Stochastic Six-Degree-of-Freedom Flight Simulator for Passively Controlled High-Power Rockets

This paper presents a method for simulating the flight of a passively controlled rocket in six degrees of freedom, and the descent under parachute in three degrees of freedom. Also presented is a method for modeling the uncertainty in both the rocket dynamics and the atmospheric conditions using stochastic parameters and the Monte Carlo method. Included within this, we present a method for quantifying the uncertainty in the atmospheric conditions using historical atmospheric data. The core simulation algorithm is a numerical integration of the rocket’s equations of motion using the Runge-Kutta-Fehlberg method. The position of the rocket’s center of mass is described using three dimensional Cartesian coordinates and the rocket’s orientation is described using quaternions. Input parameters to the simulator are made stochastic by adding Gaussian noise. In the case of atmospheric parameters, the variance of the noise is a function of altitude and noise at adjacent altitudes is correlated. The core simulation algorithm, with stochastic parameters, is run within a Monte Carlo wrapper to evaluate the overall uncertainty in the rocket’s flight path. The results of a demonstration of the simulator, where it was used to predict the flight of real rocket, show the rocket landing within the 1σ area predicted by the simulation. Also lateral acceleration during weather cocking, which was measured in the test, shows a strong correlation with simulated values.