Multi-Agent Combinatorial Path Finding with Heterogeneous Task Duration (2311.15330v2)

Abstract: Multi-Agent Combinatorial Path Finding (MCPF) seeks collision-free paths for multiple agents from their initial locations to destinations, visiting a set of intermediate target locations in the middle of the paths, while minimizing the sum of arrival times. While a few approaches have been developed to handle MCPF, most of them simply direct the agent to visit the targets without considering the task duration, i.e., the amount of time needed for an agent to execute the task (such as picking an item) at a target location. MCPF is NP-hard to solve to optimality, and the inclusion of task duration further complicates the problem. This paper investigates heterogeneous task duration, where the duration can be different with respect to both the agents and targets. We develop two methods, where the first method post-processes the paths planned by any MCPF planner to include the task duration and has no solution optimality guarantee; and the second method considers task duration during planning and is able to ensure solution optimality. The numerical and simulation results show that our methods can handle up to 20 agents and 50 targets in the presence of task duration, and can execute the paths subject to robot motion disturbance.

• The paper proposes two novel CBSS-based methods that incorporate heterogeneous task durations into multi-agent path planning.
• It compares a post-processing approach (CBSS-TPG) and an integrated planning framework (CBSS-D) to address conflict resolution effectively.
• Numerical results reveal up to 20% cost savings and 80% conflict reduction, demonstrating the methods' practical benefits in real-world applications.

Multi-Agent Combinatorial Path Finding with Heterogeneous Task Duration

The paper "Multi-Agent Combinatorial Path Finding with Heterogeneous Task Duration" introduces innovative methods to address challenges in Multi-Agent Combinatorial Path Finding (MCPF), particularly when the task durations of agents at target locations are non-uniform. The research is motivated by practical applications in areas such as warehouse logistics, manufacturing, and surveillance, where mobile robots are required to visit multiple target locations with varying task durations.

Problem Formulation

The MCPF problem involves routing multiple agents from their initial positions to their destinations while visiting a set of intermediate target locations and minimizing the sum of arrival times. The paper generalizes this problem to include heterogeneous task durations, denoted as MCPF-D. In MCPF-D, the task duration at each target can vary for different agents and also vary across different targets for the same agent. This generalization significantly increases the complexity of the problem, which is already NP-hard.

Methods

The authors present two primary methods for solving the MCPF-D problem: CBSS-TPG and CBSS-D.

CBSS-TPG

The first method, called CBSS-TPG, combines Conflict-Based Steiner Search (CBSS) with Temporal Plan Graph (TPG). The process involves two main steps:

1. Path Planning without Task Duration: Initially, a conflict-free joint path is planned using CBSS without considering task durations, effectively reducing the problem to a standard MCPF.
2. Post-Processing with TPG: The joint path is then post-processed using a method inspired by TPG, referred to as TPG-D. This method incorporates task durations into the plan and ensures that the resultant paths are conflict-free.

While CBSS-TPG offers a pragmatic solution, it does not guarantee optimality since the initial path planning step disregards task durations.

CBSS-D

The second method, termed CBSS-D, modifies the CBSS framework to take task durations into account during the path planning phase, ensuring optimality. The key modifications include:

1. Transformation for Sequencing: The method adapts the transformation used in CBSS to integrate task durations when computing target sequences.
2. Enhanced Branching Rules: CBSS-D introduces new branching rules to resolve conflicts more efficiently. When a conflict related to task duration is detected, the new rules generate additional constraints that prevent subsequent conflicts arising from the same task execution, thus reducing the required number of conflict resolution iterations.

Numerical Results

The methods were tested on various scenarios with different configurations of agents and targets on standard maps from an online dataset. The key findings are:

• Cost Efficiency: CBSS-D consistently finds cheaper solutions compared to CBSS-TPG, particularly when task durations are large. The cost reduction can be up to 20%.
• Success Rates: Both methods exhibit similar success rates across different scenarios, but CBSS-D is able to handle the complexity introduced by task durations more effectively.
• Conflict Reduction: The new branching rule in CBSS-D significantly reduces the number of conflicts that need to be resolved, up to 80% in some cases, showing its efficiency over the regular branching rule used in CBSS.

Implications and Future Directions

These methods have significant implications for practical applications involving multi-agent systems. The ability to account for heterogeneous task durations enhances the feasibility of deploying multi-robot systems in real-world settings such as automated warehouses and manufacturing floors, where tasks at intermediate locations can vary widely in duration.

The paper's findings open several pathways for future research. Potential extensions include the incorporation of time window constraints and the handling of additional precedence constraints between tasks, which would further generalize and enhance the applicability of the proposed methods.

Overall, this paper presents a thorough exploration of MCPF-D and introduces robust methods that balance between practical applicability and computational efficiency, contributing valuable insights to the field of multi-agent systems.