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：我们研究欧几里得平面上自主移动机器人的群体行为。每个机器人具有目标函数，用于根据所有机器人的位置确定其目的地。传统上，群体中所有机器人采用相同目标函数。我们允许群体中机器人采用不同目标函数，并研究不同目标函数数量对问题解决能力的影响。具体而言，我们关注在全体机器人采用相同目标函数时不可解的已知问题中，需要多少种不同目标函数才能解决这些问题，将目标函数视为与时间和消息类似的问题求解资源。解决问题Π所需的不同目标函数的最小数量称为Π的最小算法规模（MAS）。（若即使机器人拥有唯一目标函数也无法解决Π，则MAS为∞。）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：存在一类散射问题cSCT（1 ≤ c ≤ n），其中cSCAT的MAS为c，这里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一点的问题，无论崩溃故障数量（小于n）如何，其MAS为3。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一点问题的MAS为∞。