We consider several convergence problems for autonomous mobile robots under the $\cal SSYNC$ model. Let $\Phi$ and $\Pi $ be a set of target functions and a problem, respectively. If the robots whose target functions are chosen from $\Phi$ always solve $\Pi$, 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 $\Pi$. Note that even if both $\phi$ and $\phi'$ are algorithms for $\Pi$, $\{ \phi, \phi' \}$ may not be compatible with respect to $\Pi$. 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 problem, assuming crash failures. We classify these problems from the viewpoint of compatibility; the group of the convergence, FC(1), FC(1)-PO and FC($f$)-CP, and the group of the gathering and FC($f$)-PO for $f \geq 2$ have completely opposite properties. FC($f$) for $f \geq 2$ is placed in between.

翻译：我们考虑$\cal SSYNC$模型下自主移动机器人的若干汇聚问题。设$\Phi$和$\Pi$分别为目标函数集合和问题。若其目标函数取自$\Phi$的机器人总能解决$\Pi$，则称$\Phi$关于$\Pi$是兼容的。若$\Phi$关于$\Pi$兼容，则每个目标函数$\phi \in \Phi$都是$\Pi$的算法。值得注意的是，即使$\phi$和$\phi'$同为$\Pi$的算法，$\{ \phi, \phi' \}$也可能关于$\Pi$不兼容。我们研究了崩溃故障情形下的汇聚问题、容错$(n,f)$-汇聚问题（FC($f$)）、向$f$个点的容错$(n,f)$-汇聚问题（FC($f$)-PO）、向凸$f$边形的容错$(n,f)$-汇聚问题（FC($f$)-CP）以及聚集问题。我们从兼容性角度对这些问题进行归类：汇聚问题、FC(1)、FC(1)-PO和FC($f$)-CP构成一组，而聚集问题及$f \geq 2$时的FC($f$)-PO则具有完全相反的性质。当$f \geq 2$时，FC($f$)介于两者之间。