SCIENTIA SINICA Informationis, Volume 49 , Issue 11 : 1472-1487(2019) https://doi.org/10.1360/SSI-2019-0132

Autonomous trajectory planning for launch vehicle under thrust drop failure

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  • ReceivedJun 24, 2019
  • AcceptedSep 17, 2019
  • PublishedNov 13, 2019


An online autonomous rescue strategy and the algorithm for launch vehicle are studied in the case of a thrust drop during ascending flight. First, an iterative guidance method and numerical integration are used to evaluate the remaining carrying capacity. When the target orbit is unreachable, but the lowest safe orbit could be met, an optimal rescue orbit (ORO) needs to be solved. Using the geocentric angle estimation, orbit coordinate system transformation, and convexification, the maximum-height circular orbit in the orbit plane determined by states at failure time, is found under the constraint of geocentric angle. Then, an optimal circular orbit (OCO) relaxing the above constraint is solved by the adaptive collocation method (ACM) using the former solution as initial values. Finally, a decision whether to adjust other orbital elements by comparing the height between OCO and target orbit is made. The algorithm gives priority to the orbit height, optimizes the ORO based on the objective function weights, and makes full use of the advantages of geocentric angle estimation: simplifying the terminal constraints, making the convex optimization achieve good convergence, and improving the effectiveness of the ACM under reasonable initial guess. The simulation results show that the proposed strategy and algorithm are adaptable and, convergent for onboard application.

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  • Figure 1

    (Color online) Autonomous rescue strategy logic diagram

  • Figure 2

    (Color online) Planning of the highest circular orbit

  • Figure 3

    Rescue orbit optimization interval

  • Figure 4

    Optimal rescue flight trajectory in 250 s fault. (a) Semimajor axis;(b) height;(c) velocity;(d) orbital inclination;(e) longitude of ascending node;(f) flight path angle

  • Figure 5

    Optimal rescue flight trajectory in 150 s fault. (a) Semimajor axis;(b) height;(c) velocity;(d) orbital inclination;(e) longitude of ascending node;(f) flight path angle

  • Figure 6

    Optimal rescue flight trajectory in 90 s fault. (a) Semimajor axis;(b) height;(c) velocity;(d) orbital inclination;(e) longitude of ascending node;(f) flight path angle


    Algorithm 1 自主救援算法


    若${\rm~dm}_r\le~{\rm~dm}_0$, 则根据迭代制导指令继续向原目标轨道飞行, 转第11步(${\rm~Flag}_{\rm~Rescue}=1$);

    若${\rm~dm}_r>{\rm~dm}_0$, 则估计利用迭代制导进入最低安全轨道需要消耗的燃料${\rm~dm}_s$, 若${\rm~dm}_s>{\rm~dm}_0$, 则转第4步, 否则转第5步;

    故障状态下火箭无法将载荷送入最低安全轨道, 转第11步(${\rm~Flag}_{\rm~Rescue}=0$);

    计算当前状态对应的轨道面($i_0$和$\Omega_0$), 并根据式(9)估计预报入轨点对应的地心夹角$\Phi_k$, 从而建立轨道坐标系;


    利用原始对偶内点法快速求解Subproblem3, 将最优解转换至发射惯性系下, 并作为最优圆救援轨道问题Subproblem4的初始猜测值;

    利用自适应配点算法求解Subproblem4, 若最优圆救援轨道高度大于原目标轨道近地点高度, 转第9步, 否则转第11步(${\rm~Flag}_{\rm~Rescue}=2$);


    利用自适应配点算法求解Subproblem5, 得到最优椭圆救援轨道(${\rm~Flag}_{\rm~Rescue}=3$);

    流程结束, 返回${\rm~Flag}_{\rm~Rescue}$.

  • Table 1   Simulation parameters
    Symbol Variable Value
    $t_s$ Second stage start time 0 s
    $m_s$ Second stage initial mass 100000 kg
    $m_f$ Total mass of second stage structure and payload 22000 kg
    $T_{\rm~ref}$ Standard thrust amplitude 700 kN
    $I_{\rm~sp}$ Engine specific impulse 350 s
    $\kappa$ Thrust percentage after dropping 0.7, 0.75, 0.8
    $t_0$ Failure time $\left\{~{30i\left|~{i~=~1,2,\ldots,7}~\right.}~\right\}$ s
    $R_0$ Earth radius 6378140 m
    $\mu$ Gravitational coefficient of the earth 3.986$\times10^{14}$ m$^3$/s$^2$
    $g_0$ Sea level gravity acceleration 9.8 m/s$^2$
    $H_0$ Second stage initial altitude 110 km
    $V_0$ Second stage initial velocity 2750 m/s
    $h_{\rm~safe}$ Minimum safe orbit height 160 km
  • Table 2   Orbital elements of optimal rescue method and IGM in 150 s fault
    Variable $a$ (m) $e$ $i~(^{\circ})$ $\Omega~(^{\circ})$ $w$ ($^\circ$) ${\rm~hp}$ (km) ${\rm~ha}$ (km)
    Target orbit 6628140 $7.54\times10^{-3}$ 42.00 315.00 160 200.0 300.0
    Circular rescue orbit 6589303 0 41.58 315.33 211.2 211.2
    IGM orbit 6582461 $1.2\times10^{-3}$ 42.00 315.00 107.00 196.5 212.1
    Elliptical rescue orbit (OPT1) 6627556 $7.46\times10^{-3}$ 41.58 315.33 173.91 200.0 298.8
    Elliptical rescue orbit (OPT2) 6627081 $7.39\times10^{-3}$ 42.00 315.11 174.05 200.0 297.9
    Elliptical rescue orbit (OPT3) 6626479 $7.29\times10^{-3}$ 42.19 315.00 174.13 200.0 296.7
    Elliptical rescue orbit (OPT4) 6625825 $7.20\times10^{-3}$ 42.00 315.00 174.11 200.0 295.4
  • Table 3   Orbital elements of optimal rescue method and IGM in 90 s fault
    Variable $a$ (m) $e$ $i~(^\circ)$ $\Omega~(^\circ$) $w$ ($^\circ$) hp (km) ha (km)
    Target orbit 6628140 $7.54\times10^{-3}$ 42.00 315.00 160 200 300
    IGM orbit 6409930 0.0264 42.02 315.00 351.54 $-$137.5 201.0
    Circular rescue orbit 6554274 0 40.97 315.73 261.47 176.1 176.1

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