New Guidance Law Keeps Off-Axis Seekers Locked On While Guaranteeing a Precise Kill

Hitting a maneuvering target in the vacuum of space is one of the hardest problems in flight control. There is no aerodynamic lift to lean on, no atmosphere to shape the trajectory, and only milliseconds of margin at the closing speeds involved in an exo-atmospheric intercept. A team at Beihang University in Beijing, led by Muhammad Mushtaq, Wenbin Yu, and Wanchun Chen of the School of Astronautics, has now proposed a new homing guidance law designed for exactly this regime, published in the International Journal of Aeronautical and Space Sciences. Their approach targets a specific and awkward class of interceptor: one steered by a divert-and-attitude-control system and fitted with an off-axis seeker, a sensor arrangement that is increasingly common on kill vehicles but notoriously unforgiving in the final seconds of an engagement.

To understand why the problem is difficult, it helps to unpack the hardware. A divert-and-attitude-control system, usually abbreviated DACS, uses solid-propellant thrusters to shove the interceptor sideways and to rotate its body. Unlike a missile with aerodynamic fins, a DACS-equipped kill vehicle can translate laterally even while its nose stays pointed where it was. That decoupling is a blessing for maneuverability and a curse for the seeker. Many exo-atmospheric interceptors carry their infrared seeker offset from the longitudinal axis of the body, an off-axis configuration that widens the usable field of regard and simplifies the mechanical layout. The price is a hard constraint: if the interceptor’s body pitches or yaws too far relative to the line of sight to the target, the target drifts out of the seeker’s field of view, and the engagement is effectively lost. Conventional proportional navigation, the workhorse guidance scheme dating back decades, commands the interceptor to rotate its velocity toward the target, and in doing so it can easily drive the body attitude out of the seeker’s cone.

The Beihang team’s answer is built around a quantity that guidance engineers have trusted for more than half a century: the zero-effort-miss, or ZEM. The ZEM is the predicted miss distance, the distance by which the interceptor would miss the target if both vehicles stopped maneuvering from that instant onward and simply coasted. It condenses the entire future of the engagement into a single vector that the guidance computer can watch in real time. If the ZEM shrinks toward zero, a collision is on track; if it grows or refuses to settle, the interceptor must act. Classical proportional navigation can be derived as the law that drives the ZEM to zero, and the closed-form solutions of pure and true proportional navigation worked out by earlier researchers remain foundational references in the field. What classical laws do not do, however, is promise anything about how fast the ZEM converges or how small it will be when time runs out.

That gap is precisely where the new work positions itself. The authors construct a generalized form of the zero-effort-miss suited to their interceptor’s dynamics and then design the guidance law so that the ZEM is guaranteed to converge, in finite time, into a small neighborhood that the designer chooses in advance. The mathematical machinery behind this guarantee is prescribed performance control, a technique introduced in the adaptive control literature by Bechlioulis and Rovithakis, in which a prescribed performance function wraps the tracking error in a decaying boundary. As long as the error stays inside that funnel, its transient behavior and its final bound are both known before the controller ever runs. Applied to guidance, the idea means the designer can specify, up front, the terminal miss-distance accuracy the interceptor must achieve and the shape of the convergence path, and the control law then enforces those bounds throughout the homing phase.

Prescribed performance ideas have appeared in guidance research before. Earlier studies used them to impose terminal line-of-sight angle constraints against maneuvering targets, to handle missile autopilot lag, and to build adaptive sliding-mode guidance laws. Robust intercept guidance with predesigned ZEM convergence has also been explored for capturing maneuvering targets. The distinctive contribution of the Beihang paper is the combination: a generalized ZEM formulation, a prescribed performance controller enforcing finite-time convergence of that ZEM within prescribed terminal bounds, and, critically, a design that holds the look angle fixed so the off-axis seeker never loses its lock. The fixed look angle is not an afterthought but a structural feature of the law. By keeping the angle between the interceptor’s body axis and the line of sight constant, the guidance commands are shaped so that the target remains comfortably inside the seeker’s field of view from the start of the engagement to the moment of closest approach.

The interplay between the two requirements is subtle. A DACS kill vehicle has two channels of actuation: divert thrusters that produce lateral acceleration and attitude thrusters that rotate the body. Spending divert authority on correcting the ZEM and attitude authority on managing the look angle would be the obvious division of labor, but the two channels are coupled through the engagement geometry, and both consume finite propellant. The guidance law must therefore thread a needle, driving the ZEM into its prescribed funnel fast enough to guarantee a small miss distance against a maneuvering target, while simultaneously respecting the seeker’s field-of-view limit that earlier work on strapdown and off-axis seekers has shown to be a first-class constraint rather than a nuisance. Studies of line-of-sight rate estimation for off-axis seekers on two-axis gimbals and of guidance strategies accounting for minimum field-of-view constraints have documented how easily naive commands violate the limit, particularly when the initial heading error is large or the target maneuvers late.

Maneuvering targets are the stress test for any homing law. In an exo-atmospheric scenario, the target may be a ballistic warhead executing evasive lateral pulses in the last seconds of flight, and every meter of miss distance matters because the interceptor’s lethality radius is finite. The ZEM formulation is attractive here precisely because target acceleration enters the prediction directly: an unanticipated target maneuver shows up immediately as a jump in the ZEM, giving the guidance law an unambiguous error signal to cancel. By wrapping the generalized ZEM in a prescribed performance function, the Beihang design converts that error signal into commands with a guaranteed convergence envelope, so that even under maneuvering, the miss distance is forced into the small terminal neighborhood the designer prescribed, in finite time rather than merely asymptotically. Asymptotic convergence, the standard promise of many classical controllers, is a luxury an interceptor does not have; the engagement ends at a definite instant, so the guarantee must hold before that instant arrives.

The authors validate the approach through extensive numerical simulations, and they state that all mathematical models and simulation parameters are detailed in the manuscript, facilitating direct implementation in MATLAB/Simulink. That level of reproducibility matters in a field where claims of terminal accuracy are easy to make and hard to check. The simulation campaign, illustrated across the paper’s figures, exercises the guidance law in the scenarios that matter: engagements of maneuvering targets by a DACS-equipped, off-axis-seeker interceptor, with the ZEM trajectory, the look angle history, and the resulting miss distance all under scrutiny. The reported behavior supports the central claim, that the ZEM converges within the prescribed bounds while the seeker maintains continuous lock throughout the engagement.

The broader context for this work is the long-running evolution of interceptor guidance. The literature spans THAAD-like high-altitude theater missile defense analyses, optimal guidance-to-collision laws for accelerating exo-atmospheric interceptors, energy-effective guidance-to-collision strategies, blended control strategies for high-speed targets at high altitude, and collision-control guidance based on speed control for kill vehicles. Sliding-mode precursor interceptor guidance, solid-propulsion attitude control for exo-atmospheric kill vehicles, switching logic for DACS, and DACS missile controllers that explicitly consider the seeker’s field-of-view limit have all chipped away at pieces of the problem. Unified formulations of optimal guidance-to-collision laws for accelerating and decelerating targets and nonlinear optimal impact-angle-constrained guidance with large initial heading error round out a rich toolbox. What most of these methods share is a focus on the collision condition itself; the Beihang law instead focuses on sculpting the convergence of the predicted miss distance, with the seeker constraint folded into the design from the first equation.

For the field, the significance is twofold. Practically, the law offers designers of off-axis-seeker interceptors a way to guarantee terminal accuracy without gambling on the seeker’s field of view, which could simplify integration of offset sensor architectures on future kill vehicles. Methodologically, it demonstrates that prescribed performance control, born in the adaptive control of strict-feedback systems, extends cleanly to the generalized ZEM dynamics of a space intercept, providing finite-time, bounded-error convergence guarantees in a domain where such guarantees are rare and valuable. The work, received in October 2025 and published on 14 October 2026 after revision, was communicated by Zongyi Guo, and the authors acknowledge Prof. Wanchun Chen’s guidance throughout the research. As missile defense engagements push to higher altitudes, higher closing speeds, and more agile evaders, guidance laws that make explicit, provable promises about the final miss distance, while respecting the physical limits of the sensors that must see the target through to the end, are likely to shape the next generation of kill vehicle design.

Subject of Research: Prescribed-performance homing guidance for exo-atmospheric interceptors with off-axis seekers and divert-and-attitude-control systems

Article Title: Generalized Intercept Guidance Law with Prescribed Zero-Effort-Miss Convergence for Off-Axis Seeker-Based Interceptors

Article References: Generalized Intercept Guidance Law with Prescribed Zero-Effort-Miss Convergence for Off-Axis Seeker-Based Interceptors. (n.d.). https://doi.org/10.1007/s42405-026-01307-3

Image Credits: AI Generated

DOI: 10.1007/s42405-026-01307-3

Keywords: guidance law, zero-effort-miss, off-axis seeker, exo-atmospheric interceptor, prescribed performance control, DACS, maneuvering target, homing guidance, miss distance, Beihang University, finite-time convergence, field of view