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Iterative Planning for Multi-agent Systems: An Application in Energy-Aware UAV-UGV Cooperative Task Site Assignments

Neelanga Thelasingha, Agung Julius, James Humann, Jean-Paul Reddinger, James Dotterweich, Marshal Childers

TL;DR

The paper tackles energy-aware, multi-agent planning in hybrid state spaces by casting the problem as a transition-system task where multiple solvers can iteratively improve a plan under bounded compute. It introduces a unifying framework that uses sampled transition systems and monotone specifications to guarantee recursive feasibility as solvers autonomously refine plans, with shrinking-horizon execution enabling continual re-planning. The approach is validated on a UAV-UGV cooperative routing task, showing substantial reductions in total mission time and real-time feasibility compared to MIP, GA, and BO baselines. This framework enables anytime, implementable solutions for complex multi-agent tasks while providing formal guarantees and practical performance advantages for energy-constrained operations.

Abstract

This paper presents an iterative planning framework for multi-agent systems with hybrid state spaces. The framework uses transition systems to mathematically represent planning tasks and employs multiple solvers to iteratively improve the plan until computation resources are exhausted. When integrating different solvers for iterative planning, we establish theoretical guarantees on the mathematical framework to ensure recursive feasibility. The proposed framework enables continual improvement of solution optimality, efficiently using allocated computation resources. The proposed method is validated by applying it to an energy-aware UGV-UAV cooperative task site assignment. The results demonstrate the continual solution improvement while preserving real-time implementation ability compared to algorithms proposed in the literature.

Iterative Planning for Multi-agent Systems: An Application in Energy-Aware UAV-UGV Cooperative Task Site Assignments

TL;DR

The paper tackles energy-aware, multi-agent planning in hybrid state spaces by casting the problem as a transition-system task where multiple solvers can iteratively improve a plan under bounded compute. It introduces a unifying framework that uses sampled transition systems and monotone specifications to guarantee recursive feasibility as solvers autonomously refine plans, with shrinking-horizon execution enabling continual re-planning. The approach is validated on a UAV-UGV cooperative routing task, showing substantial reductions in total mission time and real-time feasibility compared to MIP, GA, and BO baselines. This framework enables anytime, implementable solutions for complex multi-agent tasks while providing formal guarantees and practical performance advantages for energy-constrained operations.

Abstract

This paper presents an iterative planning framework for multi-agent systems with hybrid state spaces. The framework uses transition systems to mathematically represent planning tasks and employs multiple solvers to iteratively improve the plan until computation resources are exhausted. When integrating different solvers for iterative planning, we establish theoretical guarantees on the mathematical framework to ensure recursive feasibility. The proposed framework enables continual improvement of solution optimality, efficiently using allocated computation resources. The proposed method is validated by applying it to an energy-aware UGV-UAV cooperative task site assignment. The results demonstrate the continual solution improvement while preserving real-time implementation ability compared to algorithms proposed in the literature.
Paper Structure (48 sections, 7 theorems, 41 equations, 14 figures, 4 tables, 2 algorithms)

This paper contains 48 sections, 7 theorems, 41 equations, 14 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Motivation
  3. Overview
  4. Contributions
  5. Related Work
  6. Preliminaries
  7. Notation
  8. Transition Systems
  9. Trajectories and Implementations
  10. Monotone Transition Systems
  11. Output Behavior
  12. Task Site Assignment in a Transition System
  13. Sampled Transition System
  14. Key States, Key Transitions, and Specifications
  15. Monotone Specifications
  16. ...and 33 more sections

Key Result

Theorem 1

Given a sampled transition system $S_d=(X_d,T_d,L,Y_d,H)$ of an infinite state transition system $S=(X, T, L, Y, H)$, and a specification $M \subset \Sigma(S_d)$ for a task site assignment $\Xi$, if a plan(trajectory) $\tau \in \Sigma(S_d)$ satisfies $M$, then its implementation $\zeta$ has the outp

Figures (14)

  • Figure 1: Example - SMT solver that operates in discrete-time on discrete-nodes and a VRP solver that operates in continuous-time on discrete-nodes generating implementations for a system in continuous-time on continuous-space.
  • Figure 2: States, labels and transitions.
  • Figure 3: Sampled transition system for a discrete solver.
  • Figure 4: Key states and Key transitions: The state space $X$ of the transition system $S$ contains all key states. However, sampled transition system $S_d$ only contains $A,C,D$. Thus, key state $B$ forms a key transition for $\tau_d$ as $t=(A,\ell^\prime_0,C)$ as there exists an implementation for $\tau_d$ that traverses through $B$.
  • Figure 5: Problem space for iterative planning: Solvers are called iteratively with the task site assignment and the current implementation to generate a better plan to be implemented on the transition system.
  • ...and 9 more figures

Theorems & Definitions (24)

  • Definition 1: Transition System
  • Definition 2: Execution Trajectories
  • Definition 3: Implementation
  • Definition 4: Monotone Transition Systems
  • Definition 5: Output Behavior
  • Definition 6: Task Site Assignment
  • Definition 7: Sampled Transition System
  • Definition 8: Key State Classes
  • Definition 9: Key Transition Classes
  • Definition 10: Specification
  • ...and 14 more