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

Nikolay Atanasov, Valentin Duruisseaux, Thai Duong, Melvin Leok

Publication date: 29 November 2022

Abstract: 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.

Has companion code repository: https://github.com/thaipduong/LieFVIN

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Robot dynamics and control of rigid bodies (70E60) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Artificial intelligence for robotics (68T40) Symplectic and canonical mappings (37J11)

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