Modeling and Control of a Tetrahedron-Shaped Inverted Pendulum with Torque-Actuation

Abstract

Abstract This paper provides a methodical procedure for the modeling and control of a tetrahedron-shaped inverted pendulum, balancing on one of its corners. The presented implementation realizes actuation by four motorized reaction wheels with high rotary inertia on the tetrahedron’s internal sides. By applying a controlled torque on the tetrahedron’s center of mass, the system can be rotated in its environment. The considered system is implemented as a real prototype, which is briefly introduced. The modeling of the tetrahedron-shaped pendulum leads to a non-linear state space model that can be used for a much greater class of inverted pendulums with arbitrary number of reaction wheels, only by changing the parameterization. Further, the non-linear model is linearized and an appropriate control concept stabilizes the system in one of its instable equilibrium positions: standing on a corner.