Aligator

Aligator is an efficient and versatile trajectory optimization library for robotics and beyond.

It can be used for motion generation and planning, optimal estimation, deployment of model-predictive control on complex systems, and much more.

Developing advanced, open-source, and versatile robotic software such as Aligator takes time and energy while requiring a lot of engineering support. In recognition of our commitment, we would be grateful if you would quote our papers and software in your publications, software, and research articles. Please refer to the Citation section for further details.

Features

Aligator is a C++ template library, which provides

• a modeling interface for optimal control problems, node-per-node
• a set of efficient solvers for constrained trajectory optimization
• multiple routines for factorization of linear problems arising in numerical OC
• support for the pinocchio rigid-body dynamics library and its analytical derivatives
• an interface to the Crocoddyl trajectory optimization library which can be used as an alternative frontend
• Python bindings leveraging eigenpy

Aligator provides efficient implementations of the following algorithms for (constrained) trajectory optimization:

• ProxDDP: Proximal Differentiable Dynamic Programming, detailed in this paper
• FeasibleDDP: Feasible Differentiable Dynamic Programming, detailed in this paper

Installation

From Conda

From either conda-forge or our channel.

conda install -c conda-forge aligator

From source with Pixi

To build aligator from source the easiest way is to use Pixi.

Pixi is a cross-platform package management tool for developers that will install all required dependencies in .pixi directory. It's used by our CI agent so you have the guarantee to get the right dependencies.

Run the following command to install dependencies, configure, build and test the project:

pixi run test

The project will be built in the build directory. You can run pixi shell and build the project with cmake and ninja manually.

Build from source

git clone https://github.com/Simple-Robotics/aligator --recursive
cmake -DCMAKE_INSTALL_PREFIX=your_install_folder -S . -B build/ && cd build/
cmake --build . -jNCPUS

Dependencies

• proxsuite-nlp
• Eigen3 >= 3.3.7
• Boost >= 1.71.0
• OpenMP
• fmtlib >= 10.0.0 | conda
• (optional) eigenpy>=3.4.0 | conda (Python bindings)
• (optional) Pinocchio | conda
• (optional) Crocoddyl | conda
• (optional) example-robot-data | conda (required for some examples and benchmarks)
• a C++17 compliant compiler

Python dependencies

• typed-argument-parser
• matplotlib

Notes

• For developers, add the -DCMAKE_EXPORT_COMPILE_COMMANDS=1 when working with language servers e.g. clangd.
• To use the Crocoddyl interface, add -DBUILD_CROCODDYL_COMPAT=ON
• By default, building the library will instantiate the templates for the double scalar type.
• To build against a Conda environment, activate the environment and run export CMAKE_PREFIX_PATH=$CONDA_PREFIX before running CMake and use $CONDA_PREFIX as your install folder.

Benchmarking

We recommend using Flame Graphs to evaluate performance. If you have the Rust toolchain and cargo installed, we suggest you install cargo-flamegraph. Then, you can create a flame graph with the following command:

flamegraph -o my_flamegraph.svg -- ./build/examples/example-croc-talos-arm

Citing Aligator

To cite Aligator in your academic research, please use the following bibtex entry:

@misc{aligatorweb,
  author = {Jallet, Wilson and Bambade, Antoine and El Kazdadi, Sarah and Justin, Carpentier and Nicolas, Mansard},
  title = {aligator},
  url = {https://github.com/Simple-Robotics/aligator}
}

Please also consider citing the reference paper for the ProxDDP algorithm:

@misc{jalletPROXDDPProximalConstrained2023,
  title = {{PROXDDP: Proximal Constrained Trajectory Optimization}},
  author = {Jallet, Wilson and Bambade, Antoine and Arlaud, Etienne and {El-Kazdadi}, Sarah and Mansard, Nicolas and Carpentier, Justin},
  year = {2023},
  abstract = {Trajectory optimization (TO) has proven, over the last decade, to be a versatile and effective framework for robot control. Several numerical solvers have been demonstrated to be fast enough to allow recomputing full-dynamics trajectories for various systems at control time, enabling model predictive control (MPC) of complex robots. These first implementations of MPC in robotics predominantly utilize some differential dynamic programming (DDP) variant for its computational speed and ease of use in constraint-free settings. Nevertheless, many scenarios in robotics call for adding hard constraints in TO problems (e.g., torque limits, obstacle avoidance), which existing solvers, based on DDP, often struggle to handle. Effectively addressing path constraints still poses optimization challenges (e.g., numerical stability, efficiency, accuracy of constraint satisfaction) that we propose to solve by combining advances in numerical optimization with the foundational efficiency of DDP. In this article, we leverage proximal methods for constrained optimization and introduce a DDP-like method to achieve fast, constrained trajectory optimization with an efficient warm-starting strategy particularly suited for MPC applications. Compared to earlier solvers, our approach effectively manages hard constraints without warm-start limitations and exhibits commendable convergence accuracy. Additionally, we leverage the computational efficiency of DDP, enabling real-time resolution of complex problems such as whole-body quadruped locomotion. We provide a complete implementation as part of an open-source and flexible C++ trajectory optimization library called ALIGATOR. These algorithmic contributions are validated through several trajectory planning scenarios from the robotics literature and the real-time whole-body MPC of a quadruped robot.},
  langid = {english},
  note = {https://inria.hal.science/hal-04332348v1}
}

Contributors

• Antoine Bambade (Inria): mathematics and algorithms developer
• Justin Carpentier (Inria): project instructor
• Wilson Jallet (LAAS-CNRS/Inria): main developer and manager of the project
• Sarah Kazdadi: linear algebra czar
• Quentin Le Lidec (Inria): feature developer
• Joris Vaillant (Inria): core developer
• Nicolas Mansard (LAAS-CNRS): project coordinator
• Guilhem Saurel (LAAS-CNRS): core maintainer
• Fabian Schramm (Inria): core developer
• Ludovic De Matteïs (LAAS-CNRS/Inria): feature developer
• Ewen Dantec (Inria): feature developer

Acknowledgments

The development of Aligator is actively supported by the Willow team @INRIA and the Gepetto team @LAAS-CNRS.

Associated scientific and technical publications

• E. Ménager, A. Bilger, W. Jallet, J. Carpentier, and C. Duriez, ‘Condensed semi-implicit dynamics for trajectory optimization in soft robotics’, in IEEE International Conference on Soft Robotics (RoboSoft), San Diego (CA), United States: IEEE, Apr. 2024. doi: 10.1109/RoboSoft60065.2024.10521997.
• W. Jallet, N. Mansard, and J. Carpentier, ‘Implicit Differential Dynamic Programming’, in 2022 International Conference on Robotics and Automation (ICRA), Philadelphia, United States: IEEE Robotics and Automation Society, May 2022. doi: 10.1109/ICRA46639.2022.9811647.
• W. Jallet, A. Bambade, N. Mansard, and J. Carpentier, ‘Constrained Differential Dynamic Programming: A primal-dual augmented Lagrangian approach’, in 2022 IEEE/RSJ International Conference on Intelligent Robots and Systems, Kyoto, Japan, Oct. 2022. doi: 10.1109/IROS47612.2022.9981586.
• W. Jallet, A. Bambade, N. Mansard, and J. Carpentier, ‘ProxNLP: a primal-dual augmented Lagrangian solver for nonlinear programming in Robotics and beyond’, in 6th Legged Robots Workshop, Philadelphia, Pennsylvania, United States, May 2022. Accessed: Oct. 10, 2022. [Online]. Available: https://hal.archives-ouvertes.fr/hal-03680510
• W. Jallet, A. Bambade, E. Arlaud, S. El-Kazdadi, N. Mansard, and J. Carpentier, ‘PROXDDP: Proximal Constrained Trajectory Optimization’. 2023. [Online]. Available: https://inria.hal.science/hal-04332348v1
• S. Kazdadi, J. Carpentier, and J. Ponce, ‘Equality Constrained Differential Dynamic Programming’, presented at the ICRA 2021 - IEEE International Conference on Robotics and Automation, May 2021. Accessed: Sep. 07, 2021. [Online]. Available: https://hal.inria.fr/hal-03184203
• A. Bambade, S. El-Kazdadi, A. Taylor, and J. Carpentier, ‘PROX-QP: Yet another Quadratic Programming Solver for Robotics and beyond’, in Robotics: Science and Systems XVIII, Robotics: Science and Systems Foundation, Jun. 2022. doi: 10.15607/RSS.2022.XVIII.040.
• W. Jallet, E. Dantec, E. Arlaud, N. Mansard, and J. Carpentier, ‘Parallel and Proximal Constrained Linear-Quadratic Methods for Real-Time Nonlinear MPC’, in Proceedings of Robotics: Science and Systems, Delft, Netherlands, Jul. 2024. doi: 10.15607/RSS.2024.XX.002.
• E. Dantec, W. Jallet, and J. Carpentier, ‘From centroidal to whole-body models for legged locomotion: a comparative analysis’, presented at the 2024 IEEE-RAS International Conference on Humanoid Robots, Nancy, France: IEEE, Jul. 2024. [Online]. Available: https://inria.hal.science/hal-04647996