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arXiv · 2510.00942

Non-submodular Visual Attention for Robot Navigation

Reza Vafaee·Kian Behzad·Milad Siami·Luca Carlone·Ali Jadbabaie
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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.

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Reza Vafaee, Kian Behzad, Milad Siami, Luca Carlone, Ali Jadbabaie. 2025-10-01. Non-submodular Visual Attention for Robot Navigation. https://arxiv.org/abs/2510.00942

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