Engagement-Zone-Aware Input-Constrained Guidance for Safe Target Interception in Contested Environments
Authors: Praveen Kumar Ranjan, Abhinav Sinha, Yongcan Cao
Organizations: Unmanned Systems Lab, Department of Electrical Engineering, The University of Texas at San Antonio, San Antonio, TX, 78249 · Guidance, Autonomy, Learning, and Control for Intelligent Systems (GALACxIS) Lab, Department of Aerospace Engineering and Engineering Mechanics, University of Cincinnati, OH 45221, USA
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.
Figure 2: Illustration of EZ for single defender ( [xD,yD]⊤=[00]⊤ with RD=1 m and cD=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 β .
Figure 5: Variation of the safety function boundary with tightening parameter Δ .
Region
Mode
Condition on α
Guidance Law
Interpretation
I
Pure target interception
α=0
aAd=aAT
The attacker is sufficiently far from all engagement zones; the guidance law focuses entirely on target interception.
II
Pure EZ avoidance
α=1
aAd=aAb
The attacker is near an engagement boundary; the safety component is fully activated to prevent entry into the engagement zone.
III
Blended mode
0<α<1
aAd=(1−α)aAT+αaAb
Both interception and safety terms contribute to the commanded acceleration. This region represents the transition between interception and safety dominance, where α varies continuously due to its locally Lipschitz and nonincreasing properties.
Table 1: Operating regions of the proposed guidance law.
Figure 6: Target interception by avoiding two stationary defenders.
Figure 7: Comparison of attacker performance with three moving defenders.
Figure 8: Comparison of attacker performance with six moving defenders.
Figure 9: Comparison of the tightening parameter variation.
This paper proposes a nonlinear guidance strategy capable of intercepting a constant-velocity, non-maneuvering target while strictly satisfying the prescribed bounds on the control input (commanded acceleration). Unlike conventional strategies that estimate time-to-go using linearization or small-angle approximations, the proposed strategy employs true proportional-navigation guidance (TPNG) as a baseline, which utilizes an exact time-to-go formulation and is applicable over a wide range of target motions. In contrast to most existing strategies, which do not incorporate control input bounds into the guidance design, the proposed approach explicitly accounts for these limits by modeling the interceptor acceleration as a dynamic variable. Based on the sliding mode control technique, an effective guidance law that achieves time-constrained interception while accounting for bounded input is then derived. The performance of the proposed strategy is evaluated for various engagement scenarios.
Intelligent Systems & Control (ISaC) Lab, Department of Aerospace Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India · Guidance, Autonomy, Learning, and Control for Intelligent Systems (GALACxIS) Lab, Department of Aerospace Engineering and Engineering Mechanics, University of Cincinnati, OH 45221, USA
This paper considers the problem of simultaneously controlling an interceptor's impact time and impact angle using its lateral acceleration as the sole control input. With a single control input, the nonlinear engagement kinematics is inherently underactuated, which complicates guidance law synthesis. To overcome this challenge, a hierarchical sliding mode-based guidance law is developed to concurrently regulate the two terminal constraints. The proposed architecture consists of a two-layer sliding manifold. The first layer comprises two sub-sliding surfaces corresponding to the impact time and impact angle error dynamics, respectively, while the second layer introduces a composite sliding manifold that combines the two individual sub-surfaces. Then, a variable-gain adaptive guidance law is designed to ensure time and angle-constrained interception against a stationary target, which is further extended to intercept a constant velocity target. Simulations are conducted for various engagement scenarios to attest to the efficacy of the proposed approach.
Shivam Bajpai, Abhinav Sinha
Guidance, Autonomy, Learning, and Control for Intelligent Systems (GALACxIS) Lab, Department of Aerospace Engineering and Engineering Mechanics, University of Cincinnati, Cincinnati, OH, 45221, USA
We study multi-agent terminal interception when one of several moving candidates is the unknown target and both target identity and candidate terminal locations are uncertain. We develop a receding-horizon deferred-decision trajectory optimization (DDTO) controller that combines conformal terminal-location prediction, sequential candidate rejection, capacity-constrained assignment, and candidate-contingent planning. Under exchangeability conditions for terminal and identity residuals, with predictable querying, we establish fixed-time terminal-location coverage and anytime-valid target retention. At the final replan, when one control step remains, we bound the joint probability that a tightened-set DDTO plan passes nonlinear rollout verification but capture fails. The closed-loop controller applies fallback guidance to any agent without a verified DDTO plan and, across 100 paired scenarios, captures 79% of targets under the strict control-effort budget and 85% when that budget is relaxed.
Farbod Siahkali, Mengxue Hou, Vijay Gupta
Department of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47906, USA · Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA