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Streamlining the Action Dependency Graph Framework: Two Key Enhancements

Joachim Dunkel

TL;DR

The study tackles robustness and efficiency in multi-robot MAPF by refining the ADG framework. It proves wait actions are unnecessary for correct execution and introduces SCP, an ADG construction method that skips redundant dependencies to achieve near-linear-time performance. Empirical results show SCP dramatically lowers construction time and reduces type2 dependencies, while removing wait actions shortens makespan by exploiting faster consecutive motion. Collectively, these contributions improve scalability and practical viability of ADG-based execution in dynamic, real-world robot systems.

Abstract

Multi Agent Path Finding (MAPF) is critical for coordinating multiple robots in shared environments, yet robust execution of generated plans remains challenging due to operational uncertainties. The Action Dependency Graph (ADG) framework offers a way to ensure correct action execution by establishing precedence-based dependencies between wait and move actions retrieved from a MAPF planning result. The original construction algorithm is not only inefficient, with a quadratic worst-case time complexity it also results in a network with many redundant dependencies between actions. This paper introduces two key improvements to the ADG framework. First, we prove that wait actions are generally redundant and show that removing them can lead to faster overall plan execution on real robot systems. Second, we propose an optimized ADG construction algorithm, termed Sparse Candidate Partitioning (SCP), which skips unnecessary dependencies and lowers the time complexity to quasi-linear, thereby significantly improving construction speed.

Streamlining the Action Dependency Graph Framework: Two Key Enhancements

TL;DR

The study tackles robustness and efficiency in multi-robot MAPF by refining the ADG framework. It proves wait actions are unnecessary for correct execution and introduces SCP, an ADG construction method that skips redundant dependencies to achieve near-linear-time performance. Empirical results show SCP dramatically lowers construction time and reduces type2 dependencies, while removing wait actions shortens makespan by exploiting faster consecutive motion. Collectively, these contributions improve scalability and practical viability of ADG-based execution in dynamic, real-world robot systems.

Abstract

Multi Agent Path Finding (MAPF) is critical for coordinating multiple robots in shared environments, yet robust execution of generated plans remains challenging due to operational uncertainties. The Action Dependency Graph (ADG) framework offers a way to ensure correct action execution by establishing precedence-based dependencies between wait and move actions retrieved from a MAPF planning result. The original construction algorithm is not only inefficient, with a quadratic worst-case time complexity it also results in a network with many redundant dependencies between actions. This paper introduces two key improvements to the ADG framework. First, we prove that wait actions are generally redundant and show that removing them can lead to faster overall plan execution on real robot systems. Second, we propose an optimized ADG construction algorithm, termed Sparse Candidate Partitioning (SCP), which skips unnecessary dependencies and lowers the time complexity to quasi-linear, thereby significantly improving construction speed.

Paper Structure

This paper contains 16 sections, 5 theorems, 4 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. Problem Description
  3. Action Dependency Graph Construction
  4. Approach
  5. Wait Actions are redundant
  6. Improved ADG-Construction via Candidate Partitioning
  7. Skipping Redundant Dependencies with Sparse Candidate Parititioning (SCP)
  8. SCP Construction Algorithm
  9. Proving Theorem \ref{['theorem:only_the_overall_last_action_is_relevant']}
  10. Runtime Analysis of
  11. Experimental Evaluation
  12. -Construction Algorithm Comparison
  13. -Construction Runtime Comparison
  14. Influence of -Construction Algorithm on created type2 Dependencies.
  15. Influence of Wait Actions on Execution Performance
  16. ...and 1 more sections

Key Result

Proposition 1

For every action $b \in A$, if $b.t > 1$ then there exists a previous action $a \in A$ with $b.s = a.g \land b.t = a.t + 1 \land b.R = a.R$

Figures (4)

  • Figure 1: Runtime comparison of construction algorithms on the Paris map, comparing the exhaustive method with and . The exhaustive method shows an orders of magnitudes worse runtime than both and .
  • Figure 2: Comparison of -Construction runtime between and . demonstrates improved overall runtime performance for all maps in the benchmark.
  • Figure 3: Comparing and on the number of created type2 dependencies across all maps in the benchmark. generates significantly fewer type2 dependencies then
  • Figure 4: Comparison of makespan for simulations with (blue) and without (green) wait actions across varying numbers of agents. Simulations without wait actions generally finish a few seconds earlier, due to allowing agents to better take advantage of consecutive movement.

Theorems & Definitions (11)

  • Definition 1
  • Definition 2
  • Definition 3
  • Proposition 1
  • Definition 4
  • Definition 5
  • Theorem 1
  • Theorem 2
  • Definition 6
  • Theorem 3
  • ...and 1 more