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‎index.html

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<li><a href="publications/loik-solver"> Low complexity differential inverse kinematics solver.</a></li>
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<li><a href="https://arxiv.org/abs/2304.06372"> Analysis of contact models in robotics.</a></li>
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<li><a href="https://hal.science/hal-04438175/"> About limitations and extensions of RaiSim simulator.</a></li>
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<li><a href="publications/constrainedABA"> Constrained Articulated Body Algorithms</a></li>
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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="https://ieeexplore.ieee.org/abstract/document/10697298"> Optimal complexity OSIM/Delassus algorithm.</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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</ul>
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</body>

‎publications/pv-osimr/README.md

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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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```

‎publications/pv-osimr/index.html

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<!DOCTYPE html>
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content="PV-OSIMr: A Lowest Order Complexity Algorithm for Computing the Delassus Matrix">
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<title>PV-OSIMr: A Lowest Order Complexity Algorithm for Computing the Delassus Matrix</title>
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Constrained Dynamics
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Differentiable Simulation
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GJK++: accelerated collision detection
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<h1 class="title is-1 publication-title">PV-OSIMr: A Lowest Order Complexity Algorithm for Computing the Delassus Matrix</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>1</sup>,</span>
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<a href="https://scholar.google.com/citations?user=ZgAnArUAAAAJ&hl">Wilm Decré</a><sup>2</sup>,</span>
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<a href="https://scholar.google.com/citations?user=X_fnO1YAAAAJ&hl">Jan Swevers</a><sup>2</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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<span class="author-block"><sup>1</sup> Willow, Inria, DI-ENS Paris, PSL University, 75006 Paris, France. </span>
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</div>
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<div class="is-size-5 publication-authors">
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<span class="author-block"> <sup>2</sup> Division of Robotics, Automation and Mechatronics, Department of Mechanical Engineering, KU
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Leuven, and FlandersMake@KULeuven, 3000 Leuven, Belgium. </span>
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<a href="https://github.com/stack-of-tasks/pinocchio/blob/4a769cbec934fe847d84722e133b821f5501d4d5/include/pinocchio/algorithm/delassus.hxx#L435"
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<h2 class="title is-3">Abstract</h2>
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<p>
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We present PV-OSIMr, an efficient algorithm for computing the Delassus matrix (also known as the inverse operational space inertia matrix) for a kinematic tree, with the lowest order computational complexity known in literature. PV-OSIMr is derived by optimizing the recently proposed PV-OSIM algorithm using the compositionality of the force and motion propagators. It has a computational complexity of $O(n+m^2)$ compared to $O(n+m^2d)$ of the PV-OSIM algorithm and $O(n+md+m^2)$ of the extended force propagator algorithm (EFPA), where $n$ is the number of joints, $m$ is the number of constraints and $d$ is the depth of the kinematic tree. Since the Delassus matrix is an $m×m$ sized matrix and its computation must consider all the n joints, PV-OSIMr's asymptotic computational complexity is optimal. We further benchmark our algorithm and find it to be often more efficient than the PV-OSIM and EFPA in practice.
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<h2 class="title is-3">Overview</h2>
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<image src="./static/images/tab_overview.png" alt="Overview computational complexity of algorithms." style="width:60%"></image>
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<section class="section" id="BibTeX">
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<h2 class="title">BibTeX</h2>
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<pre><code>@ARTICLE{sathya_pvosimr_2024,
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author={Sathya, Ajay Suresha and Decré, Wilm and Swevers, Jan},
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journal={IEEE Robotics and Automation Letters},
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title={PV-OSIMr: A Lowest Order Complexity Algorithm for Computing the Delassus Matrix},
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year={2024},
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volume={9},
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number={11},
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pages={10224-10231},
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keywords={Heuristic algorithms;Force;Kinematics;Aerospace electronics;Robot kinematics;End effectors;Computational complexity;Computational efficiency;Dynamics;multi-contact whole-body motion planning and control;whole-body motion planning and control},
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doi={10.1109/LRA.2024.3469829}}
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</code></pre>
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