⚡ electrical engineering

Capture, Shield, or Neutralize: Engagement-Aware Pursuit-Evasion

This paper presents a hierarchical control architecture that combines a zero-sum receding-horizon game with an inner-loop discrete-time Control Barrier Function to enable multi-agent swarms to fluidly switch between aggressive pursuit, perimeter defense, and area denial tactics while guaranteeing collision-free operation.

Original authors: Ananya Acharya, Trenton Goyette, Masoud Ataei, Adrian Stoica, Vikas Dhiman, Mohammad Javad Khojasteh

Published 2026-07-14

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Ananya Acharya, Trenton Goyette, Masoud Ataei, Adrian Stoica, Vikas Dhiman, Mohammad Javad Khojasteh

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a high-stakes game of tag, but instead of kids running around a playground, you have a swarm of robot drones playing against a sneaky, fast-moving intruder. The goal isn't just to catch the intruder; sometimes the goal is to gently herd them away, and other times it's to stop them from breaking into a safe zone. The big question is: How do you program a team of robots to switch between these different "rules of the game" instantly, without crashing into each other or the target?

This paper introduces a new "brain" for robot swarms that can do exactly that. It's like giving the robots a two-part thinking process: a Strategist and a Safety Guard.

The Two-Part Brain

1. The Strategist (The Game Player)
At the top level, the robots use a clever math trick called a "zero-sum game." Think of it like a chess match where every move the intruder makes to get away is a point they gain, and every move the robots make to get closer is a point they lose. The robots try to minimize their loss while the intruder tries to maximize their gain.

Instead of just reacting to where the intruder is right now (like a dog chasing a ball), this Strategist looks a few steps ahead. It simulates the next few seconds of the game over and over again, asking, "If I go there, where will they go? If they go there, where should I be?" This allows the robots to predict the intruder's path and block it before it happens.

2. The Safety Guard (The Inner Loop)
Here is the tricky part: If the Strategist gets too excited, the robots might crash into each other or accidentally bump the intruder when they aren't supposed to. That's where the Safety Guard comes in. This is a "Control Barrier Function" (CBF), which acts like an invisible, super-fast force field.

The Safety Guard sits in the inner loop of the robot's brain. It checks the Strategist's plan every single moment. If the plan says, "Dive straight at the intruder!" but the Safety Guard sees, "Wait, that will cause a crash," it instantly tweaks the command just enough to keep everyone safe. It's like a co-pilot who gently nudges the steering wheel to avoid a pothole without changing the driver's destination.

Switching the Rules of the Game

The coolest feature of this system is how it handles different "Rules of Engagement" (ROE). Usually, if you want robots to change their behavior (like from "catch the bad guy" to "protect the perimeter"), you have to rewrite the whole computer code. This paper shows a way to just turn a dial.

By simply changing a few numbers (weights) in the math, the whole swarm can instantly switch modes:

Capture Mode: The robots get aggressive. They try to get as close as possible to the intruder to catch them.
Perimeter Defense: The robots form a wall. They don't try to grab the intruder; they just make sure the intruder can't cross a specific line.
Neutralization: The robots might try to physically intercept the intruder to stop them.

The paper demonstrates this by running 100 simulated games in a 2D world and then testing it again with 3D flying drones (quadrotors). In the 2D tests, when the robots started in a perfect circle around the intruder, they caught them nearly 100% of the time. Even when they started in random, messy positions, they still managed to catch the intruder most of the time, proving the system is tough enough to handle chaos.

What This Is (and Isn't)

It's important to know what this paper actually proves. The authors did not build a real-life army of robots and test them in a park. Everything described here happened inside a computer simulation. They used mathematical models to represent the robots' movements (like "double integrator" physics for flat ground and complex 3D physics for flying drones).

The paper explicitly rules out the idea that you need to completely redesign the robot's brain to change its mission. They argue against using simple, reactive heuristics (like "if it moves left, I move left") because those don't work well against smart opponents. Instead, they show that a hierarchical system (Strategist + Safety Guard) is the better way to go.

They also note that their current setup assumes the robots know exactly where everyone is (perfect information) and that the world is predictable. They don't claim to have solved the problem for situations where sensors are broken or the intruder is unpredictable in a way the math can't guess.

The Bottom Line

In these simulations, the team showed that by combining a smart, forward-looking game planner with a strict, instant safety filter, a swarm of robots can fluidly switch between catching, blocking, and herding an intruder. They successfully scaled this up from flat ground to 3D flying, showing that the robots could coordinate in the air, avoid crashing into each other, and still secure the target.

While this is a simulation and not a real-world deployment yet, the results suggest that this "two-brain" approach is a robust way to handle complex, adversarial games where safety and strategy need to happen at the same time. The code is even available for others to try, inviting more researchers to see if this works in even more chaotic scenarios.

Technical Summary: Engagement-Aware Pursuit-Evasion

Problem Statement

The paper addresses the challenge of controlling multi-agent pursuer teams in adversarial pursuit-evasion scenarios. Traditional approaches often struggle to balance strategic task planning (e.g., capture vs. area denial) with rigorous safety constraints (collision avoidance) in real-time. Solving for a global equilibrium in continuous-time differential games is computationally intractable for multi-agent systems. Furthermore, existing methods often lack the flexibility to adapt to varying "Rules of Engagement" (ROE)—such as shifting from aggressive capture to perimeter defense or neutralization—without redesigning the underlying control logic. The core problem is to develop a hierarchical control architecture that decouples strategic planning from safety assurance, allowing a swarm to fluidly switch between engagement modes while guaranteeing collision-free operation.

Methodology

The authors propose a hierarchical control architecture consisting of two distinct layers: a high-level Receding-Horizon Minimax Model Predictive Control (MPC) planner and a low-level Discrete-Time Control Barrier Function (CBF) safety filter.

1. High-Level Planning: Minimax MPC

The interaction is formulated as a finite-horizon, zero-sum dynamic game. The pursuer team seeks to minimize a shared cost function $J$ , while the evader seeks to maximize it. To avoid the intractability of solving the full Hamilton-Jacobi-Isaacs equation, the system employs an iterative minimax scheme:

Iterative Best-Response: At each time step, the pursuers solve for an optimal control trajectory assuming a frozen nominal evader trajectory. Subsequently, the evader solves for its optimal trajectory assuming the pursuers' updated trajectory. This process repeats for a fixed number of Nash iterations.
Dual Game Formulations: The cost function $J$ $J$ is modified to support different ROE:
- Pursuit-Evasion Tracking: The cost penalizes the relative distance between pursuers and the evader. Crucially, it includes a transverse velocity penalty that geometrically nullifies velocity components perpendicular to the line-of-sight, forcing pursuers onto a direct collision course rather than relying on reactive heuristics.
- Perimeter Defense: The cost shifts priority from absolute capture to boundary tracking. Pursuers are penalized for deviating from assigned target points on a defense polygon, while the evader is penalized for making progress toward the protected region.

2. Low-Level Execution: CBF Safety Filter

To ensure safety without compromising the convexity of the MPC, a discrete-time Control Barrier Function (CBF) operates as an inner-loop filter.

Safety Filter: The nominal control input ( $u_{des}$ ) generated by the MPC is passed to a Quadratic Program (QP). The QP minimizes the deviation from $u_{des}$ while satisfying discrete-time CBF constraints.
Kinematic Barrier: The barrier function $h(x_k)$ is velocity-aware, evaluating the current rate of approach against the available braking distance under maximum acceleration limits. This ensures agents have sufficient time to prevent breaching a safe distance $D_{safe}$ .
Slack Variables: Slack variables are included in the QP to ensure strict feasibility even in dense clusters, heavily penalized to discourage safety violations.

3. Rules of Engagement (ROE) Adaptation

The framework achieves adaptability by tuning the weights of the shared zero-sum payoff and the CBF constraints (specifically slack penalties and safe distance margins). By adjusting these parameters online, the system can transition between:

Capture: Aggressive pursuit with relaxed standoff constraints.
Deterrence/Deflection: Strict perimeter defense or redirection away from protected zones.
Neutralization: Selective relaxation of safety constraints to permit physical interception when recovery is not an option.

Key Contributions

Engagement-Aware Framework: The paper introduces a hierarchical architecture that treats ROE as control-design objects, allowing the swarm to switch tactics (capture, shielding, neutralization) without structural changes to the control logic.
Computationally Tractable Minimax Solver: A receding-horizon minimax solver is developed at the planning layer, enabling defensive teams to strategically anticipate adversarial actions through iterative best-response optimization.
Integrated Safety and Engagement Filter: A discrete-time CBF-QP filter is integrated at the execution layer. It modifies nominal MPC commands to enforce inter-pursuer collision avoidance and pursuer-evader standoff constraints, separating the objectives of task satisfaction (MPC) and survival (CBF).

Experimental Results

The framework was evaluated in simulations across 2D planar double integrator dynamics and fully nonlinear 3D quadrotor dynamics.

2D Pursuit-Evasion: In 100 simulated games, the system achieved nearly 100% capture rates when pursuers were initialized in a radial ring. Even with random uniform initialization (a stress test for the CBF filter), capture rates remained competitive, demonstrating the solver's ability to recover from chaotic formations.
2D Perimeter Defense: The swarm successfully blocked an evader from breaching a defined 2D boundary, efficiently allocating agents along the boundary arclengths to minimize the evader's progress.
3D Quadrotor Dynamics: The architecture scaled to 6-DOF nonlinear quadrotor dynamics. The system maintained dynamic stability and successfully coordinated in 3D space to minimize the evader's escape volume and secure capture, accounting for pitch/roll dynamics in the safety filter.
ROE Modulation: Simulations demonstrated seamless transitions between "evader-preservation" (strict standoff) and "evader-neutralization" (physical interception) modes by modulating mission parameters and filter weights.

Significance and Claims

The paper claims that this framework provides a robust solution for adversarial swarm control by decoupling strategic planning from safety enforcement. The significance lies in the system's ability to:

Adapt Dynamically: Switch between capture, defense, and neutralization tactics simply by tuning weights, rather than re-engineering the controller.
Ensure Safety: Guarantee collision-free operation and standoff constraints via the CBF inner-loop without disrupting the convexity of the MPC optimization.
Scale: Operate effectively in both 2D and complex 3D nonlinear environments.

The authors note that the current work assumes deterministic dynamics and a single adversarial target. Future work is proposed to extend the solver to $M$ -pursuer, $N$ -evader settings, incorporate dynamic uncertainty, and integrate state estimation from sensor measurements to relax the assumption of perfect state knowledge.