Abstract: The agility performance of spacecraft with reaction wheels is primarily determined by the wheel configuration and allocation law. Due to the fact that complex allocation laws can easily lead to issues such as discontinuous speed commands for the reaction wheels, which in turn cause reliability problems, the pseudo-inverse allocation is the most widely adopted method in engineering applications. However, there are currently no reference guidelines for optimizing the reaction wheel configuration under this allocation. To address this issue, this study focuses on spacecraft with four identical reaction wheels in a pyramid configuration. The angular velocity and angular acceleration envelopes were derived and a methodology for optimizing the reaction wheel configuration was proposed. Firstly, the pseudo-inverse allocation was transformed into a linear algebraic constraint related to the angular momentum of individual wheels. Using spatial analytic geometry and linear system theory, it was proved for the first time that both the angular velocity and angular acceleration envelopes under the pseudo-inverse allocation are octahedrons. Subsequently, it was demonstrated that the optimal azimuth angle of the pyramid is zero. Thus the problem of designing parameters for attitude path was reformulated as the geometric task of identifying the maximum-area square within a right-angled triangle. Consequently, an analytical solution for both the maximum edge length and the corresponding skew angle of the pyramid was derived. Ultimately, the optimal configuration was determined by comparing the maximum edge lengths under each symmetry-axis layout. Simulation case studies showed that configuration angle optimization achieved a 27.2% expansion in both angular velocity and angular acceleration envelopes compared with conventional 54.74° skew angle, while symmetry-axis screening added a further 71.9% enhancement. By considering the most widely adopted wheel configuration and allocation law, the proposed methodology establishes a comprehensive theoretical foundation for analyzing the agility performance of spacecraft, quantitative benchmarks for attitude planning, and systematic optimization procedures for reaction wheel configurations.

Key words: agility performance, pseudo-inverse allocation, pyramid configuration, configuration angle optimization