Publications

2026

1. arXiv

   CaLiSym: Learning Symplectic Dynamics of Real-World Systems through Structured Canonical Lifts

   Aristotelis Papatheodorou^*, Pranav Vaidhyanathan^*, Natalia Ares, Ioannis Havoutis, and Gerard J. Milburn

   arXiv preprint arXiv:2607.06824, 2026

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   Physics-informed learning promises data-efficient and stable dynamics prediction, yet its strongest geometric guarantees have largely remained confined to closed conservative systems. This excludes robotic systems of interest, where actuation, dissipation, and constraints exchange energy and momentum with the environment. We introduce CaLiSym, a lightweight framework that extends symplectic learning to such systems by changing where the geometric prior is imposed. Rather than enforcing symplecticity on the measured state, CaLiSym embeds the state and its ports into a lifted phase space, where the dynamics evolve through a symplectic map. The lift is explicit and algebraic, requiring neither recurrent latent states, transformer decoders, implicit optimization, nor inference-time numerical integration. We instantiate the framework with SympNet predictors and introduce GRB-SympNet, a B-spline variant combining approximation with exact symplectic structure. Experiments on a controlled dissipative double pendulum, a real-world quadrotor, and a contact-constrained real-world quadruped demonstrate the lowest out-of-distribution autoregressive rollout error across systems, improving by up to 69.5% while using fewer parameters and up to 85x fewer floating-point operations per step than sequence-model baselines. The lifted dynamics preserve the symplectic form to numerical precision, extending symplectic learning beyond conservative mechanics toward real-world robotics.

   @article{papatheodorou2026calisym,
     title = {CaLiSym: Learning Symplectic Dynamics of Real-World Systems through Structured Canonical Lifts},
     author = {Papatheodorou, Aristotelis and Vaidhyanathan, Pranav and Ares, Natalia and Havoutis, Ioannis and Milburn, Gerard J.},
     journal = {arXiv preprint arXiv:2607.06824},
     year = {2026},
   }

2. arXiv

   Elastic ODYN: Differentiable Optimization for Infeasible Control and Learning in Robotics

   Aristotelis Papatheodorou, Jose Rojas, Ioannis Havoutis, and Carlos Mastalli

   arXiv preprint arXiv:2606.16564, 2026

   Abs arXiv Bib PDF Video

   Robotic systems routinely encounter conflicting objectives, modeling errors, and degenerate contact conditions that render quadratic programs (QPs) infeasible. Yet most optimization solvers and differentiable QP layers assume feasibility, leading to numerical failures, unstable gradients, or solver breakdown when constraints cannot be simultaneously satisfied. We present Elastic ODYN, a primal-dual non-interior-point QP solver that handles infeasibility through smooth squared-\ell_2 elastic relaxations. The formulation remains well posed under ill-conditioning and degeneracy, supports warm starting, and converges to closest-to-feasible solutions, with lightweight refinement recovering physically meaningful dual variables. Building on this framework, we develop Elastic ODYNLayer, a differentiable QP layer with stable gradients under infeasibility, and Elastic OdynSQP, an SQP method that resolves inconsistent subproblems and intrinsically infeasible optimal control tasks through selective constraint elasticity. Across benchmark QPs, singular contact mechanics, differentiable parameter identification, and quadrupedal and humanoid trajectory optimization, Elastic ODYN outperforms state-of-the-art elastic QP solvers in robustness, warm-start performance, and convergence reliability, enabling optimization, simulation, control, and learning beyond standard feasibility assumptions.

   @article{papatheodorou2026elastic,
     title = {Elastic ODYN: Differentiable Optimization for Infeasible Control and Learning in Robotics},
     author = {Papatheodorou, Aristotelis and Rojas, Jose and Havoutis, Ioannis and Mastalli, Carlos},
     journal = {arXiv preprint arXiv:2606.16564},
     year = {2026},
   }

3. arXiv

   ODYN: An All-Shifted Non-Interior-Point Method for Quadratic Programming in Robotics and AI

   Jose Rojas, Aristotelis Papatheodorou, Sergi Martinez, Andrea Patrizi, Ioannis Havoutis, and Carlos Mastalli

   arXiv preprint arXiv:2602.16005, 2026

   Abs arXiv Bib PDF Video

   We introduce ODYN, a novel all-shifted primal-dual non-interior-point quadratic programming (QP) solver designed to efficiently handle challenging dense and sparse QPs. ODYN combines all-shifted nonlinear complementarity problem (NCP) functions with proximal method of multipliers to robustly address ill-conditioned and degenerate problems, without requiring linear independence of the constraints. It exhibits strong warm-start performance and is well suited to both general-purpose optimization, and robotics and AI applications, including model-based control, estimation, and kernel-based learning methods. We provide an open-source implementation and benchmark ODYN on the Maros-Mészáros test set, demonstrating state-of-the-art convergence performance in small-to-high-scale problems. The results highlight ODYN’s superior warm-starting capabilities, which are critical in sequential and real-time settings common in robotics and AI. These advantages are further demonstrated by deploying ODYN as the backend of an SQP-based predictive control framework (OdynSQP), as the implicitly differentiable optimization layer for deep learning (ODYNLayer), and the optimizer of a contact-dynamics simulation (ODYNSim).

   @article{rojas2026odyn,
     title = {ODYN: An All-Shifted Non-Interior-Point Method for Quadratic Programming in Robotics and AI},
     author = {Rojas, Jose and Papatheodorou, Aristotelis and Martinez, Sergi and Patrizi, Andrea and Havoutis, Ioannis and Mastalli, Carlos},
     journal = {arXiv preprint arXiv:2602.16005},
     year = {2026},
   }

4. TMLR

   MetaSym: A Symplectic Meta-learning Framework for Physical Intelligence

   Pranav Vaidhyanathan^*, Aristotelis Papatheodorou^*, Mark Mitchison, Natalia Ares, and Ioannis Havoutis

   Transactions on Machine Learning Research, 2026

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   Scalable and generalizable physics-aware deep learning has long been considered a significant challenge with various applications across diverse domains ranging from robotics to molecular dynamics. Central to almost all physical systems are symplectic forms, the geometric backbone that underpins fundamental invariants like energy and momentum. In this work, we introduce a novel deep learning framework, MetaSym. In particular, MetaSym combines a strong symplectic inductive bias obtained from a symplectic encoder, and an autoregressive decoder with meta-attention. This principled design ensures that core physical invariants remain intact, while allowing flexible, data efficient adaptation to system heterogeneities. We benchmark MetaSym with highly varied and realistic datasets, such as a high-dimensional spring-mesh system Otness et al. (2021), an open quantum system with dissipation and measurement backaction, and robotics-inspired quadrotor dynamics. Crucially, we fine-tune and deploy MetaSym on real-world quadrotor data, demonstrating robustness to sensor noise and real-world uncertainty. Across all tasks, MetaSym achieves superior few-shot adaptation and outperforms larger state-of-the-art (SOTA) models.

   @article{vaidhyanathan2025metasym,
     title = {MetaSym: A Symplectic Meta-learning Framework for Physical Intelligence},
     author = {Vaidhyanathan, Pranav and Papatheodorou, Aristotelis and Mitchison, Mark and Ares, Natalia and Havoutis, Ioannis},
     journal = {Transactions on Machine Learning Research},
     year = {2026},
   }

2025

1. RSS Workshop

   Learning Physical Systems: Symplectification via Gauge Fixing in Dirac Structures

   Aristotelis Papatheodorou^*, Pranav Vaidhyanathan^*, Natalia Ares, and Ioannis Havoutis

   In Robotics: Science and Systems (RSS) Workshop on Equivariant Systems: Theory and Applications in State Estimation, Artificial Intelligence and Control, 2025

   Abs arXiv Bib PDF Video

   Physics-informed deep learning has achieved remarkable progress by embedding geometric priors, such as Hamiltonian symmetries and variational principles, into neural networks, enabling structure-preserving models that extrapolate with high accuracy. However, in systems with dissipation and holonomic constraints, ubiquitous in legged locomotion and multibody robotics, the canonical symplectic form becomes degenerate, undermining the very invariants that guarantee stability and long-term prediction. In this work, we tackle this foundational limitation by introducing Presymplectification Networks (PSNs), the first framework to learn the symplectification lift via Dirac structures, restoring a non-degenerate symplectic geometry by embedding constrained systems into a higher-dimensional manifold. Our architecture combines a recurrent encoder with a flow-matching objective to learn the augmented phase-space dynamics end-to-end. We then attach a lightweight Symplectic Network (SympNet) to forecast constrained trajectories while preserving energy, momentum, and constraint satisfaction. We demonstrate our method on the dynamics of the ANYmal quadruped robot, a challenging contact-rich, multibody system. To the best of our knowledge, this is the first framework that effectively bridges the gap between constrained, dissipative mechanical systems and symplectic learning, unlocking a whole new class of geometric machine learning models, grounded in first principles yet adaptable from data.

   @inproceedings{papatheodorou2025learning,
     title = {Learning Physical Systems: Symplectification via Gauge Fixing in Dirac Structures},
     author = {Papatheodorou, Aristotelis and Vaidhyanathan, Pranav and Ares, Natalia and Havoutis, Ioannis},
     booktitle = {Robotics: Science and Systems (RSS) Workshop on Equivariant Systems: Theory and Applications in State Estimation, Artificial Intelligence and Control},
     year = {2025},
   }

2. arXiv

   QuantGraph: A Receding-Horizon Quantum Graph Solver

   Pranav Vaidhyanathan^*, Aristotelis Papatheodorou^*, David Arvidsson-Shukur, Mark Mitchison, Natalia Ares, and Ioannis Havoutis

   arXiv preprint arXiv:2512.15476, 2025

   Abs arXiv Bib PDF

   Dynamic programming is a cornerstone of graph-based optimization. While effective, it scales unfavorably with problem size. In this work, we present QuantGraph, a two-stage quantum-enhanced framework that casts local and global graph-optimization problems as quantum searches over discrete trajectory spaces. The solver is designed to operate efficiently by first finding a sequence of locally optimal transitions in the graph (local stage), without considering full trajectories. The accumulated cost of these transitions acts as a threshold that prunes the search space (up to 60% reduction for certain examples). The subsequent global stage, based on this threshold, refines the solution. Both stages utilize variants of the Grover-adaptive-search algorithm. To achieve scalability and robustness, we draw on principles from control theory and embed QuantGraph’s global stage within a receding-horizon model-predictive-control scheme. This classical layer stabilizes and guides the quantum search, improving precision and reducing computational burden. In practice, the resulting closed-loop system exhibits robust behavior and lower overall complexity. Notably, for a fixed query budget, QuantGraph attains a 2x increase in control-discretization precision while still benefiting from Grover-search’s inherent quadratic speedup compared to classical methods.

   @article{vaidhyanathan2025quantgraph,
     title = {QuantGraph: A Receding-Horizon Quantum Graph Solver},
     author = {Vaidhyanathan, Pranav and Papatheodorou, Aristotelis and Arvidsson-Shukur, David and Mitchison, Mark and Ares, Natalia and Havoutis, Ioannis},
     journal = {arXiv preprint arXiv:2512.15476},
     year = {2025},
   }

2024

1. CoRL

   Gaitor: Learning a Unified Representation Across Gaits for Real-World Quadruped Locomotion

   Alexander L. Mitchell, Wolfgang Merkt, Aristotelis Papatheodorou, Ioannis Havoutis, and Ingmar Posner

   In Conference on Robot Learning, 2024

   Abs arXiv Bib PDF Video

   The current state-of-the-art in quadruped locomotion is able to produce a variety of complex motions. These methods either rely on switching between a discrete set of skills or learn a distribution across gaits using complex black-box models. Alternatively, we present Gaitor, which learns a disentangled and 2D representation across locomotion gaits. This learnt representation forms a planning space for closed-loop control delivering continuous gait transitions and perceptive terrain traversal. Gaitor’s latent space is readily interpretable and we discover that during gait transitions, novel unseen gaits emerge. The latent space is disentangled with respect to footswing heights and lengths. This means that these gait characteristics can be varied independently in the 2D latent representation. Together with a simple terrain encoding and a learnt planner operating in the latent space, Gaitor can take motion commands including desired gait type and swing characteristics all while reacting to uneven terrain. We evaluate Gaitor in both simulation and the real world on the ANYmal C platform. To the best of our knowledge, this is the first work learning a unified and interpretable latent space for multiple gaits, resulting in continuous blending between different locomotion modes on a real quadruped robot. An overview of the methods and results in this paper is found at https://youtu.be/eVFQbRyilCA.

   @inproceedings{mitchell2024gaitor,
     title = {Gaitor: Learning a Unified Representation Across Gaits for Real-World Quadruped Locomotion},
     author = {Mitchell, Alexander L. and Merkt, Wolfgang and Papatheodorou, Aristotelis and Havoutis, Ioannis and Posner, Ingmar},
     booktitle = {Conference on Robot Learning},
     year = {2024},
   }

2. IROS

   Momentum-Aware Trajectory Optimisation using Full-Centroidal Dynamics and Implicit Inverse Kinematics

   Aristotelis Papatheodorou, Wolfgang Merkt, Alexander L. Mitchell, and Ioannis Havoutis

   In 2024 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2024

   Abs DOI arXiv Bib PDF

   The current state-of-the-art gradient-based optimisation frameworks are able to produce impressive dynamic manoeuvres such as linear and rotational jumps. However, these methods, which optimise over the full rigid-body dynamics of the robot, often require precise foothold locations apriori, while real-time performance is not guaranteed without elaborate regularisation and tuning of the cost function. In contrast, we investigate the advantages of a task-space optimisation framework, with special focus on acrobatic motions. Our proposed formulation exploits the system’s high-order nonlinearities, such as the nonholonomy of the angular momentum, in order to produce feasible, high-acceleration manoeuvres. By leveraging the full-centroidal dynamics of the quadruped ANYmal C and directly optimising its footholds and contact forces, the framework is capable of producing efficient motion plans with low computational overhead. Finally, we deploy our proposed framework on the ANYmal C platform, and demonstrate its true capabilities through real-world experiments, with the successful execution of high-acceleration motions, such as linear and rotational jumps. Extensive analysis of these shows that the robot’s dynamics can be exploited to surpass its hardware limitations of having a high mass and low-torque limits.

   @inproceedings{papatheodorou2023momentum,
     title = {Momentum-Aware Trajectory Optimisation using Full-Centroidal Dynamics and Implicit Inverse Kinematics},
     author = {Papatheodorou, Aristotelis and Merkt, Wolfgang and Mitchell, Alexander L. and Havoutis, Ioannis},
     booktitle = {2024 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)},
     pages = {11940--11947},
     year = {2024},
     doi = {10.1109/IROS58592.2024.10801374},
   }

2022

1. CLAWAR

   Learning Energy-Efficient Trotting for Legged Robots

   Athanasios S. Mastrogeorgiou, Aristotelis Papatheodorou, Konstantinos Koutsoukis, and Evangelos Papadopoulos

   In International Conference on Climbing and Walking Robots and the Support Technologies for Mobile Machines, 2022

   DOI Bib Video

   @inproceedings{mastrogeorgiou2022learning,
     title = {Learning Energy-Efficient Trotting for Legged Robots},
     author = {Mastrogeorgiou, Athanasios S. and Papatheodorou, Aristotelis and Koutsoukis, Konstantinos and Papadopoulos, Evangelos},
     booktitle = {International Conference on Climbing and Walking Robots and the Support Technologies for Mobile Machines},
     pages = {204--215},
     year = {2022},
     doi = {10.1007/978-3-031-15226-9_21},
   }

2021

1. ROSCon

   Middleware Interconnecting ROS/ROS2 with the EtherCAT Protocol

   Aristotelis Papatheodorou, Athanasios S. Mastrogeorgiou, Konstantinos Machairas, Konstantinos Koutsoukis, and Evangelos Papadopoulos

   In ROSCon (ROS World), 2021

   Bib Video

   @inproceedings{papatheodorou2021middleware,
     title = {Middleware Interconnecting ROS/ROS2 with the EtherCAT Protocol},
     author = {Papatheodorou, Aristotelis and Mastrogeorgiou, Athanasios S. and Machairas, Konstantinos and Koutsoukis, Konstantinos and Papadopoulos, Evangelos},
     booktitle = {ROSCon (ROS World)},
     year = {2021},
   }

2. Design & implementation of a real-time distributed EtherCAT-based motion control system for a multi-DoF quadruped robot

   Aristotelis Papatheodorou

   National Technical University of Athens, 2021

   DOI Bib

   @mastersthesis{papatheodorou2021design,
     title = {Design \& implementation of a real-time distributed EtherCAT-based motion control system for a multi-DoF quadruped robot},
     author = {Papatheodorou, Aristotelis},
     school = {National Technical University of Athens},
     year = {2021},
     doi = {10.26240/HEAL.NTUA.21436},
   }

2020

1. ROS World

   Real-Time EtherCAT Master for ROS

   Aristotelis Papatheodorou, Athanasios S. Mastrogeorgiou, Konstantinos Machairas, Konstantinos Koutsoukis, and Evangelos Papadopoulos

   In ROS World (Lightning Talk), 2020

   Bib Video

   @inproceedings{papatheodorou2020realtime,
     title = {Real-Time EtherCAT Master for ROS},
     author = {Papatheodorou, Aristotelis and Mastrogeorgiou, Athanasios S. and Machairas, Konstantinos and Koutsoukis, Konstantinos and Papadopoulos, Evangelos},
     booktitle = {ROS World (Lightning Talk)},
     year = {2020},
   }