  We study the path planning problem for continuum-arm robots, in which we are
given a starting and an end point, and we need to compute a path for the tip of
the continuum arm between the two points. We consider both cases where
obstacles are present and where they are not. We demonstrate how to leverage
the continuum arm features to introduce a new model that enables a path
planning approach based on the configurations graph, for a continuum arm
consisting of three sections, each consisting of three muscle actuators. The
algorithm we apply to the configurations graph allows us to exploit parallelism
in the computation to obtain efficient implementation. We conducted extensive
tests, and the obtained results show the completeness of the proposed algorithm
under the considered discretizations, in both cases where obstacles are present
and where they are not. We compared our approach to the standard inverse
kinematics approach. While the inverse kinematics approach is much faster when
successful, our algorithm always succeeds in finding a path or reporting that
no path exists, compared to a roughly 70% success rate of the inverse
kinematics approach (when a path exists).
