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Optimal control on Lie groups with applications to attitude control

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Abstract

In this paper we solve a class of optimal control problems on Lie groups in the sense that we derive differential equations which the optimal controls must satisfy. These results are applied to the attitude control of a spacecraft modeled as a rigid body. Specifically, we derive control laws (both in open-loop and closed-loop form) to maneuver the spacecraft between two given rotational states in finite time. The laws are such that a cost functional measuring the over-all angular velocity during the spacecraft’s motion is minimized. They do not require recourse to numerical methods and hence can be easily implemented in an on-board attitude control system. After dealing with a three-axis controlled spacecraft we also discuss the case that only torques about two principal axes of an axisymmetric spacecraft can be exerted.

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  1. Fachbereich Mathematik, Naturwissenschaften, Datenverarbeitung und Umwelttechnik, Fachhochschule Wiesbaden, Kurt-Schumacher-Ring 18, D-65197, Wiesbaden, Germany

    Karlheinz Spindler

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  1. Karlheinz Spindler
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Correspondence to Karlheinz Spindler.

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Spindler, K. Optimal control on Lie groups with applications to attitude control. Math. Control Signal Systems 11, 197–219 (1998). https://doi.org/10.1007/BF02741891

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  • DOI: https://doi.org/10.1007/BF02741891

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