This paper presents a new nonlinear quaternion feedback controller that makes rigid spacecrafts reoriented efficiently from arbitrary initial conditions to prescribed final conditions. The nonlinear spacecraft dynamics, comprised of Euler and quaternion kinematic equation, is shown to be formulated as linear parameter-varying (LPV) system, which is widely recognized as a systematic framework to design the traditional gain-scheduling controller for nonlinear systems. Then a new nonlinear quaternion controller is derived using the LPV framework. Compared to the published linear quaternion controller, this controller is shown to yield improved transient responses because of optimized high-order nonlinear terms of spacecraft dynamics. With this example, this paper also demonstrates that the LPV framework can provide an efficient and systematic tool to a class of nonlinear control design.
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