Non-submodular Visual Attention for Robot Navigation

2025-10-01

AI Summary

This paper addresses the trade-off between real-time performance and accuracy in feature selection for resource-constrained visual-inertial navigation (VIN). We propose a task-oriented computational framework. Our core contributions are threefold: (i) a non-submodular mean-square-error objective function coupled with a simplified dynamic pre-estimation model to enable vision-guided attention; (ii) four polynomial-time approximation algorithms, the first to establish rigorous performance bounds based on submodularity ratio and curvature, thereby overcoming the NP-hardness barrier; and (iii) integration of greedy selection, low-rank acceleration, randomized sampling, and first-order Taylor linearization to significantly reduce computational complexity while preserving theoretical approximation guarantees. Extensive evaluation on standard benchmarks and custom embedded hardware demonstrates that our method achieves both high estimation accuracy and near-real-time performance, enabling practical deployment in real-world VIN applications.

Technology Category

• Computer Vision: Learning & Optimization for CV
• Intelligent Robots: State Estimation
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Large-scale security measurements

Abstract

This paper presents a task-oriented computational framework to enhance Visual-Inertial Navigation (VIN) in robots, addressing challenges such as limited time and energy resources. The framework strategically selects visual features using a Mean Squared Error (MSE)-based, non-submodular objective function and a simplified dynamic anticipation model. To address the NP-hardness of this problem, we introduce four polynomial-time approximation algorithms: a classic greedy method with constant-factor guarantees; a low-rank greedy variant that significantly reduces computational complexity; a randomized greedy sampler that balances efficiency and solution quality; and a linearization-based selector based on a first-order Taylor expansion for near-constant-time execution. We establish rigorous performance bounds by leveraging submodularity ratios, curvature, and element-wise curvature analyses. Extensive experiments on both standardized benchmarks and a custom control-aware platform validate our theoretical results, demonstrating that these methods achieve strong approximation guarantees while enabling real-time deployment.

Problem

• Enhancing robot visual-inertial navigation with limited resources
• Selecting visual features using non-submodular optimization methods
• Developing efficient approximation algorithms for NP-hard navigation problems

Innovation

• Uses non-submodular objective function for feature selection
• Introduces four polynomial-time approximation algorithms
• Establishes performance bounds using curvature analyses