Communication-Aware Map Compression for Online Path-Planning: A Rate-Distortion Approach

TL;DR

This paper presents a rate-distortion based method for compressing map data in collaborative robot navigation, optimizing communication efficiency and task relevance under bandwidth constraints.

Contribution

It introduces a convex rate-distortion formulation with a closed-form solution for real-time, task-aware map compression in multi-robot path planning.

Findings

Effective compressed maps guide path planning under bandwidth limits.

Closed-form solution enables real-time implementation.

Independent inference of compression decisions reduces communication overhead.

Abstract

This paper addresses the problem of collaborative navigation in an unknown environment, where two robots, referred to in the sequel as the Seeker and the Supporter, traverse the space simultaneously. The Supporter assists the Seeker by transmitting a compressed representation of its local map under bandwidth constraints to support the Seeker's path-planning task. We introduce a bit-rate metric based on the expected binary codeword length to quantify communication cost. Using this metric, we formulate the compression design problem as a rate-distortion optimization problem that determines when to communicate, which regions of the map should be included in the compressed representation, and at what resolution (i.e., quantization level) they should be encoded. Our formulation allows different map regions to be encoded at varying quantization levels based on their relevance to the Seeker's path-planning task. We demonstrate that the resulting optimization problem is convex, and admits a closed-form solution known in the information theory literature as reverse water-filling, enabling efficient, low-computation, and real-time implementation. Additionally, we show that the Seeker can infer the compression decisions of the Supporter independently, requiring only the encoded map content and not the encoding policy itself to be transmitted, thereby reducing communication overhead. Simulation results indicate that our method effectively constructs compressed, task-relevant map representations, both in content and resolution, that guide the Seeker's planning decisions even under tight bandwidth limitations.