UAV Formation Control — Dynamic Event-Triggered Communication

Roadmap for Dynamic Event-Triggered Communication Mechanism (DECM) + Time-Varying Formation Tracking (TVFT) for multi-agent UAV systems.

Project Overview

What This Does

• 5 UAVs maintain a rotating pentagon formation (radius 1 m)
• Formation tracks a moving center (0.3 m/s constant velocity)
• DECM mechanism reduces communication bandwidth by ~50% vs. periodic sampling
• Proven Lyapunov stability via Linear Matrix Inequalities (LMI)

Key Innovation

Instead of broadcasting every 50 ms (periodic), each UAV broadcasts only when a dynamic threshold is crossed. The threshold itself shrinks over time as the formation converges, balancing performance and communication load.

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Project Structure

UAV formation/
├── config/                 # System parameters and configuration
│   ├── params.py          # Main config file (num UAVs, sampling rate, etc.)
│   └── __init__.py
├── lmi/                    # LMI solver and controller design
│   ├── lmi_solve.py       # Formulate and solve the LMI (Theorem 1)
│   ├── controller.py      # Controller implementation
│   └── __init__.py
├── sim/                    # Simulation engine
│   ├── simulator.py       # Main simulation loop
│   ├── dynamics.py        # UAV dynamics (double integrator + DECM)
│   ├── decm.py            # Event-triggered mechanism
│   └── __init__.py
├── plots/                  # Post-processing and visualization
│   ├── plotter.py         # Generate figures (formation, bandwidth, convergence)
│   └── __init__.py
├── requirements.txt        # Python dependencies
├── README.md              # This file
└── PHASE_1_TASKS.md       # Phase 1 checklist (theory foundation)

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Getting Started

1. Set Up Python Environment

cd C:\Users\Username\UAV formation
python -m venv venv
.\venv\Scripts\Activate.ps1
pip install -r requirements.txt

2. Verify Installation

python -c "from config import params; print(params.N_UAVS, params.L)"

Should output:

5
[[ 2. -1.  0.  0. -1.]
 [-1.  2. -1.  0.  0.]
 [ 0. -1.  2. -1.  0.]
 [ 0.  0. -1.  2. -1.]
 [-1.  0.  0. -1.  2.]]

3. Start Phase 1

Open PHASE_1_TASKS.md and work through the 5 theory tasks:

1. Graph theory & Laplacian
2. Linear systems & LMI basics
3. Multi-agent formation control (paper review)
4. Environment setup ✓ (already done)
5. Event-triggered control theory

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Key Files by Phase

Phase 1 (Theory)

• PHASE_1_TASKS.md — 5 tasks with deliverables

Phase 2 (System Modelling)

• config/params.py — System matrices, topology, formation reference

Phase 3 (Controller Design)

• lmi/lmi_solve.py — Solve the LMI for K, Φ, Ω (Theorem 1)
• lmi/controller.py — Implement feedback law u = Kx + q

Phase 4 (Parameter Tuning)

• Jupyter notebook: tune σ(0), ρ, and other gains

Phase 5 (Stability Validation)

• Figures-(trajectories, formation, bandwidth savings)

Phase 6 (Full Simulation + Enhancements)

• sim/simulator.py — 20-second closed-loop simulation

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LMI Formulation

The core of the project is solving the block LMI.

Find P̃, Q̃, R̃, Φ̃, Ω̃, S̃, K̃ such that:

$$\Upsilon = \begin{bmatrix} \Upsilon_{11} & \Upsilon_{12} & \Upsilon_{13} \

• & \Upsilon_{22} & 0 \
• & * & -R̃ \end{bmatrix} < 0$$

with constraints on σ(0) ∈ [0, 1) and ρ > 0.

This ensures:

• Closed-loop stability of the formation error dynamics
• Convergence to the moving reference
• Proof that DECM triggers reduce bandwidth without sacrificing stability

Implementation: lmi/lmi_solve.py uses cvxpy to solve this feasibility problem.

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Expected Results

• 5 UAVs converge to rotating pentagon (radius 1 m, ω = 0.5 rad/s)
• Center tracks reference trajectory at 0.3 m/s
• Trigger probabilities: 38.5–62.5% (∼50% bandwidth savings)
• Lyapunov convergence guaranteed by LMI feasibility
• All eigenvalues of closed-loop system in left-half plane

What You Will Produce

• Trajectory plots of all 5 UAVs
• Formation shape evolution over time
• Communication event histogram (broadcasts per second)
• Bandwidth usage: periodic vs. DECM
• Convergence plots: formation error → 0

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References

Core Paper

• Xiang et al. (2023). "Dynamic Event-Triggered Formation Control for UAVs..."
  IEEE IECON 2023 · Northwestern Polytechnical University

Foundational Works

• Dong et al. (2015). "Cooperative formation control for multi-agent systems..."
• Ge & Han (2017). "Distributed formation stabilization via event-triggered communication"
• Ren & Beard (2005). "Consensus seeking in multiagent systems..."

Software

• cvxpy: Python convex optimization package
• NumPy/SciPy: Numerical linear algebra
• Matplotlib: Visualization

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Each phase builds on the previous; skip no steps. Theory (Phase 1) foundations are critical for understanding the controller design (Phase 3) and debugging the simulation (Phase 6).

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