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Risk-Aware Input-Constrained Safe Intercept Guidance Against Multiple Moving Defenders
Praveen Kumar Ranjan, Abhinav Sinha, Yongcan Cao, Alexander Von Moll, Isaac E. Weintraub
TL;DR
Interception guidance must account for defender threats and attacker control limits, while existing approaches may impose restrictive assumptions or conservative safety rules. This paper uses DMC-based risk tolerances and a smooth-minimum aggregation to guide an attacker against multiple moving defenders without online optimization. Its analysis establishes preservation of risk and input bounds under pointwise feasibility, and finite-time interception when target-directed motion remains permitted.
Problem
Interception guidance must account for directional defender threats and finite maneuvering authority, while existing approaches may rely on restrictive assumptions or conservative distance-based safety constraints.
Source: §I · p. 1Method
The guidance law bounds DMC-based geometric risk, aggregates multiple defenders’ constraints through a smooth minimum, and combines target pursuit with preemptive avoidance under a lateral-acceleration bound.
Source: §I · p. 2Results
Risk constraints and input bounds are preserved under pointwise feasibility, and finite-time interception holds when the risk constraints permit sustained target-directed motion.
Source: §I · p. 2, §III · p. 5Takeaways & Limitations
The formulation allows recoverable geometric exposure instead of requiring strict defender avoidance, while maintaining prescribed risk bounds and actuator constraints under appropriate engagement conditions.
Source: §V · p. 6Future work will consider adaptive defender-dependent risk tolerances, uncertainty in defender parameters and measurements, and three-dimensional experimental validation.
Source: §V · p. 6
Abstract
from arXiv · showhide
This paper develops a risk-aware guidance law for an attacker to intercept a stationary target in the presence of multiple moving defenders while respecting the control input limits. We represent defender threats via engagement zones (EZs) (regions of state-space from which attacker interception is feasible) and employ the dynamic maneuvering cue (DMC) (minimum heading correction to exit EZs) as a deterministic measure of geometric risk. Safety is enforced through a prescribed bound on the DMC to enable controlled EZ penetration subject to a specified risk tolerance. For multiple defenders, the corresponding safety constraints are combined through a smooth-minimum aggregation. The proposed guidance strategy drives the attacker toward the target when the engagement remains safe and transitions to an avoidance maneuver as the prescribed safety boundary is approached. The resulting online optimization-free guidance law directly bounds the applied lateral acceleration and initiates a bounded preemptive maneuver before corrective action is required. Closed-loop analysis establishes preservation of the prescribed risk constraints under pointwise bounded-input feasibility and finite-time target interception under a sustained target-accessibility condition. Numerical studies validate the proposed strategy and illustrate the tradeoff between allowable geometric risk and interception performance.
I. INTRODUCTION
Existing interception and avoidance methods may rely on restrictive assumptions or distance-based safety rules that miss directional threat and can be conservative. This work motivates a risk-aware guidance strategy that accommodates recoverable engagement-zone penetration, multiple moving defenders, and bounded maneuvering without online optimization.
I. INTRODUCTION
- Existing attacker-side TAD and pursuit-evasion approaches use differential games, optimal guidance, robust control, or data-driven methods, but may depend on restrictive strategy, dynamics, or game-structure assumptions.Distance-based constraints can also miss directional threat and produce conservative avoidance, while collision-oriented geometric methods do not represent a defender’s finite interception capability.Source: §I · p. 1
- The dynamic maneuvering cue (DMC) measures the heading correction needed to recover a safe engagement and supports a prescribed risk tolerance instead of strict engagement-zone avoidance.This motivates controlled penetration while requiring actuator-constrained safety maneuvers to remain feasible.Source: §I · p. 1
- The work targets guidance that jointly quantifies geometric risk, permits controlled engagement-zone penetration, handles multiple moving defenders, and respects physical maneuvering limits without defender policies or online optimization.The stated motivation is the challenge of satisfying all these requirements simultaneously.Source: §I · pp. 1–2
- The framework bounds defender exposure through a prescribed DMC tolerance, allowing controlled penetration inside the threat zone rather than requiring strict avoidance.The tolerance provides a direct way to specify allowable recoverable geometric exposure.Source: §I · p. 2
- The proposed optimization-free law combines target interception with preemptive avoidance, aggregates multiple defenders’ risk constraints through a smooth minimum, and respects the attacker’s lateral-acceleration bound.It is designed to act before corrective action is required.Source: §I · p. 2
- Risk constraints and the input bound are preserved under pointwise feasibility, with finite-time interception once the risk constraints permit sustained target-directed motion.The interception guarantee is conditional on that sustained target-accessibility condition.Source: §I · p. 2
II. PROBLEM FORMULATION
The formulation models an attacker pursuing a stationary target while multiple moving defenders can launch interceptors from their current positions. It defines defender risk through engagement zones and a dynamic maneuvering cue, then specifies a finite-time capture objective subject to risk-tolerance and acceleration constraints.
II. PROBLEM FORMULATION
- Each moving defender launches an interceptor from its instantaneous platform position; after launch, the interceptor moves independently, creating a heading-dependent engagement zone.The defender platform is modeled at constant speed and has a maximum engagement distance of R_i + c_i.Source: §II · p. 2
- An engagement zone is the set of attacker-relative states from which a defender can intercept the attacker if it maintains its current heading.The boundary is described by ρ_i(σ_Ai), and crossing it places the attacker within the defender’s feasible capture region.Source: §II · p. 2
- For a fixed attacker-defender range, the DMC is the minimum instantaneous heading correction needed to reach the nearest engagement-zone-admissible heading.The cue is zero when the current heading is admissible, finite inside the zone where an admissible heading exists, and unbounded when no admissible heading exists.Source: §II · pp. 2–3
- A prescribed DMC tolerance permits engagement-zone penetration when the required recovery turn remains within budget; zero tolerance recovers strict avoidance.For positive tolerance, the admissible region includes some states inside the engagement zone.Source: §II · p. 3
- The DMC bound is equivalently represented by a nonnegative radial margin, giving a boundary-based condition for subsequent guidance design.Lemma 1 states that B_i ≥ 0 is equivalent to |DMC_i| ≤ ε_i across the described range regimes.Source: §II · p. 3
- The guidance problem requires reaching the target capture radius in finite time while maintaining every defender’s prescribed DMC constraint and keeping lateral acceleration below its bound.The stated safety condition is B_i ≥ 0 for all defenders throughout the engagement, with |a_A(t)| < a_max.Source: §II · p. 3
III. RISK-AWARE GUIDANCE DESIGN
The guidance design combines smooth risk margins across defenders with target-seeking and preemptive avoidance commands under an acceleration bound. Under pointwise feasibility, it preserves the prescribed DMC constraints and input bounds; finite-time interception additionally requires sustained target-directed motion under the stated accessibility condition.
III. RISK-AWARE GUIDANCE DESIGN
- A fixed branch direction smooths each nonsmooth risk margin, and the resulting surrogate is conservative relative to the original margin.The paper states b_Bi ≤ B_i and uses nonnegative surrogate margins to guarantee the original DMC constraints.Source: §III · p. 3
- The aggregate H lower-bounds the minimum conservative defender margin within β log n, with smaller β tightening the approximation but sharpening transitions between dominant defenders.H ≥ 0 is sufficient to keep every conservative margin nonnegative and preserve the individual DMC constraints.Source: §III · p. 4
- The controller combines target-interception and risk-preserving commands, transitioning smoothly toward avoidance as the target-command risk residual falls below the anticipation margin.The preemptive maneuver is bounded, and its attenuation depends on a turning-authority threshold.Source: §III · p. 4
- If H(0) ≥ 0 and pointwise feasibility M(x(t), t) ≥ 0 holds almost everywhere throughout engagement, prescribed DMC constraints are preserved and lateral acceleration remains within admissible bounds.Source: §III · pp. 4–5
- Finite-time capture follows when target-directed guidance is sustained from outside the capture radius and the target-heading error remains within the stated invariant cone.The cone boundary points inward, while range decreases at a strictly negative rate under the specified condition.Source: §III · p. 5
IV. SIMULATIONS
The simulations show that increasing prescribed DMC tolerance trades greater engagement-range penetration for shorter interception time. In stationary and moving-defender scenarios, the guidance maintains the reported safety and input bounds while achieving interception.
IV. SIMULATIONS
- Across simulations, attacker speed is 1 m/s; moving defenders travel at 0.5 m/s, and stationary trials test ε_i values from 0° to 50°.The stationary defenders are located at [0, ±1.2]^T m, with the attacker initialized at [−10, 0]^T m.Source: §IV · p. 5
- With two stationary defenders, larger ε_i produces deeper engagement-range penetration while DMC safety stays positive and lateral acceleration remains within limits.The avoidance maneuver activates after approximately 5 seconds to preserve the prescribed risk constraints.Source: §IV · p. 5, Figure 2 · p. 6
- With six moving pure-pursuit defenders at ε_i=50°, the attacker intercepts while safety measures and input feasibility stay positive and acceleration remains bounded.The aggregate and individual safety measures remain positive throughout the engagement.Source: §IV · p. 5, Figure 3 · p. 6
- Increasing DMC tolerance reduces interception time while increasing engagement-range penetration, showing a risk–performance tradeoff.The reported interception time decreases as tolerance rises, while penetration increases.Source: §IV · pp. 5–6, Figure 4 · p. 6
V. CONCLUSIONS
The conclusion frames safe interception as a trade between strict avoidance and prescribed recoverable geometric exposure. The closed-loop results report preservation of risk and actuator constraints alongside interception under appropriate engagement conditions.
V. CONCLUSIONS
- The DMC-based risk tolerance distinguishes penetrations requiring excessive recovery maneuvers from admissible penetrations the attacker can recover from.This permits a prescribed level of recoverable geometric exposure rather than strict defender avoidance.Source: §V · p. 6
- The guidance law combines multiple defender constraints, anticipates loss of effective turning authority, and respects available lateral-acceleration limits.Source: §V · p. 6
- Closed-loop results show prescribed risk bounds and actuator constraints can be maintained while enabling target interception under appropriate engagement conditions.The paper identifies adaptive defender-dependent risk tolerances, parameter and measurement uncertainty, and three-dimensional experimental validation as future work.Source: §V · p. 6