Nullspace MPC

Nullspace MPC is a novel multi-objective control framework for explicitly handling task priorities. It demonstrates agile and smooth navigation through a narrow environment with a swerve drive vehicle.

Setup

[Option 1] Native Environment

Note: This is the recommended setup for optimal performance.

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1. Prerequisites

   • Ubuntu 20.04
   • ROS Noetic

2. Clone the repository.

   cd <path-to-your-workspace>
   git clone https://github.com/MizuhoAOKI/nullspace_mpc

3. Install packages not handled by rosdep.

   cd <path-to-your-workspace>/nullspace_mpc
   sudo make install_deps

4. Initialize rosdep, update it, and install ROS dependencies.

   cd <path-to-your-workspace>/nullspace_mpc
   sudo rosdep init # Skip if already initialized
   rosdep update
   rosdep install -y --from-paths src --ignore-src --rosdistro noetic

5. Build the project.

   cd <path-to-your-workspace>/nullspace_mpc
   make build

[Option 2] Docker Environment

GPU Accelerated Environment

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1. Prerequisites

   • Docker
     • For Ubuntu users, you can use the convenience script:

       curl -fsSL https://get.docker.com -o get-docker.sh
       sudo sh get-docker.sh

   • NVIDIA Container Toolkit
     • This is required to allow Docker containers to access the host's GPU.
   • NVIDIA GPU & Driver
     • An NVIDIA GPU and a compatible driver for the base image (nvidia/cuda:12.4.1-devel-ubuntu20.04) are required.

2. Clone the repository.

   cd <path-to-your-workspace>
   git clone https://github.com/MizuhoAOKI/nullspace_mpc

3. Build the Docker image (first-time setup).

   cd <path-to-your-workspace>/nullspace_mpc
   make setup_docker_gpu

4. Run the Docker container and start a bash session inside.

   cd <path-to-your-workspace>/nullspace_mpc
   make run_docker_gpu

5. [Inside the docker container] Build the project.

   cd ~/nullspace_mpc
   make build

CPU-Only Environment

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Warning: This setup runs entirely on the CPU. Performance is significantly lower, and on my test system it was not sufficient for stable control. Use GPU or native setup whenever possible.

1. Prerequisites

   • Docker
     • For Ubuntu users:

       curl -fsSL https://get.docker.com -o get-docker.sh
       sudo sh get-docker.sh

2. Clone the repository.

   cd <path-to-your-workspace>
   git clone https://github.com/MizuhoAOKI/nullspace_mpc

3. Build the Docker image (first-time setup).

   cd <path-to-your-workspace>/nullspace_mpc
   make setup_docker_cpu

4. Run the Docker container and start a bash session inside.

   cd <path-to-your-workspace>/nullspace_mpc
   make run_docker_cpu

5. [Inside the docker container] Build the project.

   cd ~/nullspace_mpc
   make build

Usage

This package supports two operation modes:

1. Manual Goal Mode — you set a 2D Nav Goal in RViz and the robot navigates to it.
2. Demo (Multi-Goal) Mode — the robot automatically visits a sequence of goals defined in an agenda file.

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1) Manual Goal Mode

Set a 2D Nav Goal in RViz, and the robot will navigate to the goal.

• Nullspace MPC (Proposed)

  cd <path-to-your-workspace>/nullspace_mpc
  make navigation_nullspace_mpc

  Try this setting for reduced computational load.

  cd <path-to-your-workspace>/nullspace_mpc
  make navigation_nullspace_mpc_lite

• MPPI (Baseline)

  cd <path-to-your-workspace>/nullspace_mpc
  make navigation_mppi

2) Demo (Multi-Goal) Mode

Runs an evaluation script that automatically sends multiple goals in sequence (defined in data/eval_demo/agenda.yaml) and logs results to ./result/.

• Nullspace MPC (Proposed)

  cd <path-to-your-workspace>/nullspace_mpc
  make eval_demo_nullspace_mpc

• MPPI (Baseline)

  cd <path-to-your-workspace>/nullspace_mpc
  make eval_demo_mppi

Note

Due to the asynchronous nature of ROS simulations and the sampling-based algorithm relying on multi-threading computation, the controllers' performance can vary depending on your system environment.

Citation

If you use this software in your research, please consider citing the following papers.

Nullspace MPC is a core component of my Ph.D. dissertation, which was made publicly available on October 1, 2025. You can access the full paper via the project website.

  @phdthesis{mizuho2025phd,
    author    = {Mizuho Aoki},
    title     = {{Nonlinear Model Predictive Control for Autonomous Vehicles: Enhancement via Simplified Physics-Aware Prediction and Decomposed Optimization}},
    school    = {Nagoya University},
    year      = {2025},
    type      = {Ph.D. Dissertation},
    language  = {English},
    url       = {https://mizuhoaoki.github.io/projects/nullspace_mpc}
  }

The baseline MPPI controller is based on the following work and is available in a dedicated repository: mppi_swerve_drive_ros

@inproceedings{mizuho2024iros,
  author={Aoki, Mizuho and Honda, Kohei and Okuda, Hiroyuki and Suzuki, Tatsuya},
  booktitle={2024 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)}, 
  title={{Switching Sampling Space of Model Predictive Path-Integral Controller to Balance Efficiency and Safety in 4WIDS Vehicle Navigation}}, 
  year={2024},
  pages={3196-3203},
  doi={10.1109/IROS58592.2024.10802359}
}

License & Acknowledgements

This project is licensed under the MIT License, with the exception of its core QP solving capability, which is provided by QpSolverCollection, located in the src/third_party directory and licensed under the BSD 2-Clause License.

Special thanks to the authors of QpSolverCollection for their excellent work.