Oblivious Robots Performing Different Tasks on Grid Without Knowing their Team Members

TL;DR

This work tackles the problem of two teams of oblivious robots operating on an infinite grid under an asynchronous scheduler, performing gathering for one team and arbitrary pattern formation for the other simultaneously, without shared coordinates or team recognition. It introduces a global coordinate agreement mechanism based on the smallest enclosing rectangle and lexicographic binary strings to fix a common frame, then executes an eight-stage, collision-free plan that coordinates head, tail, and inner robots to achieve both tasks from any asymmetric initial configuration. The key contribution is proving that gathering and APF can be achieved concurrently in a discrete grid with weak multiplicity detection, expanding prior two-task work from continuous planes to discrete grid environments. The approach offers a foundation for robust multi-task swarm robotics in grid-like settings and suggests future work on limited visibility and finite grids.

Abstract

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 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.

Figures (6)

• Figure 1: $ABCD$ is the smallest enclosing rectangle of initial configuration. $\mathcal{H}$ and $\mathcal{T}$ are head and tail of the configuration. $A$ is the origin and the target configuration will be embedded with respect to $(0.2)$. $A'B'C'D'$ is the smallest enclosing rectangle of target configuration
• Figure 2: Case-1: $\mathcal{C'}$ has a vertical symmetry and $tail$ will move rightwards
• Figure 3: Case-2: $\mathcal{C'}$ has a vertical symmetry and $tail$ will move leftwards
• Figure 4: Any $r_i \in \mathcal{T}_g$ moves to $A$ and $r_i \in \mathcal{T}_{Apf}$ moves to fixed target positions one by one.
• Figure 5: A multiplicity point at $A$ and some of the $\mathcal{T}_{Apf}$ robots form the pattern

Theorems & Definitions (18)

• theorem thmcountertheorem
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