ControlBarrierFunctions.jl

A package for implementing control barrier functions (CBFs) in Julia.

Overview

This toolbox provides utilities to construct nonlinear systems and control policies based on control barrier functions (CBFs).

Installation

To download this package open the Julia REPL, enter the package manager (type ] into the REPL) and run

using Pkg
Pkg.add(url="https://github.com/maxhcohen/ControlBarrierFunctions.jl")

Usage

# Load in packages
using ControlBarrierFunctions
using LinearAlgebra
using Plots

# Create a single integrator
n = 2
m = 2
f(x) = zeros(2)
g(x) = diagm(ones(2))
Σ = ControlAffineSystem("single integrator", n, m, f, g)

# Create a CBF for an obstacle
xo = [-1.0, 1.0]
ro = 0.4
h(x) = norm(x - xo)^2 - ro^2
α(r) = r
cbf = ControlBarrierFunction(h, Σ, α);

# Nominal controller
kd(x) = -x

# Create a safety filter
k = ExplicitSafetyFilter(cbf, Σ, kd);

# Run a simulation
x0 = [-2.1, 2.0]
T = 15.0
sol = simulate(Σ, k, x0, T)

# Set up plots
default(fontfamily="Computer Modern", palette=:tab10, framestyle=:box, grid=false, lw=2)

# Plot trajectory
plot(sol, idxs=(1,2), label="")
contour!(-1.5:0.01:-0.5, 0.5:0.01:1.5, (x,y) -> h([x,y]), levels=[0.0], colorbar=false, c="black")