Dynamic model of a gyroscopic wheel

We develop a dynamic model of a gyroscopic wheel, an important component of Gyrover, a single-wheel robot developed at Carnegie Mellon University. The Gyrover robot consists of a single wheel, and is actuated through a spinning flywheel attached through a two-link manipulator at the wheel bearing. The flywheel can be tilted to achieve steering, and can be driven forwards and backwards to accelerate the robot. This paper focuses on developing a 3D model of the wheel part of the Gyrover. We first describe the Gyrover robot. We then develop the dynamic model of the wheel through the Lagrangian constrained generalized formulation. Finally, we implement the resulting equations of motion and present simulation results for the unactuated Gyrover in the different gravitational environments of Earth, the Moon, and Mars