Gathering Autonomous Mobile Robots Under the Adversarial Defected View Model

TL;DR

This paper studies the gathering problem for a set of autonomous mobile robots operating in the Euclidean plane under the distributed Look-Compute-Move model and proves finite-time gathering in the adversarial defected view setting, resolving a previously open case without requiring additional capabilities or coordinate agreement.

Abstract

This paper studies the gathering problem for a set of $N \ge 2$ autonomous mobile robots operating in the Euclidean plane under the distributed Look-Compute-Move model. We consider oblivious robots executing under the adversarial defected view model, in which an activated robot may observe only a restricted subset of robots due to adversarial visibility faults. Consequently, the information obtained during each Look phase may be incomplete and dynamically altered. The objective is to guarantee deterministic finite-time gathering at a location not known a priori despite such sensing restrictions. We present two distributed algorithms under distinct scheduling assumptions. In the fully synchronous (FSYNC) model, we prove finite-time gathering in the adversarial (4, 2) defected view setting, resolving a previously open case without requiring additional capabilities or coordinate agreement. In the asynchronous (ASYNC) model, we establish finite-time gathering under the general adversarial (N, K) defected view model, where an activated robot observes at most K of the other $N - 1$ robots for any $1 \le K < N - 1$. Both results hold under non-rigid motion. The proposed algorithm for the ASYNC model assumes agreement in the direction and orientation of one coordinate axis.

Figures (14)

• Figure 1: Solid points represent the robots observed by the active robot $r_i$, and (o) denotes the missed robots by $r_i$.
• Figure 2: An edge between two positions does not imply mutual visibility. Arrows indicate the observation relationships among the robots.
• Figure 7: $\mathbb{P}(t)$ is collinear.
• Figure 8: (An illustration of Lemma \ref{['1.2']}) The convex hull $CH(t)$ contains neither equilateral nor isosceles triangle.
• Figure 9: An example showing the non-rigid movement of robots towards the respective destination points.

Theorems & Definitions (20)

• lemma 1
• proof
• lemma 2
• proof
• lemma 3
• proof
• lemma 4
• proof
• lemma 5
• proof