Virtual Thrust-Based Control Formulation for Multiple Kinetic Impactor Asteroid Deflection

Abstract

This paper introduces virtual thrust (VT), a continuous low-thrust control abstraction applied directly to asteroid deflection, as a way to design multiple-kinetic-impactor (MKI) campaigns. The method first solves a continuous VT optimal-control problem with sequential convex programming, then transcribes the resulting thrust profile into a set of dense impulses, and finally compiles those impulses into a finite impact campaign. Two VT cases are studied: one maximizes deflection for a fixed control budget, and the other minimizes the asteroid velocity change needed to reach a prescribed target deviation. The method is tested on an Apophis-style case with different lead times, impact speeds, cadence limits, and control authority levels. The compiled campaigns retain almost all of the continuous VT deflection. In the cases with a fixed budget, they also closely match a separate direct impulse allocation baseline. The minimum-Δv cases require only a modest number of extra impact opportunities. These results show that VT is a useful intermediate representation: it solves the deflection problem once as a continuous control problem, while the same VT profile can be recompiled into different effective MKI campaigns as mission assumptions change.