps, it started at 10, increasing by 5. For each number of agents, all 25 instances were solved. The start and target direction were assigned to be North for each instance to ensure replicability.

Efficient Multi Agent Path Finding with Turn Actions

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Most frequently asked questions

1. How can MAPF T be solved optimally?

2. What is the objective of MAPF T problem?

3. What is CBS in MAPF?

4. How does Multi-Valued Decision Diagrams (MDD) identify conflict types in CBS?

5. How do follow-up conflicts arise in target reasoning?

6. What is the impact of redundant nodes in high-level search?

7. How does pruning reduce CT tree size?

8. What are the domains used in the experiments and how are the number of agents determined for each map?

Citations

Scaling Lifelong Multi-Agent Path Finding to More Realistic Settings: Research Challenges and Opportunities

Multi-Agent Path Finding with Real Robot Dynamics and Interdependent Tasks for Automated Warehouses

References

A multiagent approach to autonomous intersection management

Conflict-based search for optimal multi-agent pathfinding

Conflict-based search for optimal multi-agent path finding

Cooperative pathfinding

Multi-Agent Pathfinding: Definitions, Variants, and Benchmarks

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