  The paper deals with motion planning for a spin-rolling sphere when the
sphere follows a straight path on a plane. Since the motion of the sphere is
constrained by the straight line, the control of the sphere's spin motion is
essential to converge to a desired configuration of the sphere. In this paper,
we show a new geometric-based planning approach that is based on a full-state
description of this nonlinear system. First, the problem statement of the
motion planning is posed. Next, we develop a geometric controller implemented
as a virtual surface by using the Darboux frame kinematics. This virtual
surface generates arc-length-based inputs for controlling the trajectories of
the sphere. Then, an iterative algorithm is designed to tune these inputs for
the desired configurations. The feasibility of the proposed approach is
verified by simulations.
