Control Barrier Function for Tactical Conflict Resolution

Overview

This simulation models Tactical Conflict Resolution for a grid-based urban airspace where aircraft (represented as 2D point-mass vehicles) travel along orthogonal corridors. The core logic implements Control Barrier Functions (CBFs) to modulate vehicle speeds and maintain safe separation at intersections. The control is centralised and ground-based, making it ideal for UAS Traffic Management systems operating in structured low-altitude corridors.

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Key Concepts and Notation

Let:

• $i, j \in [1, \ldots, N ]$ index the vehicles
• $\mathbf{p}_i(t) \in \mathbb{R}^2$: position of vehicle i at time t
• $s_i(t) \in \mathbb{R}$: scalar path parameter for vehicle i
• $v_i(t) = \dot{s}_i(t)$: scalar speed of vehicle i
• $\mathcal{L}_{ij} = |\mathbf{p}_i(t) - \mathbf{p}_j(t)|^2 - d^2$: safety constraint, with $d > 0$ as the loss-of-separation threshold

A Control Barrier Function (CBF) is defined for each conflicting pair $(i, j)$ as:

$$h_{ij}(t) = \|\mathbf{p}_i(t) - \mathbf{p}_j(t)\|^2 - d^2$$

To ensure safety, we enforce the CBF condition:

$$\dot{h}_{ij}(t) + \alpha h_{ij}(t) \geq 0$$

where $\alpha > 0$ is a tunable CBF gain.

The goal is to find an admissible control (speed) $v_i(t)$ such that all pairwise CBF constraints are satisfied.

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Script Structure

main()

Initialises the simulation, runs each timestep, and visualises the result.

Simulation class

Encapsulates simulation logic:

• Detects potential conflicts
• Computes feasible speed intervals $[LB_i, UB_i]$
• Applies clipped speed control:
  $v_i(t) = \text{clip}(v_{\text{nominal}}, LB_i, UB_i)$

ControlBarrier

Holds the LoS threshold and the gain $\alpha$ used in the inequality constraint.

Traffic

Tracks scalar path positions, previous velocities, and full position histories.

Airspace

Defines a structured grid of flight paths. Horizontal and vertical vehicles are assigned based on their index.

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Conflict Detection Logic

Only orthogonal vehicles may conflict (horizontal vs vertical).

Each vehicle computes its arrival time at the intersection:

$t_i = \frac{s^\text{int}_i - s_i}{v_i}, \quad t_j = \frac{s^\text{int}_j - s_j}{v_j}$

A conflict is resolved only if $t_i > t_j$, assigning priority to vehicle j.

The CBF condition then yields a linear constraint on $v_i$, used to adjust its bounds for safety.

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Visualisation

The plot includes:

• Corridor boundaries as dashed lines
• Real-time vehicle positions
• Vehicle markers with unique colours
• An animated playback of the simulation

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How to Run

python3 controlBarrierFunction.py

Ensure dependencies are installed:

pip install numpy matplotlib

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Academic Reference

This implementation demonstrates a discrete-time, single-integrator CBF method for tactical deconfliction in urban airspace corridors. It is suitable for fast-time simulation and evaluation of centralised ground-based safety nets in UTM.

Frémond, R. (2025). Centralised Tactical Conflict Resolution Using Control Barrier Functions in Grid-Based Airspace. Internal Project Note.

Keywords: Control Barrier Function, Tactical Conflict Resolution, Unmanned Aircraft System Traffic Management (UTM), Separation Assurance, Grid-Based Airspace.

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