Trajectory Tracking, Estimation, and Control of a Pendulum-Driven Spherical Robot

A methodology is presented to design the feedforward controller based on the kinematics and dynamics of the spherical robot rolling in a circular motion. Using this method, the desired trajectory is approximated using circles as basis functions. It was shown that the feedforward controller realizes tracking of the spherical robot about a desired trajectory in the absence of external disturbances and model uncertainty. When the spherical robot had nonzero initial conditions relative to the desired trajectory, the linear feedback control law was shown to drive the error between the velocity and the desired velocity of the spherical robot to zero.