Constrained Differential Dynamic Programming (CDDP) solver in C++

This repository contains a C++ implementation of constrained differential dynamic programming (CDDP) and related solvers for trajectory optimization and model predictive control.

Overview

This is an optimal control solver library using constrained differential dynamic programming (CDDP) written in C++. This library is particularly useful for mobile robot trajectory optimization and model predictive control (MPC).

The CDDP library solves problems in the form:

$$ \min_{\mathbf{U}} J(\mathbf{x}_0, \mathbf{U}) = \phi(\mathbf{x}_N) + \sum \ell(\mathbf{x}_k,\mathbf{u}_k) $$

$$ \mathrm{s.t.~} \mathbf{x}_{k+1} = \mathbf{f}(\mathbf{x}_k,\mathbf{u}_k) $$

$$ \quad \mathbf{g}(\mathbf{x}_k,\mathbf{u})_k\leq 0 $$

$$ \quad \mathbf{h}(\mathbf{x}_N)=0,;\mathbf{g}_N(\mathbf{x}_N)\leq 0 $$

$$ \quad {\mathbf{x}}_{0} = \mathbf{x}{(t_0)} $$

$$ \quad k = 0,1,\cdots N-1 $$

For interior-point solves, IPDDP supports path inequalities, terminal equalities, terminal inequalities, and mixed path/terminal constrained problems with warm-started multiplier and slack state. In the C++ API, terminal constraints are attached with CDDP::addTerminalConstraint(...) and should use the built-in TerminalEqualityConstraint or TerminalInequalityConstraint classes.

Examples

The maintained example surface is now split:

• a small C++ reference set in examples/, built when CDDP_CPP_BUILD_EXAMPLES=ON
• the Python portfolio for plotting, animation, and notebook workflows

The kept C++ examples are:

• cddp_pendulum.cpp
• cddp_cartpole.cpp
• cddp_unicycle.cpp
• cddp_quadrotor_point.cpp
• cddp_manipulator.cpp

The wider historical C++ example inventory has been removed to keep the example surface focused. The kept C++ examples are intentionally minimal and do not depend on visualization libraries.

Python Portfolio

The Python bindings now ship with a small animation-focused portfolio built on top of the same solver models used by the C++ examples:

source .venv/bin/activate
python examples/python_portfolio.py --demo all

This generates GIFs under docs/assets/python_portfolio/ for:

• pendulum swing-up
• cart-pole swing-up
• unicycle obstacle avoidance
• full-lap MPCC racing line tracking

See docs/python_portfolio.md for the gallery and regeneration command.

Pendulum swing-up:

Cart-pole swing-up:

Unicycle obstacle avoidance:

MPCC racing line tracking:

The MPCC portfolio example is a lightweight kinematic contouring-control demo. Its vendored track data in examples/data/ is derived from the alexliniger/MPCC project.

The portfolio currently emphasizes animated path-constrained examples. The terminal-constraint cases added to IPDDP are covered by the regression suite rather than by a dedicated gallery animation.

Installation

Dependencies

• CMake (Build System)

sudo apt-get install cmake # For Ubuntu
brew install cmake # For macOS

• Eigen (Linear Algebra Library in CPP)

sudo apt-get install libeigen3-dev # For Ubuntu
brew install eigen # For macOS

Python package

Tagged releases publish the Python bindings to PyPI:

pip install pycddp

Prebuilt wheels are intended for CPython 3.10-3.13 on Linux, macOS, and Windows. If a wheel is not available for your platform yet, install from source using the steps below.

Building from source

git clone https://github.com/astomodynamics/cddp-cpp
cd cddp-cpp
mkdir build && cd build
cmake ..
make -j4
make test

Documentation

The project site is published through GitHub Pages at:

https://astomodynamics.github.io/cddp-cpp/

The Pages workflow builds the Markdown docs from docs/ using MkDocs.

ROS

If you want to use this library for ROS2 MPC node, please refer CDDP MPC Package. You do not need to install this library to use the package. MPC package will automatically install this library as a dependency.

References

• Y. Tassa, N. Mansard and E. Todorov, "Control-limited differential dynamic programming," 2014 IEEE International Conference on Robotics and Automation (ICRA), 2014, pp. 1168-1175, doi: <10.1109/ICRA.2014.6907001>.
• Pavlov, A., Shames, I., and Manzie, C., “Interior Point Differential Dynamic Programming,” IEEE Transactions on Control Systems Technology, Vol. 29, No. 6, 2021, pp. 2720–2727.
• Liniger, A., Domahidi, A., and Morari, M., “Optimization-based autonomous racing of 1:43 scale RC cars,” Optimal Control Applications and Methods, 2015. doi: <10.1002/oca.2123>.

Third Party Libraries

This library uses the following open-source libraries as core dependencies:

• autodiff (MIT License)

This library also uses the following open-source libraries for optional features:

• Ipopt (EPL License)
• CasADi (GPL License)

Citing

If you use this work in an academic context, please cite this repository.

License

This project is licensed under the Apache License 2.0 - see the LICENSE file for details.

Collaboration

Contributions are welcome.

Start with:

• CONTRIBUTING.md for setup, validation, and PR expectations
• CODE_OF_CONDUCT.md for community standards
• SECURITY.md for vulnerability reporting guidance

Use GitHub issues for bug reports and feature requests, and open pull requests against master.

TODO

• improve python binding ergonomics
• improve parallelization
• add simulation examples and Python visualizations
  • Quadruped robot
  • Manipulator
  • Humanoid