MPC-based Unicycle Trajectory Tracking with Control Barrier Functions (CBFs)

Overview

This repository contains an example that implements a Model Predictive Control (MPC) controller for trajectory tracking of a unicycle while enforcing safety constraints using Control Barrier Functions (CBFs). The goal is to follow a predefined reference trajectory while avoiding an obstacle and staying within a safe region.

There are already many repositories with similar implementations, but most of them are using CasADi or MATLAB. This repository instead is a Python implementation that uses CVXPY for the QP subproblem and jax for autograd as well as parallelization.

Requirements

• Python 3.10+
• jax
• cvxpy
• numpy
• matplotlib

Demo

To run the demo, simply run the sqp_mpccbf_tracking.ipynb notebook in Google Colab .

Key Features of the MPC-DCBF Implementation

• Trajectory tracking with NMPC.
• Discrete Control Barrier Functions (CBFs) to enforce h[k+1] - h[k] >= -a;pha * h[k] as a MPC constraint
• Sequential Quadratic Programming (SQP) for handling nonlinearities and updating the linearization at each iteration.
• QP formulation using cvxpy with cp.Parameter for warm-starting and fast updates.

Trouble Shooting

• OSQP failed: remove time_limit argument in prob.solve(...) or increase max_sqp_iter or try different QP solvers.