Asteroid deflection strategies based on kinetic impactors have traditionally focused on single, high-mass spacecraft designed to impart an impulsive momentum change to the target body. Although effective in theory, such monolithic architectures impose significant technological, operational, and risk-related constraints, which motivates increasing interest in multiple kinetic impactor (MKI) concepts. MKI architectures offer advantages over single-impactor missions including redundancy, increased resilience to individual spacecraft failures, scalability with available launch capabilities, and improved robustness to navigation and execution uncertainties. In these architectures, the total deflection is achieved through a sequence of smaller impacts distributed in time, introducing new challenges in the selection of impact timing, geometry, and coordination. 

In this work, we introduce a control-inspired formulation for MKI-based asteroid deflection by modeling the asteroid as being acted upon by a fictitious thrust system, referred to as virtual thrust. Rather than directly solving a high-dimensional, combinatorial optimization problem over multiple interceptor trajectories, the deflection problem is first posed as a continuous low-thrust control problem acting on the asteroid’s orbit over a prescribed warning time. For a given Earth–asteroid orbital configuration and lead time, this proxy problem yields an optimal or near-optimal thrust direction profile that maximizes a deflection metric such as minimum orbital intersection distance or B-plane displacement. The obtained intermediate continuous solution provides a structured “target” actuation history that is physically interpretable and can serve as a benchmark for assessing the efficiency of discrete MKI campaigns. 

The resulting continuous thrust profile is then approximated by a finite sequence of impulsive velocity changes, representing individual kinetic impacts. This discretization process provides a systematic framework for selecting impact times, impulse magnitudes, and directions, while enabling the explicit incorporation of practical constraints such as minimum temporal separation between impacts, bounds on achievable impulse per impactor, and mission-level transfer geometry limitations. In this sense, the methodology acts as a “compiler” that maps continuous deflection strategies into realizable MKI campaigns.  A key advantage of this two-stage approach is in its modularity: operational constraints and feasibility considerations can be enforced primarily in the compilation step, and the simpler framework naturally supports rapid re-synthesis of an impact sequence if one impact opportunity is lost or an interceptor underperforms, without re-optimizing the entire multi-spacecraft design from scratch.  

Preliminary numerical investigations indicate that the proposed approach reproduces key features reported in traditional MKI optimization studies, including the clustering of impacts near early interception windows and predominantly tangential impulse components for long warning times. By decoupling the deflection objective from the multi-vehicle campaign realization, this two-stage formulation reduces search complexity and yields solutions that are easier to interpret in terms of how and when deflection is accumulated along the orbit. It also allows mission constraints such as launch cadence, minimum separation between impacts, and limits on the impulse delivered by each impactor to be handled directly during the discretization step, rather than being embedded within a single large global optimization problem. This paper presents quantitative comparisons against direct global optimization baselines in terms of achieved deflection, and sensitivity to timing and impact execution errors. Overall, the proposed virtual-thrust framework provides an interpretable and modular pathway for MKI mission design that bridges continuous deflection theory and impulsive interception architectures.