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The uncertainties during the return trajectory of vertical takeoff and vertical landing reusable launch vehicle weaken the ability of precision landing and make the return process more challenging. This paper is devoted to quantifying the probability uncertainty of return trajectory with uncertain parameters. The uncertainty model of return multi-flight-phase under the uncertainties of initial flight path angle, axial aerodynamic coefficient, and atmospheric density is established using the generalized polynomial chaos expansion method. By parameterizing random uncertainties and introducing random parameters into the uncertainty model, the uncertainty analysis problem of return trajectory is transformed into stochastic trajectory approximation problem. The coefficients of the polynomial basis function are solved by the stochastic collocation method. Then state solutions, statistical properties, and global sensitivity with Sobol index are established based on coefficients. The simulation results show the efficiency and accuracy of this method compared with the Monte Carlo method, the evolution process of main output parameters under random parameters, and relative importance for random parameters. Through the uncertainty analysis of the return trajectory, the robustness of return trajectory can be quantified, which is contributed to improving the safety, reliability, and robustness of recovery and landing mission.

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