Mechanical Engineering The University of Adelaide Australia

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Robotics Group

School of Mechanical

SA 5005

+61 8 8303 5460
+61 8 8303 4367

Project Picture
Photo of Ben Cazzolato

Ben Cazzolato

Photo of James Driver

James Driver

Photo of Zebb Prime

Zebb Prime

Photo of Dylan A. Thorpe

Dylan A. Thorpe

Rotational Inverted Pendulum

Ben S. Cazzolato, James Driver, Zebb D. Prime and Dylan A. Thorpe

Keywords: Robotics, control, inverted pendulum, rotational pendulum, Furuta pendulum, pendulum dynamics, rotary inverted pendulum.

(Commenced: 01-Jan-2004,Concluded: 21-Oct-2004)

The Dynamics of the (single rotational) Furuta Pendulum

The Furuta pendulum, or rotational inverted pendulum, is a system found in many control labs. It provides a compact yet impressive platform for control demonstrations and draws the attention of the control community as a platform for the development of non-linear control laws.

Despite the popularity of the platform there are very few papers which employ the correct dynamics and only one that derives the full system dynamics. To address this an internal technical report has been written where the full dynamics of the Furuta pendulum have been derived using two methods; a Lagrangian formulation and an iterative Newton-Euler formulation. Approximations are made to the full dynamics which converge to the more commonly presented expressions. The system dynamics are then linearised using a Jacobian.

The dynamics were derived using the Symbolic Toolbox in Matlab. To validate the differential equations, a Simulink / SimMechanics model was developed. A VR model was used to visualise the results.

Design and Construction of a Rotational Double Inverted Pendulum

This honours project covers the design and build of a rotational double inverted pendulum.

The non-linear dynamics were modelled in Matlab and Simulink. A LQR controller has been used to stablise the pendulums and regulate the horizontal arm. In addition, for the single inverted pendulum, a non-linear swing-up controller was designed to move the bob into a vertical position.

Virtual reality models of the single and double inverted pendulums were built to visualise the dynamics.

Finally, a physical model was built and tested. The were several practical issues necessary to realised such a system in practice. The biggest hurdle was transmitting the rotational encoder signals (used to measure the second pendulum angle) through the vertical joint between the two pendulumns. An "optical" slip ring was used for this purpose.

Dynamics of the (single) Furuta pendulum

Double Inverted Pendulum Deliverables

External Link: Commercial supplier of inverted pendulums

External Link: Other Single Stage Rotational Pendulums

External Link: Other Two single-stage Rotational

External Link: Single Stage Linear

External Link: Two Stage Linear

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