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Optimal Potential Shaping on SE(3) via Neural ODEs on Lie Groups

arXiv 2401.15107 ↗First posted 25 Jan 2024math.OC cs.LGcited by 0

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Abstract (arXiv)

This work presents a novel approach for the optimization of dynamic systems on finite-dimensional Lie groups. We rephrase dynamic systems as so-called neural ordinary differential equations (neural ODEs), and formulate the optimization problem on Lie groups. A gradient descent optimization algorithm is presented to tackle the optimization numerically. Our algorithm is scalable, and applicable to any finite dimensional Lie group, including matrix Lie groups. By representing the system at the Lie algebra level, we reduce the computational cost of the gradient computation. In an extensive example, optimal potential energy shaping for control of a rigid body is treated. The optimal control problem is phrased as an optimization of a neural ODE on the Lie group SE(3), and the controller is iteratively optimized. The final controller is validated on a state-regulation task.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 19 of its 71 references that are in the map. First posted on arXiv 25 Jan 2024.

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19 of 71 references.

References · 19

  1. 2018Neural Ordinary Differential Equationscited by 3,779
  2. 2016An overview of gradient descent optimization algorithmscited by 1,033
  3. 2021Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learningcited by 371
  4. 2021How to Train Your Robot with Deep Reinforcement Learning; Lessons We've Learnedcited by 213
  5. 2020Dissecting Neural ODEscited by 153
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  7. 2020Neural Manifold Ordinary Differential Equationscited by 81
  8. 2016Deep Learning on Lie Groups for Skeleton-based Action Recognitioncited by 42
  9. 2021Hamiltonian-based Neural ODE Networks on the SE(3) Manifold For Dynamics Learning and Controlcited by 38
  10. 2020Neural Ordinary Differential Equations on Manifoldscited by 31
  11. 2021Active Learning in Robotics: A Review of Control Principlescited by 26
  12. 2023Deep Learning Symmetries and Their Lie Groups, Algebras, and Subalgebras from First Principlescited by 22
7 more
  1. 2020Machine Learning Lie Structures & Applications to Physicscited by 13
  2. 2024Port-Hamiltonian Neural ODE Networks on Lie Groups For Robot Dynamics Learning and Controlcited by 12
  3. 2021Adaptive Control of SE(3) Hamiltonian Dynamics with Learned Disturbance Featurescited by 6
  4. 2022Lie Algebraic Cost Function Design for Control on Lie Groupscited by 5
  5. 2021Optimal Energy Shaping via Neural Approximatorscited by 4
  6. 2013Geometric Nonlinear PID Control of a Quadrotor UAV on SE(3)cited by 3
  7. 2022Discovering Efficient Periodic Behaviours in Mechanical Systems via Neural Approximatorscited by 2

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