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融合可观测度的小天体附着轨迹优化方法

Trajectory Optimization Method for Small Body Landing Integrated with Observability

  • 摘要: 针对探测器附着小天体过程中因导航系统感知能力不足而导致的状态估计精度下降问题,提出了一种融合可观测度的小天体附着轨迹优化方法。首先,基于Fisher信息矩阵量化光学导航性能,推导了可观测度解析表达式,将可观测度作为新增性能指标引入轨迹优化框架,从而实现燃料消耗与导航精度之间的工程折中;其次,利用同伦系数将燃耗-可观测度最优控制问题与能量最优控制问题相关联,通过调整同伦系数和可观测度权重系数,实现最优控制问题的迭代解算;最后,以101955 Bennu为对象进行仿真分析,仿真结果表明,该方法能以合理燃耗为代价,有效提升附着轨迹的导航性能。

     

    Abstract: Aiming at the problem of degradation of state estimation accuracy caused by insufficient perception ability of navigation system during the landing of small bodies, a trajectory optimization method integrated with observability is proposed. First, the optical navigation performance is quantified based on the Fisher information matrix. An analytical expression for the observability is derived. The observability, as a new performance index, is introduced into the trajectory optimization framework. In this way, an engineering trade-off between fuel consumption and navigation accuracy is achieved. Secondly, the homotopy coefficients are used to associate the fuel-observability optimal control problem with the energy optimal control problem. By adjusting homotopy coefficients and observability weight coefficient, the iterative solution of the optimal control problem is realized. Finally, simulation studies are conducted on 101955 Bennu. The simulation results demonstrate that the proposed method can effectively enhance the navigation performance of the landing trajectory while maintaining reasonable fuel consumption.

     

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