Wobble control of a pendulum-based spherical robot

Abstract

Spherical robots can conduct surveillance in hostile, cluttered environments without being damaged. Their protective shell can safely house sensors and sensitive components. The pendulum-based spherical robot provides a platform (yoke) for a camera to be housed inside the protective hull. However, lateral oscillations, also known as wobble, become prominent when operated at low speeds, leading to shaky camera feedback. These oscillations 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. In this paper, we propose a model-based (wobble-free) controller to navigate a pendulum-steered spherical robot to perform 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. Furthermore, we also propose quantifiable metrics for wobble by deriving expressions for radius of curvature, precession rate, wobble amplitude, and wobble frequency during circular motions and designed an input–output feedback linearization-based controller to control the robot’s heading direction and wobble. Additionally, we extend the controller’s capabilities to handle point-to-point navigation, enabling the robot to execute more complex and goal-oriented trajectories. This research ensures the robot maintains wobble-free motion across diverse paths, enhancing its navigational autonomy and the quality of camera feedback. Overall, the proposed controller enables a teleoperator to command a specific forward velocity and pendulum angle as per the desired turning radius or destination while effectively limiting the robot’s lateral oscillations.