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Newton-Kantorovich/Radau pseudospectral solution to rigid spacecraft time-optimal three-axis reorientation
Institution:1. Chongqing Technology and Business University, 401320 Chongqing, China;2. National University of Defense Technology, 410073 Changsha, China
Abstract:The Newton-Kantorovich/Radau pseudospectral method is implemented in a homotopy scheme to solve the rigid spacecraft time-optimal three-axis reorientation problem. First, the reorientation differential equations associated with the current homotopic variable are linearized about the nominal (previous homotopic variable) solution. Then, the Radau pseudospectral method is used to solve the resulting linearized differential equations. By successively updating the nominal solution with the Newton-Kantorovich approach, the linearized solving procedure is iterated to achieve high-order precision. Because no numerical integration is needed and only linear algebraic equations are solved, the proposed method is computationally efficient. Finally, performance of the proposed method is illustrated through numerical examples.
Keywords:Time-optimal reorientation  Three-axis control  Control structure  Newton-Kantorovich approach  Radau pseudospectral method
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