Two teams of oblivious asynchronous robots performing different tasks on an infinite grid without the knowledge of its team members

Two fundamental problems of distributed computing are Gathering and Arbitrary pattern formation (\textsc{Apf}). These two tasks are different in nature as in gathering robots meet at a point but in \textsc{Apf} robots form a fixed pattern in distinct positions. In most of the current literature on swarm robot algorithms, it is assumed that all robots in the system perform one single task together. Two teams of oblivious robots deployed in the same system and different teams of robots performing two different works simultaneously where no robot knows the team of another robot is a new concept in the literature introduced by Bhagat et al. [ICDCN'2020]. In this work, a swarm of silent and oblivious robots are deployed on an infinite grid under an asynchronous scheduler. The robots do not have access to any global coordinates. Some of the robots are given input of an arbitrary but unique pattern. The set of robots with the given pattern is assigned with the task of forming the given pattern on the grid. The remaining robots are assigned with the task of gathering to a vertex of the grid (not fixed from earlier and not any point where a robot that is forming a pattern terminates). Each robot knows to which team it belongs, but can not recognize the team of another robot. Considering weak multiplicity detection, a distributed algorithm is presented in this paper which leads the robots with the input pattern into forming it and other robots into gathering on a vertex of the grid on which no other robot forming the pattern, terminates.