MPC Locomotion Control of the Unitree Go2 Quadruped Robot in MuJoCo

This repository implements a Convex Model Predictive Controller (MPC) for the Unitree Go2 quadruped robot, including contact-force optimization, centroidal linearized dynamics, Raibert-style foot planning, swing-leg path generation and MuJoCo simulation.

Developed as part of the UC Berkeley Master of Engineering (MEng) capstone project in Mechanical Engineering.

Introduction

The controller is designed following the methodology described in the following publication:

"Dynamic Locomotion in the MIT Cheetah 3 Through Convex Model-Predictive Control"
https://dspace.mit.edu/bitstream/handle/1721.1/138000/convex_mpc_2fix.pdf

The objective of this project is to reproduce the main ideas presented in the paper — particularly the contact-force MPC formulation, convex optimization structure, and robust locomotion behavior—while integrating them into a modern, modular robotics control pipeline.

Locomotion Capabilities

The controller achieves the following performance in MuJoCo simulation:

Linear Motion

• Forward speed: up to 0.8 m/s
• Backward speed: up to 0.8 m/s
• Lateral (sideways) speed: up to 0.4 m/s

_{examples/ex02: Forward walking    examples/ex03: Side walking}

Rotational Motion

• Yaw rotational speed: up to 4.0 rad/s

_{examples/ex04: Trot rotation}

Supported Gaits

• Trot gait (tested at 3.0 Hz with 0.6 duty cycle)

Controller Overview

Our motion control stack includes:

• Centroidal MPC (~30-50 Hz)
  Contact-force–based MPC implemented via CasADi using OSQP, solving a convex QP each cycle. The prediction horizon spans one full gait cycle, divided into 16 time steps.

• Reference Trajectory Generator (~30-50 Hz)
  Generates centroidal trajectory for MPC based on user input.

• Swing/Stance Leg Controller (200 Hz)

  • Swing-phase: impedance control with foot trajectory and force tracking
  • Stance-phase: joint torque computation to realize MPC contact forces

• Gait Scheduler and Foot Trajectory Generator (200 Hz)

  • Determines stance/swing timing
  • Compute touchdown position for swing-foot using Raibert style foot placement method and - - Compute swing-leg trajectory using minimal jerk quintic polynomial with adjustable apex height

Libraries Used

Physics Simulation

• MuJoCo — https://github.com/google-deepmind/mujoco

Kinematics and Dynamics

• Pinocchio — https://github.com/stack-of-tasks/pinocchio

Installation and Dependencies

Linux is recommended, other OS not tested.

1. Clone the repository

git clone https://github.com/elijah-waichong-chan/go2-convex-mpc.git
cd go2-convex-mpc

2. Create a Conda environment

conda env create -f environment.yml
conda activate go2-convex-mpc

If you see import errors (e.g., ModuleNotFoundError: convex_mpc) rerun:

pip install -e .

3. Quick check

Recommended on Linux if you have pip --user packages installed:

export PYTHONNOUSERSITE=1

Run import check:

python - <<'PY'
import mujoco, pinocchio, casadi, convex_mpc
print("mujoco:", mujoco.__version__)
print("pinocchio:", pinocchio.__version__)
print("casadi:", casadi.__version__)
print("convex_mpc: OK")
PY

Run Examples

Run any demo from the repo root:

python -m examples.ex00_demo
python -m examples.ex01_trot_in_place
python -m examples.ex02_trot_forward
python -m examples.ex03_trot_sideway
python -m examples.ex04_trot_rotation

Plots

After running each example script, summary plots will be generated

The figures below are generated from running examples/ex00_demo.py:

MPC Runtime Performance

_{MPC iteration timing. Average model update time ≈ 1.03 ms, average QP solve time ≈ 1.67 ms, total MPC cycle time ≈ 2.70 ms, running comfortably within a 48 Hz real-time budget (20.8 ms).}

MPC State, Force, and Torque Logs

_{Centroidal MPC logs. Optimized ground reaction forces for all four feet, joint torques, center-of-mass position and velocity, ZYX Euler angles, and body angular velocities during a command-scheduled locomotion sequence.}

Updates

02/18/2026

• Implemented new method to discretize dynamics
• Iteration speed is 57.4% faster, or roughly 1.57x speedup
• Fixed quaternion order bug in go2_robot_data

12/24/2025

• Added URDF and MJCF model to the repo.
• Simplified installation steps — no longer need to download URDF models and the unitree_mujoco library.
• Restructured the repo into a proper Python package
• Added pyproject.toml so the project can be installed
• Added a Conda environment.yml to automate dependency setup
• Added examples/ demos

12/21/2025

• Reduced the overall controller loop from 1000 Hz → 200 Hz in preparation for real-time deployment; no observed performance degradation.
• The MPC update rate remains ~30–50 Hz, depending on gait frequency.

11/28/2025:

• Significantly faster model update and solving time per MPC iteration. Better matrix construction, implemented warm start, reduced redundant matrix update.
• Updated solve time plot style
• Updated motion demo in testMPC.py

11/26/2025:

• The controller is capable of full 2D motion and yaw rotation.
• The QP solve time for each MPC iteration are currently not capable of real-time control yet. This will be address in future updates with restructuring of the QP and more efficient matrix update.
• To adjust the cost matrix, go to centroidal_mpc.py
• To adjust the gait frequency and duty cycle, go to test_MPC.py
• To adjust the friction coefficient, go to centroidal_mpc.py, remember to change MuJoCo setting too.
• To adjust swing leg trajectory height, go to gait.py
• To adjust gait(phase offset), go to gait.py
• To adjust the desired motion, go to Trajectory Reference Setting in test_MPC.py
• To run the simulation and see the plotted results, run test_MPC.py