This paper investigates the autonomous guidance of a spacecraft orbiting in close proximity of an asteroid. As a first step, navigation is assumed to be performed continuously on board the vehicle. The latter is supposed to be equipped with an electric propulsion system with either constant or time-varying thrust magnitude. The spacecraft’s equations of motion take into account the gravitational influence of the Sun and the asteroid, plus solar radiation pressure and the thrust of the electric engine [1]. This paper develops a feedback thrust law based on Control Barrier Functions theory [2] so that the spacecraft remains in a specific region of space close to the asteroid during a given amount of time. This observation region is such that the scientific instruments on board the vehicle can map the asteroid. At each time, the computation of the thrust (or control) vector requires the on-board solution of a Quadratic Programming problem. The latter determines the minimum-norm control satisfying linear inequalities arising from the Control Barrier Functions theory. The initial conditions of the spacecraft are determined so that the magnitude of the minimum-norm control never exceeds the engine’s maximum thrust magnitude. In case of an engine with time-varying thrust magnitude, the minimum-norm control is taken as the thrust vector at each time step. However, in case of an engine with constant thrust magnitude, a thrust vector satisfying the Control Barrier Functions inequality conditions and with the same magnitude as that of the engine is determined at each time step. In the second part of the paper, a strategy is presented to make the feedback control law robust to model uncertainty and thrust errors in magnitude and direction. Numerical results are provided to illustrate the interest and effectiveness of the proposed guidance scheme. A problem inspired by the mapping of asteroid (65803) Didymos from the CubeSat Milani of the Hera mission [3] serves as a test case. Both constant- and variable-thrust engines are considered, and the robustness of the feedback thrust law to model uncertainty and thrust errors is checked through a Monte-Carlo analysis. Finally, to account for flight dynamics operations, navigation observables may not be available during given time periods, referred to as cut-off times. The limits of the robustness of the feedback control law in the presence of cut-off times or missed thrust events are determined through a Monte-Carlo simulation.
 
References
 
[1] D. J. Scheeres and F. Marzari, “Spacecraft Dynamics in the Vicinity of a Comet,” Journal of the Astronautical Sciences, Vol. 50, 2002, pp. 35–52.
 
[2] K. Garg, J. Usevitch, J. Breeden, M. Black, D. Agrawal, H. Parwana, and D. Panagou, “Advances in the Theory of Control Barrier Functions: Addressing Practical Challenges in Safe Control Synthesis for Autonomous and Robotic Systems,” Annual Reviews in Control, Vol. 57, 100945, 2024.
 
[3] C. Bottiglieri, F. Piccolo, C. Giordano, F. Ferrari, and F.  Topputo, “Applied Trajectory Design for CubeSat Close-Proximity Operations around Asteroids: The Milani Case,” Aerospace, Vol. 10, No. 5, 464, 2023.