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Scalable Networked Feature Selection with Randomized Algorithm for Robot Navigation

Vivek Pandey, Arash Amini, Guangyi Liu, Ufuk Topcu, Qiyu Sun, Kostas Daniilidis, Nader Motee

TL;DR

The paper tackles sparse visual feature selection for multi-agent localization under limited onboard computation. It proposes a scalable randomized feature-selection algorithm that uses leverage scores and matrix concentration bounds to bound information loss relative to the full feature set. A key insight is that stronger network connectivity, captured by the graph Laplacian, drives feature informativeness toward uniformity, enabling efficient uniform random sampling. Through theoretical results and extensive simulations, the method achieves near-greedy localization accuracy with substantially reduced computation, offering practical benefits for distributed robot teams.

Abstract

We address the problem of sparse selection of visual features for localizing a team of robots navigating an unknown environment, where robots can exchange relative position measurements with neighbors. We select a set of the most informative features by anticipating their importance in robots localization by simulating trajectories of robots over a prediction horizon. Through theoretical proofs, we establish a crucial connection between graph Laplacian and the importance of features. We show that strong network connectivity translates to uniformity in feature importance, which enables uniform random sampling of features and reduces the overall computational complexity. We leverage a scalable randomized algorithm for sparse sums of positive semidefinite matrices to efficiently select the set of the most informative features and significantly improve the probabilistic performance bounds. Finally, we support our findings with extensive simulations.

Scalable Networked Feature Selection with Randomized Algorithm for Robot Navigation

TL;DR

The paper tackles sparse visual feature selection for multi-agent localization under limited onboard computation. It proposes a scalable randomized feature-selection algorithm that uses leverage scores and matrix concentration bounds to bound information loss relative to the full feature set. A key insight is that stronger network connectivity, captured by the graph Laplacian, drives feature informativeness toward uniformity, enabling efficient uniform random sampling. Through theoretical results and extensive simulations, the method achieves near-greedy localization accuracy with substantially reduced computation, offering practical benefits for distributed robot teams.

Abstract

We address the problem of sparse selection of visual features for localizing a team of robots navigating an unknown environment, where robots can exchange relative position measurements with neighbors. We select a set of the most informative features by anticipating their importance in robots localization by simulating trajectories of robots over a prediction horizon. Through theoretical proofs, we establish a crucial connection between graph Laplacian and the importance of features. We show that strong network connectivity translates to uniformity in feature importance, which enables uniform random sampling of features and reduces the overall computational complexity. We leverage a scalable randomized algorithm for sparse sums of positive semidefinite matrices to efficiently select the set of the most informative features and significantly improve the probabilistic performance bounds. Finally, we support our findings with extensive simulations.
Paper Structure (16 sections, 76 equations, 5 figures, 1 table, 1 algorithm)

This paper contains 16 sections, 76 equations, 5 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Mathematical Notation
  3. Problem Statement
  4. Model for Robot Motion, Relative Measurements and Vision System
  5. Model for Robots Motion
  6. Information from Relative Measurements
  7. Model for Vision System
  8. Performance Measures
  9. Randomized Sampling Algorithm
  10. Sampling using Leverage Score
  11. Performance Bound
  12. Case Study
  13. Simulation Setup: Robots and Environment
  14. Feature Selection Algorithms and Comparison Metrics
  15. Simulation Results
  16. ...and 1 more sections

Figures (5)

  • Figure 1: Description of robots and features in environment.
  • Figure 2: Ratio of spectral norm of estimated covariance to spectral norm of covariance when states are measured \ref{['eqn:estimation_covariance_ratio']}.
  • Figure 3: Multi-agent localization error for different feature selection algorithms.
  • Figure 4: Impact of network connectivity on estimation covariance.
  • Figure 5: Histogram of leverage scores of features for varying communication strength $\beta$ and $\alpha=1$, where $\alpha$ and $\beta$ are as defined in \ref{['eqn:exponential_weight_decay']}.