Efficient modelling of small bodies gravitational potential for autonomous approach

The the main challenge of proximity operations about asteroids is their weak and non-uniform gravitational attraction. On-board measurements of relative distance and velocity, from optical navigation and LIDAR, has been proven sufficient to control the terminal leg of landing and touch-and-go trajectories. However, a spacecraft in orbit about an asteroid needs also a model of the gravitational potential in order to achieve autonomous guidance and control. Because of spacecraft's limited computational resources, the on-board gravity model has to be governed by a small number of parameters and the calculation of the effects of each of its elements has to be straightforward. Reviewing the main characteristics of the dynamical environment about asteroids, we identify a class of approximate models which are not required to be globally accurate but rather to represent well those dynamical features that can be exploited for control purposes. In particular we are interested in modelling correctly the positions, energy levels and behaviour of the equilibrium points which are present around most asteroids in uniform rotation. In this paper we propose an optimisation strategy to derive simple models of asteroids from higher accuracy data. We analyse the performance of such optimisation and we give an example of their use in a control law which negotiates the spacecraft to the equilibrium point at the lowest energy level