Bike Assisted Evacuation on a Line of Robots with Communication Faults

TL;DR

The paper studies bike-assisted evacuation for two autonomous robots on an infinite line when the exit location is unknown and communication is fault-prone under the S/R model. It introduces three algorithms tailored to bike speeds in distinct regimes ($1\le v\le 3$, $3\le v\le 10$, and $v>10$) and derives upper and lower bounds on the competitive ratio across all $v$, including asymptotic behavior as $v\to\infty$. The analysis combines opposite-direction search with bike-sharing strategies, yielding exact closed-form competitive ratios for the first two regimes and a doubling-based strategy for large $v$, with a unified lower bound showing fundamental limits. The results quantify how a non-autonomous bike and mixed communication faults affect evacuation time and demonstrate that the competitive ratio approaches 1 for large bike speeds, indicating near-optimal performance in that regime. These insights inform design choices for cooperative robotic evacuation under communication faults and resource constraints.

Abstract

Two autonomous mobile robots and a non-autonomous one, also called bike, are placed at the origin of an infinite line. The autonomous robots can travel with maximum speed $1$. When a robot rides the bike its speed increases to $v>1$, however only exactly one robot at a time can ride the bike and the bike is non-autonomous in that it cannot move on its own. An Exit is placed on the line at an unknown location and at distance $d$ from the origin. The robots have limited communication behavior; one robot is a sender (denoted by S) in that it can send information wirelessly at any distance and receive messages only in F2F (Face-to-Face), while the other robot is a receiver (denoted by R) in that it can receive information wirelessly but can send information only F2F. The bike has no communication capabilities of its own. We refer to the resulting communication model of the ensemble of the two autonomous robots and the bike as S/R. Our general goal is to understand the impact of the non-autonomous robot in assisting the evacuation of the two autonomous faulty robots. Our main contribution is to provide a new evacuation algorithm that enables both robots to evacuate from the unknown Exit in the S/R model. We also analyze the resulting evacuation time as a function of the bike's speed $v$ and give upper and lower bounds on the competitive ratio of the resulting algorithm for the entire range of possible values of $v$.

Figures (6)

• Figure 1: Depicted is Case 1 where two robots S and R are moving in opposite direction such that S finds the exit first.
• Figure 2: Depicted is Case 2 where two robots S and R are moving in opposite direction and such that R finds the exit.
• Figure 3: Graph showing the performance of the 3 algorithms by showing how the competitive ratio fluctuates in terms of the speed. Note in the pictures above Algorithms 1 is depicted in the range $[1,3]$ and Algorithms 2 and 3 are depicted in the range $[1,+\infty)$.
• Figure 4: Graph depicts the movement of two robots sharing the bike and starting at the origin in order to cover distance $d$.
• Figure 5: Graph depicts the minimal distance $x$ away from the origin at which the bike is dropped off by the sender and allows the receiver to take the bike and reach the exit sooner.

Theorems & Definitions (10)

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