Convergence of Mobile Robots with Uniformly-Inaccurate Sensors

Abstract

We consider the convergence problem of autonomous mobile robots with inaccurate sensors, which may return the erroneous location of other robots. In this paper, we newly introduce a uniform error model, which is a restricted variant of the original observation-error model proposed by Cohen and Peleg [4]. The degree of an observation error is characterized by distance errors and angle errors. While the original model (non-uniform model) allows that two or more points can have different error degrees, the uniform error model assumes that the same amount of error degree is incurred to all observed points in a single observation. The main focus of our study is to reveal how much such uniformity expands the feasibility of the convergence. In the non-uniform error model, it has been shown that no algorithm can achieve the convergence if the maximum error angle is more than or equal to π/3. This paper shows that the convergence problem is solvable under the uniform error if the maximum error angle is less than π/ 2. We also prove that there is no convergence algorithm for the maximum error angle more than or equal to π/2 even in the uniform error model, which implies the optimality of our algorithm in the sense of angle errors.