# The Optimal Quaternion Equilibrium Point - Using an Energy Function to Choose the Optimal Quaternion Equilibrium Point

### Margrete Djupaa, Rune Schlanbusch

#### Abstract

By parameterizing the attitude of a rotating rigid body in a closed-loop system with unit quaternions, the existence of dual equilibria leads to new challenges. In order to optimize the energy consumption due to control effort, the choice of the cheapest equilibria, that is, the one which requires least energy to reach, is essential. A new predicting solution of choosing the optimal equilibrium point for rotational maneuvers of a rigid body is presented in this article. This new solution consists of an energy function which base its prediction on the initial attitude on the rotational sphere, taking account for both potential and kinetic energy of the rigid body. The equilibrium energy function is developed through a previously presented statistical analysis for the system behaviour of a rigid body in closed loop attitude control.

#### References

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#### Paper Citation

#### in Harvard Style

Djupaa M. and Schlanbusch R. (2013). **The Optimal Quaternion Equilibrium Point - Using an Energy Function to Choose the Optimal Quaternion Equilibrium Point** . In *Proceedings of the 3rd International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,* ISBN 978-989-8565-69-3, pages 345-352. DOI: 10.5220/0004422903450352

#### in Bibtex Style

@conference{simultech13,

author={Margrete Djupaa and Rune Schlanbusch},

title={The Optimal Quaternion Equilibrium Point - Using an Energy Function to Choose the Optimal Quaternion Equilibrium Point},

booktitle={Proceedings of the 3rd International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,},

year={2013},

pages={345-352},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0004422903450352},

isbn={978-989-8565-69-3},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 3rd International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,

TI - The Optimal Quaternion Equilibrium Point - Using an Energy Function to Choose the Optimal Quaternion Equilibrium Point

SN - 978-989-8565-69-3

AU - Djupaa M.

AU - Schlanbusch R.

PY - 2013

SP - 345

EP - 352

DO - 10.5220/0004422903450352