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<li><a href="publications/constrainedABA"> Constrained Articulated Body Algorithms (IEEE T-RO 2024) </a></li>
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<li><a href="https://hal.science/hal-04726386/"> A data-driven contact estimation method for wheeled-biped robots.</a></li>
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<li><a href="publications/pv-osimr"> Optimal complexity OSIM/Delassus algorithm. (IEEE RA-L 2024)</a></li>
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<li><a href="https://hal.science/hal-04895583/"> Constrained Articulated Body Algorithm for Closed Loop Mechanisms.</a></li>
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<li><a href="publications/lcaba"> Constrained Articulated Body Algorithm for Closed Loop Mechanisms.</a></li>
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</ul>
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</body>
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# Simple
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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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If you find [Simple](https://github.com/Simple-Robotics/Simple) 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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}
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```

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<!DOCTYPE html>
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content="Constrained Articulated Body Algorithms for Closed-Loop Mechanisms">
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Constrained Dynamics
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Differentiable Simulation
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<h1 class="title is-1 publication-title">Constrained Articulated Body Algorithms for Closed-Loop Mechanisms</h1>
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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://www.ajaysathya.com">Ajay Suresha Sathya</a><sup></sup>,</span>
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<span class="author-block">
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<a href="https://jcarpent.github.io">Justin Carpentier</a><sup></sup>,</span>
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<span class="author-block"><sup>*</sup>Equal contribution. Authors are listed in alphabetical order.</span>
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<h2 class="title is-3">Abstract</h2>
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<p>
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Efficient rigid-body dynamics algorithms are instrumental in enabling high-frequency dynamics evaluation for resource-intensive applications (e.g., model predictive control, large-scale simulation, reinforcement learning), potentially on resource-constrained hardware. Existing recursive algorithms with low computational complexity are mostly restricted to kinematic trees with external contact constraints or are sensitive to singular cases (e.g., linearly dependent constraints and kinematic singularities), severely impacting their practical usage in existing simulators. This article introduces two original low-complexity recursive algorithms, loop-constrained articulated body algorithm (LCABA) and proxBBO, based on proximal dynamics formulation for forward simulation of mechanisms with loops. These algorithms are derived from first principles using non-serial dynamic programming, depict linear complexity in practical scenarios, and are numerically robust to singular cases. They extend the existing constrained articulated body algorithm (constrainedABA) to handle internal loops and the pioneering BBO algorithm from the 1980s to singular cases. Both algorithms have been implemented by leveraging the open-source Pinocchio library, benchmarked in detail, and depict state-of-the-art performance for various robot topologies, including over 6x speed-ups compared to existing non-recursive algorithms for high degree-of-freedom systems with internal loops such as recent humanoid robots.
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<image src="./static/images/closed_loop_examples.png" alt="Closed loop mechanism examples." style="width:100%"></image>
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<h2 class="title is-3">Selected Benchmark</h2>
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<image src="./static/images/tab_timings_turbo.png" alt="Computational timings of different algorithms." style="width:100%"></image>
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This work heavily relies on the <a
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href="https://github.com/stack-of-tasks/pinocchio">Pinocchio</a> library.
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<h2 class="title">BibTeX</h2>
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<pre><code>@unpublished{sathya:hal-04895583,
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TITLE = {{Constrained Articulated Body Algorithms for Closed-Loop Mechanisms}},
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AUTHOR = {Sathya, Ajay Suresha and Carpentier, Justin},
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URL = {https://hal.science/hal-04895583},
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NOTE = {working paper or preprint},
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YEAR = {2025},
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MONTH = Jan,
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PDF = {https://hal.science/hal-04895583v1/file/LCABA_HAL.pdf},
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HAL_ID = {hal-04895583},
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HAL_VERSION = {v1},
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}
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</code></pre>
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