Unit quaternions are a powerful tool for singularity free analysis and the control of arbitrary amplitude motion in a three-dimensional space. The authors present the use of proportional derivative quaternion feedback stabilisation for relative motion attitude control. Global asymptotic stability is guaranteed by defining a particular Lyapunov function and formal requirements are established. Conditions for a finite time control are also presented.
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Fragopoulos et al. (2004) studied this question.
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