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Merge pull request #10 from ManifoldFR/tro-proxddp
Add ProxDDP T-RO 2025 paper
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‎index.html‎

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<li><a href="publications/gjk-acceleration"> GJK++: Leveraging Acceleration Methods for Faster Collision Detection. (IEEE T-RO 2024)</a></li>
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<li><a href="publications/consensus-to-pl"> Enforcing the consensus between Trajectory Optimization and Policy Learning for precise robot control.</a></li>
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<li><a href="publications/raisim-revisited"> Reconciling RaiSim with the Maximum Dissipation Principle. (IEEE T-RO 2024)</a></li>
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<li><a href="publications/proxddp-tro-2025"> ProxDDP: Proximal Constrained Trajectory Optimization. (IEEE T-RO 2025)</a></li>
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</ul>
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</body>
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</html>

‎publications/parallel-clqr/README.md‎

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# Simple
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# Parallel constrained LQR
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This is the repository that contains source code for the RSS 2024 paper [From Compliant to Rigid Contact Simulation: a Unified and Efficient Approach](https://simple-robotics.github.io/publications/simple-contact-solver/index.html).
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This is the repository that contains source code for the RSS 2024 paper [Parallel and Proximal Constrained Linear-Quadratic Methods for Real-Time Nonlinear MPC](https://simple-robotics.github.io/publications/parallel-clqr/index.html).
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If you find [Simple](https://github.com/Simple-Robotics/Simple) to be useful for your work please cite:
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If you find the parallel solver included in [aligator](https://github.com/Simple-Robotics/aligator) to be useful for your work please cite:
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```
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@article{simplecontacts2024,
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author = {Carpentier, Justin and Le Lidec, Quentin and Montaut, Louis},
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title = {From Compliant to Rigid Contact Simulation: a Unified and Efficient Approach.},
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journal = {Robotics: Science and Systems},
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year = {2024},
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@inproceedings{jalletParallelProximalConstrained2024,
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title = {Parallel and Proximal Constrained Linear-Quadratic Methods for Real-Time Nonlinear MPC},
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booktitle = {Proceedings of Robotics: Science and Systems},
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author = {Jallet, Wilson and Dantec, Ewen and Arlaud, Etienne and Mansard, Nicolas and Carpentier, Justin},
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year = {2024},
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month = jul,
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address = {Delft, Netherlands},
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doi = {10.15607/RSS.2024.XX.002}
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}
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```

‎publications/proxddp-tro-2025/.gitignore‎

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‎publications/proxddp-tro-2025/index.html‎

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<!DOCTYPE html>
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<html>
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<head>
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<meta charset="utf-8">
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<meta name="description"
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content="Parallelized proximal constrained LQR">
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<meta name="keywords" content="Numerical optimization, Numerical optimal control, LQR, Riccati">
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<meta name="viewport" content="width=device-width, initial-scale=1">
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<title>aligator</title>
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rel="stylesheet">
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<a class="navbar-link">
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More Research
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<a class="navbar-item" href="https://ieeexplore.ieee.org/document/9981586">
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Constrained DDP: a primal-dual augmented Lagrangian approach
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</a>
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<a class="navbar-item" href="https://ieeexplore.ieee.org/document/9811647">
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Implicit differential dynamic programming
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</a>
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<a class="navbar-item" href="https://ieeexplore.ieee.org/document/10521997/">
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Condensed Semi-Implicit Dynamics for Trajectory Optimization in Soft Robotics
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</a>
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<div class="container is-max-desktop">
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<h1 class="title is-1 publication-title">PROXDDP: Proximal Constrained Trajectory Optimization</h1>
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<h2 class="subtitle is-5 is-italic">Published in IEEE Transactions on Robotics, Volume 41, 2025</h2>
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<div class="is-size-5 publication-authors">
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<span class="author-block">
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<a href="https://manifoldfr.github.io">Wilson Jallet</a><sup>1,2</sup>,
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</span>
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<span class="author-block">
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<a href="https://github.com/edantec">Antoine Bambade</a><sup>1</sup>,
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<span class="author-block">
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<a href="https://github.com/etiennear">Etienne Arlaud</a><sup>1</sup>,
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<span class="author-block">
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<a href="https://github.com/sarah-quinones">Sarah El-Kazdadi</a><sup>1</sup>,
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<span class="author-block">
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<a href="https://gepettoweb.laas.fr/index.php/Members/NicolasMansard">Nicolas Mansard</a><sup>2</sup>,
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<span class="author-block">
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<a href="https://jcarpent.github.io">Justin Carpentier</a><sup>1</sup>,
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<div class="is-size-5 publication-authors">
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<span class="author-block">
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<sup>1</sup>Willow team, INRIA and Département d'Informatique de l'École normale supérieure, Paris, France<br>
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<sup>2</sup>Gepetto team, LAAS-CNRS, 7 av. du colonel Roche, 31400 Toulouse, France
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<a href="https://github.com/Simple-Robotics/aligator"
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<span>Repository for aligator</span>
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<h2 class="title is-3">Abstract</h2>
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<p>Trajectory optimization has been a popular choice for motion generation and control in robotics for at least a decade. Several numerical approaches have exhibited the required speed to enable online computation of trajectories for real-time of various systems, including complex robots. Many of these said are based on the differential dynamic programming (DDP) algorithm—initially designed for unconstrained trajectory optimization problems— and its variants, which are relatively easy to implement and provide good runtime performance.</p>
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<p>However, several problems in robot control call for using constrained formulations (e.g., torque limits, obstacle avoidance), from which several difficulties arise when trying to adapt DDP-type methods: numerical stability, computational efficiency, and constraint satisfaction. In this article, we leverage proximal methods for constrained optimization and introduce a DDP-type method for fast, constrained trajectory optimization suited for model-predictive control (MPC) applications with easy warm-starting.</p>
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<p>Compared to earlier solvers, our approach effectively manages hard constraints without warm-start limitations and exhibits good convergence behavior. 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.</p>
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<!--/ Abstract. -->
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<h2 class="title is-3">Results</h2>
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<h3 class="title is-4">Benchmarks</h3>
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<p>
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An additional contribution of our journal paper is the inclusion of benchmarks against two other numerical solvers: IPOPT, which is a generic NLP solver often used in the OC community, and ALTRO, a tailored constrained solver.
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</p>
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<figure class="content has-text-centered">
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<img class="column is-size-2" src="./static/images/ur5_reach_iterations.svg" alt="UR5 reach, iterations">
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<img class="column is-size-2" src="./static/images/ur5_reach_perfprofile_time.svg" alt="UR5 reach, perf profile">
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<figcaption class="has-text-weight-semibold">UR5 reaching task: iterations and performance profile</figcaption>
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<img class="column" src="./static/images/ur10_ballistic_iterations.svg" alt="UR10 ballistic, iterations">
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<img class="column" src="./static/images/ur10_ballistic_perfprofile_time.svg" alt="UR10 ballistic, perf profile">
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<figcaption class="has-text-weight-semibold">UR10 ballistic task: iterations and performance profile</figcaption>
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<p>
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More details can be found in Section VIII of the paper.
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<h2 class="title is-3">Related Links</h2>
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<div class="content has-text-justified">
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This work heavily relies on the
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<a href="https://github.com/Simple-Robotics/aligator">aligator</a>
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and
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<a href="https://github.com/stack-of-tasks/pinocchio">Pinocchio</a>
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libraries, as well as the
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<a href="https://github.com/inria-paris-robotics-lab/quadruped-reactive-walking">quadruped-reactive-walking</a> framework for whole-body NMPC on Solo.
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</section>
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<section class="section" id="BibTeX">
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<div class="container is-max-desktop content">
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<h2 class="title">BibTeX</h2>
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<pre><code>@article{jalletPROXDDPProximalConstrained2025,
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title = {PROXDDP: Proximal Constrained Trajectory Optimization},
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shorttitle = {PROXDDP},
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author = {Jallet, Wilson and Bambade, Antoine and Arlaud, Etienne and {El-Kazdadi}, Sarah and Mansard, Nicolas and Carpentier, Justin},
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year = {2025},
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journal = {IEEE Transactions on Robotics},
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pages = {1--20},
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issn = {1941-0468},
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doi = {10.1109/TRO.2025.3554437},
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urldate = {2025-04-04},
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keywords = {Convergence,Heuristic algorithms,Legged Robots,Libraries,Linear systems,Minimization,Model-Predictive Control,Newton method,Optimization,Optimization and Optimal Control,Predictive control,Robots,Trajectory optimization}
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}</code></pre>
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