  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.
