  Consider a set of $n$ mobile entities, called robots, located and operating
on a continuous circle, i.e., all robots are initially in distinct locations on
a circle. The \textit{gathering} problem asks to design a distributed algorithm
that allows the robots to assemble at a point on the circle. Robots are
anonymous, identical, and homogeneous. Robots operate in a deterministic
Look-Compute-Move cycle within the circular path. Robots agree on the clockwise
direction. The robot's movement is rigid and they have limited visibility
$\pi$, i.e., each robot can only see the points of the circle which is at an
angular distance strictly less than $\pi$ from the robot.
  Di Luna \textit{et al}. [DISC'2020] provided a deterministic gathering
algorithm of oblivious and silent robots on a circle in semi-synchronous
(\textsc{SSync}) scheduler. Buchin \textit{et al}. [IPDPS(W)'2021] showed that,
under full visibility, $\mathcal{OBLOT}$ robot model with \textsc{SSync}
scheduler is incomparable to $\mathcal{FSTA}$ robot (robots are silent but have
finite persistent memory) model with asynchronous (\textsc{ASync}) scheduler.
Under limited visibility, this comparison is still unanswered. So, this work
extends the work of Di Luna \textit{et al}. [DISC'2020] under \textsc{ASync}
scheduler for $\mathcal{FSTA}$ robot model.
