We investigate swarms of autonomous mobile robots in the Euclidean plane. Each robot has a target function to determine a destination point from the robots' positions. All robots in a swarm conventionally take the same target function. We allow the robots in a swarm to take different target functions, and investigate the effects of the number of distinct target functions on the problem-solving ability. Specifically, we are interested in how many distinct target functions are necessary and sufficient to solve some known problems which are not solvable when all robots take the same target function, regarding target function as a resource to solve a problem, like time and message. The number of distinct target functions necessary and sufficient to solve a problem $\Pi$ is called the minimum algorithm size (MAS) for $\Pi$. (The MAS is $\infty$, if $\Pi$ is not solvable even for the robots with unique target functions.) We establish the MASs for solving the gathering and related problems from any initial configuration, i.e., in a self-stabilizing manner. Our results include: There is a family of the scattering problems $c$SCT $(1 \leq c \leq n)$ such that the MAS for the $c$SCAT is $c$, where $n$ is the size of the swarm. The MAS for the gathering problem is 2. It is 3, for the problem of gathering all non-faulty robots at a single point, regardless of the number $(< n)$ of crash failures. It is however $\infty$, for the problem of gathering all robots at a single point, in the presence of at most one crash failure.

翻译：我们研究了欧几里得平面上的自主移动机器人群体。每个机器人都有一个目标函数，用于根据各机器人的位置确定其目的地。传统上，群体中的所有机器人采用相同的目标函数。我们允许群体中的机器人采用不同的目标函数，并研究不同目标函数的数量对问题求解能力的影响。具体而言，我们感兴趣的是：当所有机器人采用相同目标函数时无法解决的已知问题，需要多少种不同的目标函数才能解决？我们将目标函数视为解决问题的一种资源（如同时间和消息）。解决某个问题 $\Pi$ 所需且充分的不同目标函数数量，称为该问题的**最小算法规模 (MAS)**。（若即使在机器人拥有独特目标函数的情况下 $\Pi$ 仍不可解，则 MAS 为 $\infty$）。我们建立了从任意初始配置（即自稳定方式）解决聚集及相关问题的 MAS。我们的结果包括：存在散列问题族 $c$SCT $(1 \leq c \leq n)$，使得 $c$SCAT 的 MAS 为 $c$（其中 $n$ 为群体规模）；聚集问题的 MAS 为 2；对于将所有非故障机器人聚集到单点的问题，MAS 为 3（与故障数量 $(< n)$ 无关）；然而，在最多存在一个崩溃故障的情况下，将所有机器人聚集到单点的问题的 MAS 为 $\infty$。