MPC Locomotion Control of the Unitree Go2 Quadruped Robot in MuJoCo

This repository implements a full Convex Model Predictive Controller (MPC) for the Unitree Go2 quadruped robot, including contact-force optimization, centroidal dynamics, and MuJoCo simulation.

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

*This repo is still under development and in early stage. Breaking changes are expected. File structure may change without notice.

Check "Updates" section below for latest updates.

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🐾 Introduction

This repository contains a full implementation of a Convex Model Predictive Controller (MPC) for the Unitree Go2 quadruped robot in MuJoCo simulation.

The controller is designed following the methodology described in the MIT 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.

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⚡ Locomotion Capabilities

The controller achieves the following performance in MuJoCo simulation using the convex MPC + leg controller pipeline:

🏃 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

🔄 Rotational Motion

• Yaw rotational speed: up to 4.0 rad/s

🐾 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 (1000 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 (1000 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

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🔧 Libraries Used

• MuJoCo — fast, stable physics simulation used for testing locomotion, foot contacts, and dynamic behaviors.

• Pinocchio — efficient kinematics and dynamics library for:

  • forward kinematics
  • Jacobians
  • frame placements
  • dynamics terms (M, C, g)

• unitree_mujoco — Unitree’s MuJoCo asset + URDF package https://github.com/unitreerobotics/unitree_mujoco

Together, these libraries form the computational backbone of the control and simulation environment.

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Installation and Dependencies

1. Clone the repository

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

2. Create a Conda environment

conda create -n go2 python=3.10.15 -y
conda activate go2

3. Download & copy Unitree MuJoCo assets into the repo

This project depends on the official Unitree MuJoCo models to run simulation.

git clone https://github.com/unitreerobotics/unitree_mujoco.git
cp -r unitree_mujoco ./third_party/unitree_mujoco

Your repo structure should now look like:

convex-mpc-unitree-go2/
└── third_party/
    └── unitree_mujoco/

Then update the GO2 foot friction in the MuJoCo model:

1.Open:

third_party/unitree_mujoco/unitree_robots_go2/go2.xml

2. Go to line 33 (the contact/geom friction definition for the feet) and change it to:

friction="0.8 0.02 0.01"/>

4. Download & copy Unitree GO2 URDF into the repo

The Pinocchio model requires the official GO2 URDF and its meshes.
Unitree provides them as a downloadable ZIP archive.

Download the GO2 URDF package:

wget https://oss-global-cdn.unitree.com/static/Go2_URDF.zip
unzip Go2_URDF.zip

Copy the GO2 URDF into the project:

cp -r Go2_URDF/go2_description ./third_party/unitree_go2_description

Your directory structure should now include:

convex-mpc-unitree-go2/
└── third_party/
    ├── unitree_mujoco/
    └── unitree_go2_description/

5. Install MuJoCo

MuJoCo 3.2.7, instruction to be added.

6. Install Pinocchio

Pinocchio is required for kinematics, dynamics, and centroidal model computations.

Install via conda:

conda install pinocchio -c conda-forge

7. Install CasAdi

CasADi is used for building and solving the MPC optimization problems.

Install via conda:

conda install casadi -c conda-forge

🐍 Version Recommendation

• Python: 3.10.15
• CasADi: 3.6.7
• NumPy: 1.26.4
• SciPy: 1.15.2
• Matplotlib: 3.8.4
• Pinocchio: 3.6.0
• MuJuCo: 3.2.7

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Updates

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