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

This library is actively under construction. Please wait for proper release after starring this repo ⭐ Also, I am writing this library for practical experience with C++. Any suggestions are helpful to me.

Overview

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

The CDDP library solves problems in the form:

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

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

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

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

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

Author: Tomohiro Sasaki

Installation

Dependencies

• Eigen (Linear Algebra Library in CPP)

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

Although the library automatically finds and installs the following dependencies via FetchContent, if you do not have ones, here is how you can install on your own.

• OSQP (QP solver) and osqp-cpp (C++ Wrapper for OSQP)

conda install -c conda-forge osqp

Building

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

Basic Usage

ROS

If you want to use this library for ROS2 MPC node, please refer CDDP MPC Package

References

• Zhaoming Xie, C. Karen Liu, and Kris Hauser, "Differential Dynamic Programming with Nonlinear Constraints," 2017 IEEE International Conference on Robotics and Automation (ICRA), 2017.
• Zhamming Xie's github repository https://github.com/ZhaomingXie/CDDP

Citing

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

TODO

• add state constraint handling
• add regularization process
• add initial guess functionality based on path planner solution
• add automatic differentiation
• add nonlinear objective and constraint handling
• add simulation and its plots