CBFKit: A Control Barrier Function Toolbox for Robotics Applications

CBFKit is a Python/ROS2 toolbox designed to facilitate safe planning and control for robotics applications, particularly in uncertain environments. The toolbox utilizes Control Barrier Functions (CBFs) to provide formal safety guarantees while offering flexibility and ease of use.

Table of Contents

• Key Features
• Supported Models
• Applications
• Installation
• Start with Tutorials
• ROS2
• Examples
• Citing CBFKit
• License

Key Features

• Generalized Framework: Supports the design of CBFs for various robotic systems operating in both deterministic and stochastic settings.
• ROS Integration: Seamlessly connects with ROS2, enabling multi-robot applications, environment and map encoding, and integration with motion planning algorithms.
• Diverse CBF Options: Provides a variety of CBF formulations and algorithms to address different control scenarios.
• Model-based and Model-free Control: Accommodates both model-based control strategies using system dynamics and model-free control approaches.
• Safety Guarantee: CBFs provide mathematically rigorous guarantees of safety by ensuring the system remains within a defined safe operating region.
• Flexibility: Allows users to specify custom safety constraints and barrier functions to tailor the control behavior to specific needs.
• Efficiency: Leverages JAX for efficient automatic differentiation and jaxopt for fast quadratic program (QP) solving, enabling real-time control applications.
• Code Generation: Simplifies model creation with automatic code generation for dynamics, controllers, and certificate functions.
• Usability: Includes tutorials and examples for a smooth learning curve and rapid prototyping.
• Functional Programming: Built on functional programming principles, emphasizing data immutability and programmatic determinism.

Supported Models

CBFKit accommodates a range of control-affine system models:

• Deterministic Continuous-time ODEs: $\dot{x} = f(x) + g(x)u$
• ODEs with Bounded Disturbances: $\dot{x} = f(x) + g(x)u + Mw$
• Stochastic Differential Equations (SDEs): $dx = (f(x) + g(x)u)dt + \sigma(x)dw$

Applications

CBFKit can be applied to diverse robotics applications, including:

• Autonomous Navigation: Ensure collision avoidance with static and dynamic obstacles.
• Human-Robot Interaction: Guarantee safety during collaborative tasks and physical interaction.
• Manipulation: Control robot arms while avoiding obstacles and joint limits.
• Multi-Robot Coordination: Coordinate the movement of multiple robots while maintaining safe distances and avoiding collisions.

Installation

CBFKit is readily deployable via a Docker image. After setting up Docker (refer to the official Docker documentation for detailed instructions), proceed with one of the following methods:

1. VS Code DevContainer Launch

1. Open the project in VS Code.
2. Click the green button at the bottom right of the window to launch the DevContainer.
3. All necessary components are pre-installed for immediate use.

2. Docker Command Line

1. Build the image:

   docker build -t cbfkit:latest -f Dockerfile.$(uname -m) .
   

2. Run the container:

   docker run -it --name container-name -v .:/workspace cbfkit:latest
   

Start with Tutorials

Explore the tutorials directory to help you get started with CBFKit. Open the Python notebook in the tutorials directory to get started. The script simulate_new_control_system.ipynb automatically generates the controller, plant, and certificate function for a Van der Pol oscillator. It also generates ROS2 nodes for the plant, controller, sensor, and estimator. These serve as a starting point for developing your own CBF-based controller.

Generated files/folders:

van_der_pol_oscillator
 ┣ certificate_functions
 ┃ ┣ barrier_functions
 ┃ ┃ ┣ __init__.py
 ┃ ┃ ┣ barrier_1.py
 ┃ ┃ ┗ barrier_2.py
 ┃ ┣ lyapunov_functions
 ┃ ┃ ┣ __init__.py
 ┃ ┃ ┗ lyapunov_1.py
 ┃ ┗ __init__.py
 ┣ controllers
 ┃ ┣ __init__.py
 ┃ ┣ controller_1.py
 ┃ ┗ zero_controller.py
 ┣ ros2
 ┃ ┣ __init__.py
 ┃ ┣ config.py
 ┃ ┣ controller.py
 ┃ ┣ estimator.py
 ┃ ┣ plant_model.py
 ┃ ┗ sensor.py
 ┣ __init__.py
 ┣ constants.py
 ┣ plant.py
 ┗ run_ros2_nodes.sh

ROS2

The ROS2 nodes are generated in the ros2 directory. The nodes are generated for the plant, controller, sensor, and estimator.

To run the nodes, execute the following command in the van_der_pol_oscillator directory:

bash run_ros2_nodes.sh

The generated nodes interact as follows:

• The plant_model node simulates the physical system and publishes the system state.
• The sensor node receives the system state and adds noise to simulate real-world measurements.
• The estimator node receives the noisy measurements and estimates the true system state.
• The controller node receives the estimated state and computes the control input based on the CBF formulation.

Examples

Several additional examples of how to use CBFkit to conduct full simulations of arbitrary dynamical systems are provided, including a unicycle robot, fixed-wing aerial vehicle, and more, all of which may be found in the examples folder. Any file contained within examples or any of its subdirectories whose name takes the form of *main.py is an executable example that may be referenced when a user is building their own application.

See below for the script used to simulate a unicycle robot navigating toward a goal set amidst three ellipsoidal obstacles, which may be found at examples/unicycle/vanilla_cbf_start_to_goal_main.py:

import jax.numpy as jnp

import cbfkit.systems.unicycle.models.olfatisaber2002approximate as unicycle
import cbfkit.simulation.simulator as sim
from cbfkit.controllers.model_based.cbf_clf_controllers import (
    vanilla_cbf_clf_qp_controller as cbf_controller,
)
from cbfkit.controllers.model_based.cbf_clf_controllers.utils.certificate_packager import (
    concatenate_certificates,
)
from cbfkit.controllers.model_based.cbf_clf_controllers.utils.barrier_conditions import (
    zeroing_barriers,
)

# Simulation parameters
tf = 10.0
dt = 0.01
file_path = "examples/unicycle/start_to_goal/results/"

approx_unicycle_dynamics = unicycle.plant(l=1.0)
init_state = jnp.array([0.0, 0.0, jnp.pi / 4])
desired_state = jnp.array([2.0, 4.0, 0])
actuation_constraints = jnp.array([100.0, 100.0])  # Effectively, no control limits

approx_uniycle_nom_controller = unicycle.controllers.proportional_controller(
    dynamics=approx_unicycle_dynamics,
    Kp_pos=1,
    Kp_theta=0.01,
    desired_state=desired_state,
)

obstacles = [
    (1.0, 2.0, 0.0),
    (-1.0, 1.0, 0.0),
    (0.5, -1.0, 0.0),
]
ellipsoids = [
    (0.5, 1.5),
    (1.0, 0.75),
    (0.75, 0.5),
]

barriers = [
    unicycle.certificate_functions.barrier_functions.obstacle_ca(
        certificate_conditions=zeroing_barriers.linear_class_k(2.0),
        obstacle=obs,
        ellipsoid=ell,
    )
    for obs, ell in zip(obstacles, ellipsoids)
]
barrier_packages = concatenate_certificates(*barriers)

controller = cbf_controller(
    control_limits=actuation_constraints,
    nominal_input=approx_uniycle_nom_controller,
    dynamics_func=approx_unicycle_dynamics,
    barriers=barrier_packages,
)

# Simulation imports
from cbfkit.integration import forward_euler as integrator
from cbfkit.sensors import perfect as sensor
from cbfkit.estimators import naive as estimator


x, u, z, p, data, data_keys = sim.execute(
    x0=init_state,
    dt=dt,
    num_steps=int(tf / dt),
    dynamics=approx_unicycle_dynamics,
    integrator=integrator,
    controller=controller,
    sensor=sensor,
    estimator=estimator,
    filepath=file_path + "vanilla_cbf_results",
)

Citing CBFKit

If you use CBFKit in your research, please cite the following PAPER:

@misc{black2024cbfkit,
title={CBFKIT: A Control Barrier Function Toolbox for Robotics Applications},
author={Mitchell Black and Georgios Fainekos and Bardh Hoxha and Hideki Okamoto and Danil Prokhorov},
year={2024},
eprint={2404.07158},
archivePrefix={arXiv},
primaryClass={cs.RO}
}

License

CBFKit is distributed under the BSD 3-Clause License. Refer to the LICENSE file for detailed terms.