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AI-Augmented Density-Driven Optimal Control (D2OC) for Decentralized Environmental Mapping

Kooktae Lee, Julian Martinez

TL;DR

This work tackles decentralized environmental mapping under uncertain priors by augmenting Density-Driven Optimal Control (D$^2$OC) with an AI module. It introduces a dynamic sampling process, a three-stage control loop, and a dual-MLP inference system that jointly refine local density estimates and regulate exploration through adaptive uncertainty. Theoretical convergence under the Wasserstein metric is established, and simulations demonstrate that AI-augmented D$^2$OC achieves higher-density fidelity and robust convergence compared to baselines, despite limited sensing and communication. The framework enables scalable, decentralized mapping with improved global consistency, and points toward real-world deployments in UAV-enabled environmental monitoring and disaster response.

Abstract

This paper presents an AI-augmented decentralized framework for multi-agent (multi-robot) environmental mapping under limited sensing and communication. While conventional coverage formulations achieve effective spatial allocation when an accurate reference map is available, their performance deteriorates under uncertain or biased priors. The proposed method introduces an adaptive and self-correcting mechanism that enables agents to iteratively refine local density estimates within an optimal transport-based framework, ensuring theoretical consistency and scalability. A dual multilayer perceptron (MLP) module enhances adaptivity by inferring local mean-variance statistics and regulating virtual uncertainty for long-unvisited regions, mitigating stagnation around local minima. Theoretical analysis rigorously proves convergence under the Wasserstein metric, while simulation results demonstrate that the proposed AI-augmented Density-Driven Optimal Control consistently achieves robust and precise alignment with the ground-truth density, yielding substantially higher-fidelity reconstruction of complex multi-modal spatial distributions compared with conventional decentralized baselines.

AI-Augmented Density-Driven Optimal Control (D2OC) for Decentralized Environmental Mapping

TL;DR

This work tackles decentralized environmental mapping under uncertain priors by augmenting Density-Driven Optimal Control (DOC) with an AI module. It introduces a dynamic sampling process, a three-stage control loop, and a dual-MLP inference system that jointly refine local density estimates and regulate exploration through adaptive uncertainty. Theoretical convergence under the Wasserstein metric is established, and simulations demonstrate that AI-augmented DOC achieves higher-density fidelity and robust convergence compared to baselines, despite limited sensing and communication. The framework enables scalable, decentralized mapping with improved global consistency, and points toward real-world deployments in UAV-enabled environmental monitoring and disaster response.

Abstract

This paper presents an AI-augmented decentralized framework for multi-agent (multi-robot) environmental mapping under limited sensing and communication. While conventional coverage formulations achieve effective spatial allocation when an accurate reference map is available, their performance deteriorates under uncertain or biased priors. The proposed method introduces an adaptive and self-correcting mechanism that enables agents to iteratively refine local density estimates within an optimal transport-based framework, ensuring theoretical consistency and scalability. A dual multilayer perceptron (MLP) module enhances adaptivity by inferring local mean-variance statistics and regulating virtual uncertainty for long-unvisited regions, mitigating stagnation around local minima. Theoretical analysis rigorously proves convergence under the Wasserstein metric, while simulation results demonstrate that the proposed AI-augmented Density-Driven Optimal Control consistently achieves robust and precise alignment with the ground-truth density, yielding substantially higher-fidelity reconstruction of complex multi-modal spatial distributions compared with conventional decentralized baselines.
Paper Structure (16 sections, 3 theorems, 33 equations, 3 figures, 1 table)

This paper contains 16 sections, 3 theorems, 33 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem Description and Objectives
  3. Decentralized Density-Driven Optimal Control
  4. Dynamic Sample Generation and Removal
  5. Stage A: Sample Selection and Optimal Control
  6. Stage B: Coverage-Tracking Weight Update
  7. Stage C: Communication and Merging
  8. Dual-MLP Inference for Mean–Variance and Adaptive Uncertainty Estimation
  9. Dual-MLP Architecture
  10. Integration with D$^2$OC
  11. Online Learning Procedure for Dual MLPs
  12. Convergence Analysis
  13. Simulations
  14. Simulation Setup
  15. Result Analysis
  16. ...and 1 more sections

Key Result

Lemma 1

For agent $i$ at step $l$, consider where $\pi_{lj}^* \ge 0$ denote the optimal transport coefficients. Let $\gamma_l := \sum_{j \in \mathcal{S}_{i,\mathrm{loc}}^{l}} \pi_{lj}^*$ and $q_{i,c}^{l} := \frac{1}{\gamma_l} \sum_{j \in \mathcal{S}_{i,\mathrm{loc}}^{l}} \pi_{lj}^* q_{j}^k$. Then $J_{i,\mathrm{dist}}^{l}$ is minimized by $p_i

Figures (3)

  • Figure 1: Conceptual illustration of D$^2$C/D$^2$OC.
  • Figure 2: Simulation results: (a) Initial reference samples (blue), GT distribution (shaded red), and initial positions of five agents; (b) Updated sample distribution after mission completion without AI augmentation; (c) Results of AI-augmented D$^2$OC showing improved coverage efficiency compared to (b); (d) Time history of the loss function during the adaptive learning process.
  • Figure 3: Wasserstein distance comparison with GT: initial (orange); no MLP (blue); AI-augmented (red).

Theorems & Definitions (9)

  • Lemma 1: Weighted centroid minimizes the local quadratic cost
  • Proof 1
  • Theorem 1: Analytic Receding-Horizon Control Law in D$^2$OC
  • Proof 2
  • Remark 1: Role of Stage C in Decentralized Consensus
  • Remark 2: Dual-Network Roles and Advantages
  • Theorem 2: Band-Limited Convergence of AI-Augmented D$^2$OC
  • Proof 3
  • Remark 3: On the necessity of dual MLPs