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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.
