Coordinating a fully distributed multi-agent system (MAS) can be challenging when the communication channel has very limited capabilities in terms of sending rate and packet payload. When the MAS has to deal with active obstacles in a highly partially observable environment, the communication channel acquires considerable relevance. In this paper, we present an approach to deal with task assignments in extremely active scenarios, where tasks need to be frequently reallocated among the agents participating in the coordination process. Inspired by market-based task assignments, we introduce a novel distributed coordination method to orchestrate autonomous agents' actions efficiently in low communication scenarios. In particular, our algorithm takes into account asymmetric obstacles. While in the real world, the majority of obstacles are asymmetric, they are usually treated as symmetric ones, thus limiting the applicability of existing methods. To summarize, the presented architecture is designed to tackle scenarios where the obstacles are active and asymmetric, the communication channel is poor and the environment is partially observable. Our approach has been validated in simulation and in the real world, using a team of NAO robots during official RoboCup competitions. Experimental results show a notable reduction in task overlaps in limited communication settings, with a decrease of 52% in the most frequent reallocated task.