  Spherical robots can conduct surveillance in hostile, cluttered environments
without being damaged, as their protective shell can safely house sensors such
as cameras. However, lateral oscillations, also known as wobble, occur when
these sphere-shaped robots operate at low speeds, leading to shaky camera
feedback. These oscillations in a pendulum-actuated spherical robot are caused
by the coupling between the forward and steering motions due to nonholonomic
constraints. Designing a controller to limit wobbling in these robots is
challenging due to their underactuated nature. We propose a model-based
controller to navigate a pendulum-actuated spherical robot using wobble-free
turning maneuvers consisting of circular arcs and straight lines. The model is
developed using Lagrange-D'Alembert equations and accounts for the coupled
forward and steering motions. The model is further analyzed to derive
expressions for radius of curvature, precession rate, wobble amplitude, and
wobble frequency during circular motions. Finally, we design an input-output
feedback linearization-based controller to control the robot's heading
direction and wobble. Overall, the proposed controller enables a teleoperator
to command a specific forward velocity and pendulum angle as per the desired
turning radius while limiting the robot's lateral oscillations to enhance the
quality of camera feedback.
