A mathematical model is developed for a rolling robot with a cylindrically-shaped, elliptical outer surface that has the ability to alter its shape as it rolls, resulting in a torque imbalance that accelerates or decelerates the robot. A control scheme is implemented, whereby angular position and angular velocity are used as feedback to trigger and define morphing actuation. The goal of the control is to direct the robot to follow a given angular velocity profile. Equations of motion for the rolling robot are formulated and solved numerically. Results show that by automatically morphing its shape in a periodic fashion, the rolling robot is able to start from rest, achieve constant average velocity and slow itself in order to follow a desired velocity profile with significant accuracy.

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