Controllability Properties and Time Minimal Geodesics for Attitude Control With a Single Torque
Résumé
In this article, we analyze the time-minimal geodesics for the controlled Euler-Poinsot dynamics describing the evolution of the orientation of a rigid spacecraft controlled with a single bounded torque. We discuss in detail the two underlying control problems of first the control of the angular velocity of the satellite and second the control of the attitude, our aim being to describe in fine new closed loop optimal controls based on the so-called abnormal geodesics which can be computed thanks to Pontryagin's maximum principle. The angular velocity of the abnormal geodesics are branches of a cubic which can be parameterized by P-Weierstrass functions and they lead to define mechanical gates (or strokes for swimmers) to control the attitude generalizing the stationary rotations of the uncontrolled case. They correspond to representation of attitude transfers depending upon the internal geometry of the spacecraft and abnormal angular velocities geodesics. In fine, the study will allow to satisfy the constraints in the NiceCube mission that is bounded torque and time maneuver.
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