Multi-Agent Combinatorial Path Finding with Heterogeneous Task Duration

TL;DR

This work generalizes Multi-Agent Path Finding to MCPF-D by introducing heterogeneous task durations at targets and destinations. It develops two methods: CBSS-TPG, which post-processes planar paths via a Temporal Plan Graph to accommodate durations, and CBSS-D, which integrates durations into sequencing and conflicts to guarantee optimality. Empirical results show the approach scales to up to 20 agents and 50 targets, with CBSS-D achieving up to 20% lower costs than CBSS-TPG and a branching rule that significantly reduces planning iterations. Gazebo simulations confirm robust, collision-free execution under disturbances, illustrating practical applicability in dynamic environments.

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.

Figures (8)

• Figure 1: A toy example of MCPF-D. The target locations with heterogeneous task duration are marked as the white disks in (a). (c) shows the a 4$\times$4 grid representation of the workspace in (a) and each cell is encoded with a number as shown in (b). There are three targets $6$, $9$, $10$, which are marked as square in (c). The color of the targets in (c) shows the assignment constraints. For instance, the task at target 10 can only be executed by the green agent with task duration 1, or by the yellow agent with task duration 4. The $S$ and $G$ shows the initial and goal locations of the agents.
• Figure 2: An illustration of CBSS and CBSS-D. Both of them generate K-best target sequences and leverage CBS to resolve conflicts between agents. The differences between them are represented by the transformation and constraints generation, which are highlighted by gray-filled text boxes.
• Figure 3: TPG of the example in Fig. \ref{['fig:toy_example']}. Vertex $s_t^i$ means agent $i$ moves to location $s$ at time $t$, and the number in blue is the value of $D(s_t^i)$. The orange arrows represent Type 1 edges and the red arrows represent Type 2 edges.
• Figure 4: The transformation method for the toy example in Fig. \ref{['fig:toy_example']}. Here, (a) shows the transformed graph $G_{TF}$. The cost related to task duration is denoted by $+x$, where $x$ is the corresponding task duration. (b) shows the TSP tour in $G_{TF}$ computed by a TSP solver. (c) shows the joint sequence untransformed from the TSP tour.
• Figure 5: The success rates of CBSS-TPG and CBSS-D with various number of targets $M$ and task duration $\tau$. The maze is harder than the random map in general and both algorithms achieve similar success rates.

Theorems & Definitions (13)

• Remark 1
• Remark 2
• Example 1
• Theorem 1
• Theorem 2
• Theorem 3
• Example 2
• Example 3
• Example 4
• Definition 1: Mutually Disjunctive Constraints