  Motion planning is an essential aspect of autonomous systems and robotics and
is an active area of research. A recently-proposed sampling-based motion
planning algorithm, termed 'Generalized Shape Expansion' (GSE), has been shown
to possess significant improvement in computational time over several existing
well-established algorithms. The GSE has also been shown to be
probabilistically complete. However, asymptotic optimality of the GSE is yet to
be studied. To this end, in this paper we show that the GSE algorithm is not
asymptotically optimal by studying its behaviour for the promenade problem. In
order to obtain a probabilistically complete and asymptotically optimal
generalized shape-based algorithm, a modified version of the GSE, namely 'GSE*'
algorithm, is subsequently presented. The forementioned desired mathematical
properties of the GSE* algorithm are justified by its detailed analysis.
Numerical simulations are found to be in line with the theoretical results on
the GSE* algorithm.
