Algorithm 1. The motion model-based ${\sigma }_{skip}$ numerical search algorithm.

Input: Current re-entry motion state of the vehicle Output:${\sigma }_{skip}$ Control variable:$\alpha$, $\sigma$ 1: Calculate the range-to-go$R_{togo}$ 2: Load Equation (1) state and parameters. 3: Load expected range threshold state:$e_{thres}^{*}(V_{thres}^{*},h_{thres}^{*})$. 4: for [${\widehat{\sigma }}_{skip}=0 \mathrm{to} {\sigma }_{skip\_}{}_{\max }$(increase 5 degrees per cycle) ] do 5:  for ($\mathrm{i}=0 \mathrm{to} \mathrm{N}$) do 6:   3-DOF equations numerical integration output assignment 7:    Compare $R_{thres}$ and $R_{togo}$, call Method 2; 8:   if $R_{thres}<R_{togo}$ then 9:     $\alpha ={\alpha }_{profil}$, $\sigma ={\widehat{\sigma }}_{skip}$, call Method 3; 10:   else 11:     call Method 1; 12:     $\alpha ={\alpha }_{profil}$, $\sigma ={\sigma }_{final}$, call Method 3; 13:   end 14:   $\alpha$, $\sigma$ input to 3-DOF equations and numerical integration; 15:   if $R_{togo}\le R_{thres}$ then 16:     Calculate the current state ${\mathrm{e}}_{thres}(V_{thres}^{},h_{thres})$; 17:     break; 18:   end 19:  end 20: end 21: According to ${\widehat{\sigma }}_{skip}$ given and ${\mathrm{e}}_{thres}(V_{thres}^{},h_{thres})$, ${\mathrm{e}}_{thres}(V_{thres}^{},h_{thres})$ and ${\widehat{\sigma }}_{skip}$ database is built, and $e_{thres} \mathrm{vs}. {\widehat{\sigma }}_{skip}$ curve is fitted by the least square method; 22: Input $e_{thres}^{*}(V_{thres}^{*},h_{thres}^{*})$ and calculate ${\widehat{\sigma }}_{skip}^{*}$; 23: ${\sigma }_{skip}={\widehat{\sigma }}_{skip}^{*}$.