关键词: 轨迹, 姿态算法, 四元数, Gibbs矢量

Abstract:

To address the problem that the attitude in the polynomial large-maneuver model lacks an analytical expression, a large-maneuver attitude trajectory model based on the Gibbs vector polynomial is proposed. Firstly, based on the proposed trajectory model, the analytical expressions of attitude and angular velocity are derived to obtain the true value of the reference attitude. Secondly, according to the angular velocity model fitted by a finite-order polynomial, the angular increment sub-samples required for attitude calculation are constructed. Finally, two high-precision attitude algorithms, namely Picard iteration and Taylor series expansion, are adopted to verify the correctness of the model. The simulation results show that the Picard iteration algorithm outperforms the traditional second-order algorithm when the number of iterations reaches four and converges when the number of iterations reaches six; the Taylor series expansion algorithm outperforms the traditional second-order algorithm when the expansion order reaches six and converges when the expansion order reaches seven; and the steady-state performances of the two high-order attitude algorithms are consistent after convergence. The above results not only verify the relevant discussions on the performance of high-order attitude algorithms in existing literatures, but also confirm the effectiveness of the proposed trajectory model in the performance evaluation of high-order attitude algorithms.

Key words: trajctory, attitude algorithm, quaternion, Gibbs vector