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Engagement-Zone-Aware Input-Constrained Guidance for Safe Target Interception in Contested Environments

Praveen Kumar Ranjan, Abhinav Sinha, Yongcan Cao

Abstract

We address target interception in contested environments in the presence of multiple defenders whose interception capability is limited by finite ranges. Conventional methods typically impose conservative stand-off constraints based on maximum engagement distance and neglect the interceptors' actuator limitations. Instead, we formulate safety constraints using defender-induced engagement zones. To account for actuator limits, the vehicle model is augmented with input saturation dynamics. A time-varying safe-set tightening parameter is introduced to compensate for transient constraint violations induced by actuator dynamics. To ensure scalable safety enforcement in multi-defender scenarios, a smooth aggregate safety function is constructed using a log-sum-exp operator combining individual threat measures associated with each defender's capability. A smooth switching guidance strategy is then developed to coordinate interception and safety objectives. The attacker pursues the target when sufficiently distant from threat boundaries and progressively activates evasive motion as the EZ boundaries are approached. The resulting controller relies only on relative measurements and does not require knowledge of defender control inputs, thus facilitating a fully distributed and scalable implementation. Rigorous analysis provides sufficient conditions guaranteeing target interception, practical safety with respect to all defender engagement zones, and satisfaction of actuator bounds. An input-constrained guidance law based on conservative stand-off distance is also developed to quantify the conservatism of maximum-range-based safety formulations. Simulations with stationary and maneuvering defenders demonstrate that the proposed formulation yields shorter interception paths and reduced interception time compared with conventional methods while maintaining safety throughout the engagement.

Engagement-Zone-Aware Input-Constrained Guidance for Safe Target Interception in Contested Environments

Abstract

We address target interception in contested environments in the presence of multiple defenders whose interception capability is limited by finite ranges. Conventional methods typically impose conservative stand-off constraints based on maximum engagement distance and neglect the interceptors' actuator limitations. Instead, we formulate safety constraints using defender-induced engagement zones. To account for actuator limits, the vehicle model is augmented with input saturation dynamics. A time-varying safe-set tightening parameter is introduced to compensate for transient constraint violations induced by actuator dynamics. To ensure scalable safety enforcement in multi-defender scenarios, a smooth aggregate safety function is constructed using a log-sum-exp operator combining individual threat measures associated with each defender's capability. A smooth switching guidance strategy is then developed to coordinate interception and safety objectives. The attacker pursues the target when sufficiently distant from threat boundaries and progressively activates evasive motion as the EZ boundaries are approached. The resulting controller relies only on relative measurements and does not require knowledge of defender control inputs, thus facilitating a fully distributed and scalable implementation. Rigorous analysis provides sufficient conditions guaranteeing target interception, practical safety with respect to all defender engagement zones, and satisfaction of actuator bounds. An input-constrained guidance law based on conservative stand-off distance is also developed to quantify the conservatism of maximum-range-based safety formulations. Simulations with stationary and maneuvering defenders demonstrate that the proposed formulation yields shorter interception paths and reduced interception time compared with conventional methods while maintaining safety throughout the engagement.
Paper Structure (11 sections, 4 theorems, 80 equations, 9 figures, 2 tables)

This paper contains 11 sections, 4 theorems, 80 equations, 9 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Preliminaries and Problem Formulation
  3. Vehicles' Relative Kinematics Model
  4. Defender-induced Engagement Zones (EZs)
  5. Design of the Control Objectives
  6. Engagement-Zone-Aware Input-Constrained Intercept Guidance Design
  7. Maximum Engagement-Range-based Input-Constrained Intercept Guidance Design
  8. Simulation results
  9. Target Interception avoiding Stationary Defenders
  10. Target Interception avoiding Moving Defenders
  11. Conclusions

Key Result

Lemma 1

Consider the dynamics of the safety constraint eqn:hdot and the designed tightening parameter as in eq:Delta_final. Then, for any $h(t_0)>\Delta(t_0), \forall t_0\geq 0$, the safety constraint remains non-negative over the response window $[t_0, t_0+\tau_\mathrm{resp}]$ for all admissible control in

Figures (9)

  • Figure 1: Attacker-Target-Defender engagement geometry.
  • Figure 2: Illustration of EZ for single defender ($[x_D, y_D]^\top=[0 \;0]^\top$ with $R_D=1$ m and $c_D=0.25$m).
  • Figure 3: Engagement boundary relative to the maximum range.
  • Figure 4: Variation of the safety function boundary $(h=0)$ for different choices of the parameter $\beta$.
  • Figure 5: Variation of the safety function boundary with tightening parameter $\Delta$.
  • ...and 4 more figures

Theorems & Definitions (19)

  • Remark 1
  • Definition 1: Engagement Zone (EZ)
  • Remark 2
  • Remark 3
  • Lemma 1: Safety Tightening Buffer
  • proof
  • Remark 4
  • Lemma 2
  • proof
  • Theorem 1
  • ...and 9 more