Optimal Multi-Target Overflight Using Ground-Track Adjustment

This study proposes a near-optimal, impulsive control method for overflying ground targets. A set of impulses, which adjusts the satellite ground trajectory to enable the overflight, is derived. The proposed impulsive solution is expressed in closed-form which only consists of orbital revolution numbers and target overflight errors. It allows not only simplifying the search for a minimum delta-v solution but also facilitating its extension to the multiple-target overflight problem. It is also provided in this paper an insight connecting the overflight problem to a relative orbit transfer problem controlling a phase angle or mean anomaly. Numerical examples for single-, two-, and three-target overflight verify that the controlled trajectory with the proposed impulsive solution successfully overflies the designated targets within a prescribed time. It is also demonstrated that the total delta-v required for the proposed method is near-optimal based on the performance comparison with a numerical optimization-based method which employs a very large set of initial guesses.