We investigate a swarm of autonomous mobile robots in the Euclidean plane. A robot has a function called {\em target function} to determine the destination point from the robots' positions. All robots in the swarm conventionally take the same target function, but there is apparent limitation in problem-solving ability. We allow the robots to take different target functions. The number of different target functions necessary and sufficient to solve a problem $\Pi$ is called the {\em minimum algorithm size} (MAS) for $\Pi$. We establish the MASs for solving the gathering and related problems from {\bf any} initial configuration, i.e., in a {\bf self-stabilizing} manner. We show, for example, for $1 \leq c \leq n$, there is a problem $\Pi_c$ such that the MAS for the $\Pi_c$ is $c$, where $n$ is the size of swarm. The MAS for the gathering problem is 2, and the MAS for the fault tolerant gathering problem is 3, when $1 \leq f (< n)$ robots may crash, but the MAS for the problem of gathering all robot (including faulty ones) at a point is not solvable (even if all robots have distinct target functions), as long as a robot may crash.

翻译：我们研究欧几里得平面上一群自主移动机器人。每个机器人具备一个称为**目标函数**的功能，用于根据所有机器人的位置确定其目的地。传统上，机器人群体采用相同的目标函数，但这在问题求解能力上存在明显局限。本文允许机器人采用不同的目标函数。解决某个问题π所需且充分的不同目标函数数量，被称为该问题的**最小算法规模**（MAS）。我们确立了在**任意**初始配置下（即**自稳定**方式下）解决聚集及相关问题的MAS值。例如，对于1≤c≤n，存在问题π_c，其MAS为c（n为群体规模）。当1≤f（<n）个机器人可能崩溃时，聚集问题的MAS为2，容错聚集问题的MAS为3；但只要存在机器人可能崩溃的情况，将所有机器人（包括故障机器人）聚集到一点的问题则不可解（即使所有机器人拥有不同的目标函数）。