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Multi-Robot Multitask Gaussian Process Estimation and Coverage

Lai Wei, Andrew McDonald, Vaibhav Srivastava

Abstract

Coverage control is essential for the optimal deployment of agents to monitor or cover areas with sensory demands. While traditional coverage involves single-task robots, increasing autonomy now enables multitask operations. This paper introduces a novel multitask coverage problem and addresses it for both the cases of known and unknown sensory demands. For known demands, we design a federated multitask coverage algorithm and establish its convergence properties. For unknown demands, we employ a multitask Gaussian Process (GP) framework to learn sensory demand functions and integrate it with the multitask coverage algorithm to develop an adaptive algorithm. We introduce a novel notion of multitask coverage regret that compares the performance of the adaptive algorithm against an oracle with prior knowledge of the demand functions. We establish that our algorithm achieves sublinear cumulative regret, and numerically illustrate its performance.

Multi-Robot Multitask Gaussian Process Estimation and Coverage

Abstract

Coverage control is essential for the optimal deployment of agents to monitor or cover areas with sensory demands. While traditional coverage involves single-task robots, increasing autonomy now enables multitask operations. This paper introduces a novel multitask coverage problem and addresses it for both the cases of known and unknown sensory demands. For known demands, we design a federated multitask coverage algorithm and establish its convergence properties. For unknown demands, we employ a multitask Gaussian Process (GP) framework to learn sensory demand functions and integrate it with the multitask coverage algorithm to develop an adaptive algorithm. We introduce a novel notion of multitask coverage regret that compares the performance of the adaptive algorithm against an oracle with prior knowledge of the demand functions. We establish that our algorithm achieves sublinear cumulative regret, and numerically illustrate its performance.
Paper Structure (18 sections, 7 theorems, 41 equations, 5 figures, 2 algorithms)

This paper contains 18 sections, 7 theorems, 41 equations, 5 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Background
  3. Graph Representation of Environment
  4. Single Task Coverage Problem
  5. Problem Formulation
  6. Multitask Coverage with Heterogeneous Agents
  7. Federated Communication Model
  8. Multitask Nonparametric Estimation
  9. Multitask Coverage Regret
  10. Federated multitask Coverage Control
  11. Adaptive Multiple Task Coverage Control
  12. The DSMLC Algorithm
  13. Analysis of the DSMLC algorithm
  14. Mutual Information
  15. Uncertainty Reduction
  16. ...and 3 more sections

Key Result

Lemma 1

The following statements hold for the multitask coverage cost function eq:mulcost:

Figures (5)

  • Figure 1: True demand fields: (a) $\phi^1$ and (b) $\phi^2$.
  • Figure 2: Federated multitask coverage (FMTC) under known demand.
  • Figure 3: Final deployment and multitask partition in the heterogeneous case. The red dots represent robots with superior Task 2 capability, and white dots represent other robots. The color of the partition is mapped to the robot identity with 0 and 10 indicating uncovered and multiply covered vertices, respectively. Robots with superior Task 2 capabilities have indices $\{1, 3, 6\}$.
  • Figure 4: Cumulative regret comparison in the single-task case.
  • Figure 5: Cumulative regret comparison in the heterogeneous two-task case.

Theorems & Definitions (22)

  • Definition 1: $N$-partition
  • Definition 2: $N$-covering
  • Definition 3: Centroidal Voronoi partition, DistCtrlRobotNetw
  • Definition 4: Multitask centers
  • Definition 5: Multitask equitable partitions
  • Definition 6: Multitask centroidal equitable partition
  • Definition 7: Multitask coverage regret
  • Lemma 1: Properties of the multitask coverage function
  • proof
  • Lemma 2: Lemma 3, Patel2016
  • ...and 12 more