(Preprint) AAS 21-374 LOW-THRUST TRAJECTORY OPTIMIZATION USING THE KUSTAANHEIMO-STIEFEL TRANSFORMATION
(Preprint) AAS 21-374 LOW-THRUST TRAJECTORY OPTIMIZATION USING THE KUSTAANHEIMO-STIEFEL TRANSFORMATION
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（预印本）AAS 21-374 使用 KUSTAANHEIMO-STIEFEL 变换进行低推力轨迹优化
DOI：
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Zachary Manchester
中科院分区：
文献类型：
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作者：
K. Tracy;Zachary Manchester
我们提出了一种利用Kustaanheimo-Stiefel转换的低头轨道转移问题的新型轨迹优化公式。对于不受干扰的两体运动，这种转换将非线性笛卡尔动力学映射到线性四维简单谐波振荡器。当添加扰动加速度时，动力学将变为非线性，但线性化的近似值明显优于替代状态表示。因此，Kustaanheimo-Stiefel动力学在基于梯度或牛顿的轨迹优化算法中具有强大的优势。我们通过这些动力学制定了一个低推力的轨迹优化问题，并从经验上证明可以找到推力剖面，而无需向求解器提供初始猜测，而打结点比其他状态表示较少。
We present a novel trajectory optimization formulation for the low-thrust orbital transfer problem utilizing the Kustaanheimo-Stiefel transformation. For unperturbed two-body motion, this transformation maps the nonlinear Cartesian dynamics to a linear four-dimensional simple-harmonic oscillator. When perturbing accelerations are added, the dynamics become nonlinear, but are significantly better approximated by linearization than alternative state representations. Therefore, the Kustaanheimo-Stiefel dynamics have strong advantages in gradient or Newton-based trajectory optimization algorithms. We formulate a low-thrust trajectory optimization problem with these dynamics and demonstrate empirically that thrust profiles can be found without providing an initial guess to the solver, and with fewer knot points than alternative state representations.