Abstract
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.
Highlights
E 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. is paper is devoted to quantifying the probability uncertainty of return trajectory with uncertain parameters. e 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. e coefficients of the polynomial basis function are solved by the stochastic collocation method. en state solutions, statistical properties, and global sensitivity with Sobol index are established based on coefficients. e 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. rough 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
Before we further develop future vertical takeoff and vertical landing (VTVL) reusable launch vehicle (RLV) retropropulsive return, descent, and pinpoint landing technologies, the challenges of uncertainty quantification must be addressed. erefore, knowing the evolution law of return trajectory under uncertainty is beneficial to mission design and analysis, especially for emergency return mission
Summary
Received 31 January 2020; Revised 10 May 2020; Accepted 25 May 2020; Published 11 July 2020. The actual flight performance of launch vehicle is not as expected because of the uncertainty of some important return dynamics parameters, such as separation point state, aerodynamic parameters, and atmospheric density. E method based on generalized polynomial chaos expansion (GPCE), as a nonlinear uncertainty propagation analysis method, has been successfully applied to many space missions because of its convergence, accuracy, and computational efficiency in orbit and flight dynamics [22,23,24]. E main contribution of this paper lies in the uncertainty analysis of the recovery and landing mission of VTVL RLV, in which the uncertainty propagation problem is converted into the stochastic trajectory approximation problem. E uncertainty analysis based on GPCE will be further developed in this paper to analyze the propagation process of multi-flightphase trajectory under the uncertainties of initial flight path angle, axial aerodynamic coefficient, and atmospheric density. T m_ , g0Isp where these variables are illustrated in Figure 1, O − xyz is the launch coordinate system, Ob − xbybzb is the body coordinate system, and Ob − xvyvzv is the velocity coordinate system. x, y, z are the position components in the launching coordinate system, v is the magnitude of velocity, θ is the flight path angle, and σ is the yaw angle. e former three variables describe the position of the vehicle in the
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