The Cubli: modeling and nonlinear attitude control utilizing quaternions. - Bobrow, Fabio (2022)
This thesis consists of the modeling and nonlinear attitude control of the Cubli, a cube with three reaction wheels mounted on orthogonal faces that turns into a reaction wheel based 3D inverted pendulum when positioned in one of its vertices. Although this plant is not new, the novelty of this work is the use of quaternions instead of Euler angles as feedback control states. A good advantage of using quaternions, besides avoiding singularities and trigonometric functions, is that it allows working out quite complex dynamic equations completely by hand utilizing vector notation. The entire modeling and nonlinear control law is derived without the need of any mathematical symbolic software in a very didactic and self-contained way, being a contribution to control education. In addition, the original plant utilizes six IMUs spread throughout the entire structure in previously known positions. The Cubli of this work utilizes an accelerometer together with a rate gyroscope in a quaternion based complementary lter, which requires only one IMU placed anywhere and yields equally satisfactory results. Modeling is performed utilizing Lagrange equations and it is validated through computer simulations and Poinsot trajectories analysis. The derived nonlinear control law is based on feedback linearization technique, thus being time-invariant and equivalent to a linear one dynamically linearized at the given reference. Moreover, it is characterized by only three straightforward tuning parameters. Computer simulations and experimental results are presented for validation, as well as all the mechanical, electronical and algorithm development of the system.