This paper presents a new quaternion-based attitude tracking controller. A general Lyapunov function is defined whose derivative is control dependent and a control is chosen to guarantee asymptotic stability of the zero-error state. The corresponding closed loop error dynamics are shown to reduce to a simple 1 degree of freedom description in terms of the eigen-axis angle error. The main contribution of this paper is to present a special case where the closed-loop error dynamics reduce to a simple linear oscillator description (without the need for linearisation). This means that the controller can be tuned to guarantee exponentially fast tracking with a damped response and without oscillation.
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