Abstract
Wheeled pendulum is a mobile robot composed basically of an inverted pendulum which is provided with two wheels at the bottom. This allows the robot to describe translation displacements on a plane. Variables describing robot movements are 6: two coordinates on the plane, pendulum tilt angle, robot orientation on the plane, right wheel angular position, and left wheel angular position. However, only two actuators (DC motors) are used at the wheels to provide torque to the whole robot. Thus, we say that wheeled robot is an underactuated mechanical system. This feature and the fact that an inverted pendulum is unstable render this mechanical system very interesting for control design.
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Notes
- 1.
Authors of this chapter are, V.M. Hernández-Guzmán, R.V. Carrillo-Serrano, and O. Núñez-Anguiano, Universidad Autónoma de Querétaro, Facultad de Ingeniería, Querétaro, México.
- 2.
This is an example of the class of approximations that we consider: since the battery center of mass is not on the \(y_b\) axis but it is at a distance, say r, we should add to \(I_3\), that is shown here, the quantity \(r^2m_B\). This would represent a better estimate value for battery inertia.
- 3.
In fact, recall that according to (14.148) \(\varGamma _6\dot{\theta }\rightarrow 0\) exponentially.
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Hernández-Guzmán, V.M., Silva-Ortigoza, R., Orrante-Sakanassi, J.A. (2024). Control of Wheeled Pendulum. In: Automatic Control with Experiments. Advanced Textbooks in Control and Signal Processing. Springer, Cham. https://doi.org/10.1007/978-3-031-55960-0_14
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DOI: https://doi.org/10.1007/978-3-031-55960-0_14
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