Sliding-Mode-Based Control Design for the Butterfly Robot

We present a sliding-mode-based control design for orbital stabilization of the Butterfly robot’s periodic trajectories. The Butterfly robot comprises a vertically rotating, figure-eight-shaped link actuated by a motor, with a ball that rolls freely along its surface. This system provides a challenging benchmark for algorithms in dynamic and nonprehensile robotic manipulation. The control objective is to stabilize one-directional rolling of the ball along the link’s surface. Unlike previous works that employed transverse linearization combined with a linear quadratic regulator (LQR) to stabilize the linearized transverse dynamics, the proposed approach eliminates the need for solving the LQR problem by utilizing a sliding-mode control strategy. The proposed design is experimentally validated on a hardware setup, demonstrating effective orbital stabilization of the desired periodic motion.