Convex Optimization of Stochastic Six-Degree-of-Freedom Trajectories near Asteroids

Great challenges in real-time robust control have been put forward in asteroid exploration in recent years. To deal with the complicated environment full of uncertainties and to satisfy the position as well as attitude requirements of the mission, a convex approach is proposed for stochastic six-degree-of-freedom (six-DOF) trajectories near asteroids. A stochastic six-DOF dynamic model based on modified Rodrigues parameters is built with covariance control and feedback control. Integrated path constraints and field-of-view (FOV) constraints are imposed on account of collision avoidance and sensor orientation, respectively. The constraints with uncertainties are converted to chance constraints and are convexified losslessly using auxiliary variables and virtual control. The stochastic convex problem is applied to hopping transfers on the asteroid 1996 HW1 and solved by successive solutions. The method shows great performance and applicability in optimizing trajectories under uncertainties, as proved by Monte Carlo simulation with numerous samples.