We investigate autonomous mobile robots in the Euclidean plane. A robot has a function called target function to decide the destination from the robots' positions. Robots may have different target functions. If the robots whose target functions are chosen from a set $\Phi$ of target functions always solve a problem $\Pi$, we say that $\Phi$ is compatible with respect to $\Pi$. If $\Phi$ is compatible with respect to $\Pi$, every target function $\phi \in \Phi$ is an algorithm for $\Pi$. Even if both $\phi$ and $\phi'$ are algorithms for $\Pi$, $\{ \phi, \phi' \}$ may not be compatible with respect to $\Pi$. From the view point of compatibility, we investigate the convergence, the fault tolerant ($n,f$)-convergence (FC($f$)), the fault tolerant ($n,f$)-convergence to $f$ points (FC($f$)-PO), the fault tolerant ($n,f$)-convergence to a convex $f$-gon (FC($f$)-CP), and the gathering problems, assuming crash failures. Obtained results classify these problems into three groups: The convergence, FC(1), FC(1)-PO, and FC($f$)-CP compose the first group: Every set of target functions which always shrink the convex hull of a configuration is compatible. The second group is composed of the gathering and FC($f$)-PO for $f \geq 2$: No set of target functions which always shrink the convex hull of a configuration is compatible. The third group, FC($f$) for $f \geq 2$, is placed in between. Thus, FC(1) and FC(2), FC(1)-PO and FC(2)-PO, and FC(2) and FC(2)-PO are respectively in different groups, despite that FC(1) and FC(1)-PO are in the first group.

翻译：我们研究欧几里得平面中的自主移动机器人。每个机器人具有一个称为目标函数的函数，用于根据机器人位置决定其目的地。机器人可能拥有不同的目标函数。若所有目标函数选自集合Φ的机器人总能解决某个问题Π，则称Φ关于Π是兼容的。若Φ关于Π兼容，则每个目标函数φ∈Φ都是Π的一种算法。即使φ和φ'均为Π的算法，{φ, φ'}关于Π仍可能不兼容。从兼容性角度出发，我们研究了收敛问题、容错(n,f)-收敛问题(FC(f))、容错(n,f)-收敛至f个点问题(FC(f)-PO)、容错(n,f)-收敛至凸f边形问题(FC(f)-CP)以及聚集问题，并假设存在崩溃故障。所得结果将这些归为三类：第一类包括收敛、FC(1)、FC(1)-PO和FC(f)-CP——所有能始终收缩构型凸包的目标函数集合都是兼容的；第二类包括聚集和f≥2时的FC(f)-PO——不存在能始终收缩构型凸包的目标函数集合是兼容的；第三类（f≥2时的FC(f)）则介于两者之间。因此，尽管FC(1)与FC(1)-PO同属第一类，但FC(1)与FC(2)、FC(1)-PO与FC(2)-PO、以及FC(2)与FC(2)-PO分别属于不同类别。