Multimode Control Barrier Function for Simulink

This repository contains a MATLAB/Simulink implementation of a multimode control barrier function (CBF), along with the Simulink model used to generate ROS code and a collection of simulation test cases.

How the CBF works

A control barrier function maintains system safety by turning a safety requirement into a constraint on the control input. At each simulation step, the CBF evaluates the current system state, the surrounding traffic conditions, and the nominal control command. It then determines whether the nominal command preserves the required safety margin and applies the appropriate constraint when it does not.

This implementation is multimode: the active safety constraint changes with the operating mode of the system. Mode transitions allow the CBF to represent different traffic or vehicle behaviors while preserving the safety requirement across those transitions. The resulting CBF subsystem can be inserted into a larger Simulink model between the nominal controller and the vehicle dynamics, where it provides a safety-aware control command for simulation or ROS deployment.

The state $x_n$ of the system contains the space gap $s_n$, the ego velocity $v_n$, and the relative velocity $\Delta v_n$. The constant values used by the multi-mode CBF are:

Constant	Value
$\tau$	$2.0\ \mathrm{s}$
$k$	$0.1$
$d_1^{\min}$	$15.0\ \mathrm{m}$
$d_2^{\min}$	$5.0\ \mathrm{m}$
$k_d$	$3.0$
$v_{\mathrm{slow}}$	$5.0\ \mathrm{m/s}$
$v_{\mathrm{fast}}$	$7.5\ \mathrm{m/s}$
$\epsilon$	$0.1\ \mathrm{m}$
$\tau_{1,2}$	$3.0\ \mathrm{s}$
$u_{\min}$	$-3.0\ \mathrm{m/s^2}$
$u_1^{\max}$	$1.5\ \mathrm{m/s^2}$
$u_2^{\max}$	$1.0\ \mathrm{m/s^2}$
$u_3^{\max}$	$0.5\ \mathrm{m/s^2}$

In all modes, the CBF command acceleration is calculated as:

$u_{\mathrm{cbf}}(x_n) = \frac{1}{\tau}\left[k\left(s_n - \left(\tau v_n + d_q^{\min}\right)\right)+ \Delta v_n\right]$

The command acceleration is then:

$u_{\mathrm{cmd}}(x_n)= \min[{u_{\mathrm{cbf}}(x_n),k_{\mathrm{nom}}(x_n)]}$

In the third mode, the minimum distance is calculated as:

$$ \begin{aligned} d_3^{\min}(v_n) &= d_2^{\min} & + \frac{ \left(d_1^{\min} - d_2^{\min}\right) \exp\left[ k_d\left( v_n - \frac{v_{\mathrm{slow}} + v_{\mathrm{fast}}}{2} \right) \right] }{ 1 + \exp\left[ k_d\left( v_n - \frac{v_{\mathrm{slow}} + v_{\mathrm{fast}}}{2} \right) \right] } \end{aligned} $$

The mode-transition logic is summarized below. The three operating modes are the full-range mode ($q = 1$), the stop-and-go mode ($q = 2$), and the transition mode ($q = 3$). The transition guards use the paper's notation: $s_n$ is the measured spacing, $v_n$ is the measured speed, $v_{\mathrm{slow}}$ and $v_{\mathrm{fast}}$ are speed thresholds, $d_1^{\min}$ and $d_2^{\min}$ are minimum-distance terms, $\tau$ is the time-headway parameter, and $\epsilon$ is the safety margin.

Current mode	Next mode	Transition condition
Full range ($q = 1$)	Stop-and-go ($q = 2$)	$s_n \ge \tau v_n + d_1^{\min} - \epsilon$ and $\mathrm{duration}(v_n \le v_{\mathrm{slow}}) \ge \tau_{1,2}$
Stop-and-go ($q = 2$)	Transition ($q = 3$)	$s_n \ge \tau v_n + d_2^{\min} - \epsilon$ and $v_n \ge v_{\mathrm{fast}}$
Transition ($q = 3$)	Stop-and-go ($q = 2$)	$v_n \le v_{\mathrm{slow}}$
Transition ($q = 3$)	Full range ($q = 1$)	$s_n \ge \tau v_n + d_1^{\min} - \epsilon$ and $v_n \ge v_{\mathrm{slow}}$

At every step, the active mode selects the corresponding CBF constraint. The vehicle or plant dynamics then provide the updated state and traffic measurements used to evaluate the next transition.

Repository structure

.
├── multimodecbf_subsystem.slx   # CBF subsystem
├── multimodecbf.slx             # Top-level model and ROS code-generation entry point
├── startup.m                    # Adds the repository and its subdirectories to the MATLAB path
├── test/
│   ├── case_*.slx               # Simulation test cases
│   └── test_resources/          # Reusable subsystem models used by the tests

Main models

• multimodecbf_subsystem.slx defines the multimode CBF. Open this model to inspect or modify the barrier-function subsystem.
• multimodecbf.slx is the top-level model used to integrate the CBF and generate ROS code. Use the model's configured Simulink build/code-generation workflow when producing ROS output.

Startup

• startup.m initializes the MATLAB environment by recursively adding the repository to the MATLAB path:

  addpath(genpath('.'))

Tests

The test/ directory contains the simulation test suite. Each case_*.slx file represents a scenario used to exercise the CBF and the surrounding vehicle/control models. The test/test_resources/ directory contains reusable subsystem models and supporting Simulink models consumed by those test cases.

Test case names describe the scenario being exercised, for example:

• case_01_fast_steady.slx — fast, steady-state behavior
• case_04_slow_to_fast.slx — transition from slow to fast behavior
• case_09_30_to_2_to_0.slx — a speed profile that reaches a stop
• case_13_hard_brake.slx — hard-braking behavior
• case_19_all_state_oscillation.slx — oscillation across all states

Getting started

Requirements

You will need:

• MATLAB
• Simulink
• The MATLAB/Simulink products required by the models and their configured ROS code-generation workflow

The exact MATLAB release and toolbox versions should match the environment in which the models were created and tested.

Initialize MATLAB

From the repository root, run:

startup

Alternatively, execute startup.m from the MATLAB Current Folder browser. Running the script first ensures that the top-level models and all test resources are available on the MATLAB path.

Inspect or simulate the CBF

1. Run startup.
2. Open multimodecbf_subsystem.slx to inspect the CBF implementation, or open one of the models in test/ to run a scenario.
3. Configure the model's normal Simulink simulation settings as needed.
4. Run the simulation and inspect the model outputs and scopes/logs provided by the selected model.

Generate ROS code

1. Run startup.
2. Open multimodecbf.slx.
3. Confirm that the model's ROS/code-generation configuration matches your target environment.
4. Use the Simulink build or code-generation command configured for the model.

Citation

To cite the usage of this repository, use the following:

Kate Sanborn, George Gunter, Daniel B. Work, Ricardo G. Sanfelice, Jonathan Sprinkle. "Traffic Density with Multi-Mode Control Barrier Functions at Scale." in 2026 IEEE International Conference on Intelligent Transportation Systems (ITSC), (in press) 2026.

or using bibtex:

@inproceedings{sanborn2026single,
  author    = {Sanborn, Kate and Gunter, George and Work, Daniel B. and Sanfelice, Ricardo G. and Sprinkle, Jonathan},
  title      = {Traffic Density with Multi-Mode Control Barrier Functions at Scale},
  booktitle  = {2026 IEEE International Conference on Intelligent Transportation Systems (ITSC)},
  year       = {2026},
  note       = {in press}
}

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