STOCHASTIC CONFLICT-FREE 4 D TRAJECTORY OPTIMIZATION IN THE PRESENCE OF UNCERTAINTY

STOCHASTIC CONFLICT-FREE 4 D TRAJECTORY OPTIMIZATION IN THE PRESENCE OF UNCERTAINTY
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存在不确定性时的随机无冲突 4D 轨迹优化

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发表时间：
2014
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通讯作者：
Sally C. Johnson
Sally C. Johnson
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作者：
Sally C. Johnson

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本文提出了一种几乎最优的无冲突轨迹生成算法，可以实时地从任意给定的初始状态开始确定冲突解决轨迹，而不需要实际求解最优控制问题，也不会牺牲精度。首先，考虑了风的空间相关性模型，提出了一种基于广义多项式混沌方法的概率冲突检测算法。广义多项式混沌算法能够以较高的计算效率确定复杂非线性动力系统的不确定性演化。此外，还提出了一种将广义多项式混沌方法与伪谱方法相结合的求解随机最优控制问题的数值算法。将随机最优控制方法与所提出的冲突检测算法相结合，解决了冲突消解问题。利用基于凸优化的广义多项式混沌算法构造最优无冲突轨迹的响应面，在不实际求解随机最优控制问题和牺牲精度的情况下，实时生成从任意给定初始状态出发的近最优无冲突轨迹。通过对多机间二维冲突检测与消解问题的数值仿真，对随机算法的性能和有效性进行了评估和验证。
This paper explores a near-optimal conflict-free trajectory generation algorithm to determine conflict resolution trajectories starting from any given initial states in real time without actually solving optimal control problems and sacrificing accuracy. First, the spatially correlated wind model is considered for wind uncertainty, and a probabilistic conflict detection algorithm using the generalized polynomial chaos method is proposed. The generalized polynomial chaos algorithm can determine the evolution of uncertainty in the complex nonlinear dynamical systems with high computational efficiency. In addition, a numerical algorithm that incorporates the generalized polynomial chaos method into the pseudospectral method is proposed to solve the stochastic optimal control problems. The stochastic optimal control method is combined with the proposed conflict detection algorithm to solve the conflict resolution problem. Moreover, the response surfaces of the optimal conflict-free trajectories are constructed by using the generalized polynomial chaos algorithm based on convex optimization, and the near-optimal conflictfree trajectories starting from any given initial states are generated in real time without actually solving the stochastic optimal control problems and sacrificing accuracy. Through numerical simulations of the two-dimensional conflict detection and resolution problem among multiple aircraft, the performance and effectiveness of the stochastic algorithms are evaluated and demonstrated.