Docking of a Spacecraft on a Tumbling Satellite Moving on Halo Orbits Using Lyapunov Vector Field Based Guidance Law

In this work, we address the problem of generating autonomous docking maneuvers for a chaser spacecraft approaching a tumbling target satellite evolving on a nearby halo orbit. A vector field–based guidance law, defined in the target satellite’s body frame, is employed to generate a continuous desired velocity field for the chaser. The guidance vector field induces a circulation around the docking point to align the chaser with the docking-axis direction; once the chaser enters the designated docking cone, the field transitions to attract the vehicle toward the docking port while simultaneously reducing its relative velocity to zero. The complete problem formulation and the vector field–based guidance strategy used to compute the acceleration commands required for docking with a tumbling target are presented. Simulation results for multiple scenarios are included to assess and validate the effectiveness of the proposed algorithm. Although the relative dynamics of both the chaser and the target are modeled in non-dimensional CR3BP units, all reported accelerations, velocities, and distances are converted to physical units to provide a clearer interpretation of the required control effort and achievable proximity accuracy.