  An autonomous robot with a limited vision range finds a path to the goal in
an unknown environment in 2D avoiding polygonal obstacles. In the process of
discovering the environmental map, the robot has to return to some positions
marked previously, the regions where the robot traverses to return are defined
as sequences of bundles of line segments. This paper presents a novel algorithm
for finding approximately shortest paths along the sequences of bundles of line
segments based on the method of multiple shooting. Three factors of the
approach including bundle partition, collinear condition, and update of
shooting points are presented. We then show that if the collinear condition
holds, the exactly shortest paths of the problems are determined, otherwise,
the sequence of paths obtained by the update of the method converges to the
shortest path. The algorithm is implemented in Python and some numerical
examples show that the running time of path-planning for autonomous robots
using our method is faster than that using the rubber band technique of Li and
Klette in Euclidean Shortest Paths, Springer, 53-89 (2011).
