Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Active Learning-based Model Predictive Coverage Control

Rahel Rickenbach, Johannes Köhler, Anna Scampicchio, Melanie N. Zeilinger, Andrea Carron

TL;DR

This work tackles multi-agent coverage control under nonlinear constrained dynamics in initially unknown environments. It advances two MPC-based frameworks: a two-layer approach with server-generated references for local tracking MPC and a one-layer approach that embeds reference optimization directly into the MPC cost; both are extended with active-learning strategies to handle unknown density fields. The authors prove recursive feasibility and convergence to centroidal Voronoi configurations for known and learned environments, and validate the methods on a hardware four-vehicle platform with both learning-enabled and pure tracking variants. Practically, the paper demonstrates safe, convergent, and data-efficient coverage behavior with explicit exploration-exploitation mechanisms and quantifiable bounds on residual uncertainty.

Abstract

The problem of coverage control, i.e., of coordinating multiple agents to optimally cover an area, arises in various applications. However, coverage applications face two major challenges: (1) dealing with nonlinear dynamics while respecting system and safety critical constraints, and (2) performing the task in an initially unknown environment. We solve the coverage problem by using a hierarchical framework, in which references are calculated at a central server and passed to the agents' local model predictive control (MPC) tracking schemes. Furthermore, to ensure that the environment is actively explored by the agents a probabilistic exploration-exploitation trade-off is deployed. In addition, we derive a control framework that avoids the hierarchical structure by integrating the reference optimization in the MPC formulation. Active learning is then performed drawing inspiration from Upper Confidence Bound (UCB) approaches. For all developed control architectures, we guarantee closed-loop constraint satisfaction and convergence to an optimal configuration. Furthermore, all methods are tested and compared on hardware using a miniature car platform.

Active Learning-based Model Predictive Coverage Control

TL;DR

This work tackles multi-agent coverage control under nonlinear constrained dynamics in initially unknown environments. It advances two MPC-based frameworks: a two-layer approach with server-generated references for local tracking MPC and a one-layer approach that embeds reference optimization directly into the MPC cost; both are extended with active-learning strategies to handle unknown density fields. The authors prove recursive feasibility and convergence to centroidal Voronoi configurations for known and learned environments, and validate the methods on a hardware four-vehicle platform with both learning-enabled and pure tracking variants. Practically, the paper demonstrates safe, convergent, and data-efficient coverage behavior with explicit exploration-exploitation mechanisms and quantifiable bounds on residual uncertainty.

Abstract

The problem of coverage control, i.e., of coordinating multiple agents to optimally cover an area, arises in various applications. However, coverage applications face two major challenges: (1) dealing with nonlinear dynamics while respecting system and safety critical constraints, and (2) performing the task in an initially unknown environment. We solve the coverage problem by using a hierarchical framework, in which references are calculated at a central server and passed to the agents' local model predictive control (MPC) tracking schemes. Furthermore, to ensure that the environment is actively explored by the agents a probabilistic exploration-exploitation trade-off is deployed. In addition, we derive a control framework that avoids the hierarchical structure by integrating the reference optimization in the MPC formulation. Active learning is then performed drawing inspiration from Upper Confidence Bound (UCB) approaches. For all developed control architectures, we guarantee closed-loop constraint satisfaction and convergence to an optimal configuration. Furthermore, all methods are tested and compared on hardware using a miniature car platform.
Paper Structure (36 sections, 15 theorems, 74 equations, 14 figures, 1 table, 4 algorithms)

This paper contains 36 sections, 15 theorems, 74 equations, 14 figures, 1 table, 4 algorithms.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Dynamics and Constraints
  4. Coverage Control
  5. Control and Learning Framework
  6. Nonlinear Tracking MPC
  7. Data Collection and Bayesian Linear Regression
  8. Partition Update, Collision Avoidance, and Recursive Feasibility
  9. Two-layers Coverage MPC Algorithm
  10. Known Environment
  11. Unknown Environment
  12. One-Layer Coverage MPC Algorithm
  13. Known Environment
  14. Unknown Environment
  15. Experimental Results
  16. ...and 21 more sections

Key Result

Theorem 1

Boccia2014 Let Assumptions assumption:expocostcontrollability and assumption:boundedbyd hold. Then, for any position constraint set, $\mathbb{P}_{i} \subset \mathbb{A}$, with $\mathbb{P}^{\mathrm{int}}_{i} \neq \emptyset$, any choice of$V_{\max,i} > 0$ and any $\bar{\alpha}_{N,i} \in (0,1)$, there

Figures (14)

  • Figure 1: Illustration of coverage control problem and partitioning of environment at the example of firefighting planes and environmental demands defined by the resulting heat map.
  • Figure 2: Simplified illustration of the developed two- and one-layers algorithm. Considering density $\phi$, partitions $\mathbb{O}$, references $r$, state $x$, inputs $u$, positions $p$, as well as setpoint positions $\bar{p}$.
  • Figure 3: Locational optimization cost decrease over time, applying Algorithm \ref{['alg:twolayermpcalg']} with respect to a known density $\phi_{1}$.
  • Figure 4: Configurations of cars at 2, 8, and 24 seconds applying Algorithm \ref{['alg:twolayermpcalg']} in the described set-up. The agents' location and their predicted trajectory are given in red, the Voronoi partitions in green, their centroids in blue, and the traveled paths are visualized in light grey.
  • Figure 5: Locational optimization cost (green) as well as estimated locational optimization cost versus time (rose), applying Algorithm \ref{['alg:twolayermpcalglearningimp']} in consideration of an initially unknown $\phi_{2}$. The grey background indicates time instances for which the agents are exploring.
  • ...and 9 more figures

Theorems & Definitions (18)

  • Remark 1
  • Remark 2
  • Theorem 1
  • Remark 3
  • Lemma 1
  • Proposition 1
  • Theorem 2
  • Theorem 3
  • Theorem 4
  • Theorem 5
  • ...and 8 more