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This paper investigates the task-driven exploration of unknown environments with mobile sensors communicating compressed measurements. The sensors explore the area and transmit their compressed data to another robot, assisting it in reaching a goal location. We propose a novel communication framework and a tractable multi-agent exploration algorithm to select the sensors' actions. The algorithm uses a task-driven measure of uncertainty, resulting from map compression, as a reward function. We validate the efficacy of our algorithm through numerical simulations conducted on a realistic map and compare it with two alternative approaches. The results indicate that the proposed algorithm effectively decreases the time required for the robot to reach its target without causing excessive load on the communication network.

This paper addresses the problem of the communication of optimally compressed information for mobile robot path-planning. In this context, mobile robots compress their current local maps to assist another robot in reaching a target in an unknown environment. We propose a framework that sequentially selects the optimal compression, guided by the robot's path, by balancing the map resolution and communication cost. Our approach is tractable in close-to-real scenarios and does not necessitate prior environment knowledge. We design a novel decoder that leverages compressed information to estimate the unknown environment via convex optimization with linear constraints and an encoder that utilizes the decoder to select the optimal compression. Numerical simulations are conducted in a large close-to-real map and a maze map and compared with two alternative approaches. The results confirm the effectiveness of our framework in assisting the robot reach its target by reducing transmitted information, on average, by approximately 50% while maintaining satisfactory performance.