Desensitized optimal trajectory for landing on small bodies with reduced landing error

This paper aims at desensitizing the optimal trajectory for landing on the small bodies with reduced landing error in the presence of initial state error, parameters uncertainties of the target body (the gravity and the body's rotation rate) and thrust error (the error in thrust magnitude and direction). The motion of the lander is expressed in the body-fixed coordinate frame, and the thruster is considered to be variable. Instead of directly optimizing the landing trajectory, this paper propagates the linear covariance of the stochastic landing dynamics equations, and minimizes the fuel consumption as well as the covariance. Firstly, the stochastic state equations including the effects of these uncertainties are constructed. The rotation rate is augmented as the new state of the state equations, and the uncertainties in gravity and thruster are modeled as the stochastic process noise acting on the lander. Then, the closed-loop linear covariance is derived and optimized with the fuel consumption performance index as a penalty factor. Finally, several sets of simulations are performed in the scenarios of Eros 433 and Vesta. The open-loop trajectory is firstly performed in the scenario of Eros 433 and the result shows that these uncertainties contribute greatly to the trajectory dispersions. The 3σ trajectory dispersions for tracking the optimal and desensitized optimal trajectory show that the desensitized approach reduces the landing error effectively. And the statistic landing velocities show that the desensitized approach meets the requirement of soft and stable landing on small bodies. To especially discuss the fuel consumption of optimal and desensitized optimal trajectory, the simulation in the scenario of Vesta is performed. The results show that the desensitized optimal approach takes only about 1.01 kg more fuel for the lander of 800 kg size. And the landing error of desensitized trajectory is reduced significantly compared to that of the optimal trajectory. The total simulations in the scenario of Eros 433 and Vesta indicate that the desensitized approach is fuel-saving, and can reduce the landing error effectively for landing on small bodies.