New End to End Trajectory Tracking Controller for Spherical Robot Based on Feedback Linearization and Singular Perturbation

The dynamic model of a spherical robot exhibits nonlinearity and underactuation, posing significant challenges for model-based trajectory tracking control. Previous control methods often required two cascaded controllers to compute the motor torques needed for trajectory tracking. Additionally, controllers using Taylor series expansion-based linearization methods could only maintain high accuracy near operating points. Therefore, previous control methods were complex and restricted to specific conditions. Addressing these issues, this paper proposes an end to end trajectory tracking controller based on feedback linearization and singular perturbation control. This new end to end controller directly computes the required motor torques using the desired trajectory instead of using two cascade controllers to track desired trajectory. By employing input-output feedback linearization, the nonlinear dynamic model is accurately transformed into a linear system, simplifying controller design and ensuring the convergence of the robot's motion trajectory to the desired path. Furthermore, singular perturbation control stabilizes internal dynamics without increasing control inputs, thereby ensuring the feasibility of the feedback linearization controller. Simulation results demonstrate that the proposed controller effectively enables the spherical robot to track the given trajectory.