mlsanityData to 7 Oct 2026

Lie Group Forced Variational Integrator Networks for Learning and Control of Robot Systems

arXiv 2211.16006 ↗First posted 29 Nov 2022cs.RO cs.LG math.DScited by 7

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Abstract (arXiv)

Incorporating prior knowledge of physics laws and structural properties of dynamical systems into the design of deep learning architectures has proven to be a powerful technique for improving their computational efficiency and generalization capacity. Learning accurate models of robot dynamics is critical for safe and stable control. Autonomous mobile robots, including wheeled, aerial, and underwater vehicles, can be modeled as controlled Lagrangian or Hamiltonian rigid-body systems evolving on matrix Lie groups. In this paper, we introduce a new structure-preserving deep learning architecture, the Lie group Forced Variational Integrator Network (LieFVIN), capable of learning controlled Lagrangian or Hamiltonian dynamics on Lie groups, either from position-velocity or position-only data. By design, LieFVINs preserve both the Lie group structure on which the dynamics evolve and the symplectic structure underlying the Hamiltonian or Lagrangian systems of interest. The proposed architecture learns surrogate discrete-time flow maps allowing accurate and fast prediction without numerical-integrator, neural-ODE, or adjoint techniques, which are needed for vector fields. Furthermore, the learnt discrete-time dynamics can be utilized with computationally scalable discrete-time (optimal) control strategies.

Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). Builds on 20 of its 56 references that are in the map. First posted on arXiv 29 Nov 2022.

Builds on

20 of 56 references.

References · 20

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8 more
  1. 2019Deep Lagrangian Networks for end-to-end learning of energy-based control for under-actuated systemscited by 32
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  3. 2022Learning reversible symplectic dynamicscited by 11
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  8. 2022Time-adaptive Lagrangian Variational Integrators for Accelerated Optimization on Manifoldscited by 2

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 3; 2025: 1; 2026: 3.

7 papers.

  1. 2024Imperative Learning: A Self-supervised Neuro-Symbolic Learning Framework for Robot Autonomycited by 16
  2. 2024PhysORD: A Neuro-Symbolic Approach for Physics-infused Motion Prediction in Off-road Drivingcited by 7
  3. 2024Projected Neural Differential Equations for Learning Constrained Dynamicscited by 5
  4. 2025Mission-Aligned Learning-Informed Control of Autonomous Systems: Formulation and Foundationscited by 0
  5. 2026Structure-Preserving Gaussian Processes Via Discrete Euler-Lagrange Equationscited by 0
  6. 2026Learning Forced Multibody Dynamics on Lie Groupscited by 0
  7. 2026Learning Deterministic and Stochastic Forced Hamiltonian Systemscited by 0