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

• URL: http://arxiv.org/abs/2211.16006v4
• Date: Mon, 15 May 2023 15:52:30 GMT
• Title: Lie Group Forced Variational Integrator Networks for Learning and Control of Robot Systems
• Authors: Valentin Duruisseaux, Thai Duong, Melvin Leok, Nikolay Atanasov
• Abstract summary: We introduce a new structure-preserving deep learning architecture capable of learning controlled Lagrangian or Hamiltonian dynamics on Lie groups. LieFVINs preserve both the Lie group structure on which the dynamics evolve and the symplectic structure underlying the Hamiltonian or Lagrangian systems of interest.
• Score: 14.748599534387688
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

Related papers

• ConCerNet: A Contrastive Learning Based Framework for Automated Conservation Law Discovery and Trustworthy Dynamical System Prediction [82.81767856234956]
  This paper proposes a new learning framework named ConCerNet to improve the trustworthiness of the DNN based dynamics modeling. We show that our method consistently outperforms the baseline neural networks in both coordinate error and conservation metrics.
  arXiv  Detail & Related papers  (2023-02-11T21:07:30Z)
• Physics-Inspired Temporal Learning of Quadrotor Dynamics for Accurate Model Predictive Trajectory Tracking [76.27433308688592]
  Accurately modeling quadrotor's system dynamics is critical for guaranteeing agile, safe, and stable navigation. We present a novel Physics-Inspired Temporal Convolutional Network (PI-TCN) approach to learning quadrotor's system dynamics purely from robot experience. Our approach combines the expressive power of sparse temporal convolutions and dense feed-forward connections to make accurate system predictions.
  arXiv  Detail & Related papers  (2022-06-07T13:51:35Z)
• Gradient-Based Trajectory Optimization With Learned Dynamics [80.41791191022139]
  We use machine learning techniques to learn a differentiable dynamics model of the system from data. We show that a neural network can model highly nonlinear behaviors accurately for large time horizons. In our hardware experiments, we demonstrate that our learned model can represent complex dynamics for both the Spot and Radio-controlled (RC) car.
  arXiv  Detail & Related papers  (2022-04-09T22:07:34Z)
• Neural Networks with Physics-Informed Architectures and Constraints for Dynamical Systems Modeling [19.399031618628864]
  We develop a framework to learn dynamics models from trajectory data. We place constraints on the values of the outputs and the internal states of the model. We experimentally demonstrate the benefits of the proposed approach on a variety of dynamical systems.
  arXiv  Detail & Related papers  (2021-09-14T02:47:51Z)
• Multi-Robot Deep Reinforcement Learning for Mobile Navigation [82.62621210336881]
  We propose a deep reinforcement learning algorithm with hierarchically integrated models (HInt) At training time, HInt learns separate perception and dynamics models, and at test time, HInt integrates the two models in a hierarchical manner and plans actions with the integrated model. Our mobile navigation experiments show that HInt outperforms conventional hierarchical policies and single-source approaches.
  arXiv  Detail & Related papers  (2021-06-24T19:07:40Z)
• Hamiltonian-based Neural ODE Networks on the SE(3) Manifold For Dynamics Learning and Control [15.26733033527393]
  We use machine learning techniques to approximate the robot dynamics over a training set of state-control trajectories. We develop energy shaping and damping injection control for the learned, potentially under-actuated SE(3) Hamiltonian dynamics.
  arXiv  Detail & Related papers  (2021-06-24T06:13:20Z)
• GEM: Group Enhanced Model for Learning Dynamical Control Systems [78.56159072162103]
  We build effective dynamical models that are amenable to sample-based learning. We show that learning the dynamics on a Lie algebra vector space is more effective than learning a direct state transition model. This work sheds light on a connection between learning of dynamics and Lie group properties, which opens doors for new research directions.
  arXiv  Detail & Related papers  (2021-04-07T01:08:18Z)
• Neural Dynamic Policies for End-to-End Sensorimotor Learning [51.24542903398335]
  The current dominant paradigm in sensorimotor control, whether imitation or reinforcement learning, is to train policies directly in raw action spaces. We propose Neural Dynamic Policies (NDPs) that make predictions in trajectory distribution space. NDPs outperform the prior state-of-the-art in terms of either efficiency or performance across several robotic control tasks.
  arXiv  Detail & Related papers  (2020-12-04T18:59:32Z)
• Encoding Physical Constraints in Differentiable Newton-Euler Algorithm [22.882483860087948]
  In this work, we incorporate physical constraints in the learning by adding structure to the learned parameters. We evaluate our method on real-time inverse dynamics control tasks on a 7 degree of freedom robot arm.
  arXiv  Detail & Related papers  (2020-01-24T02:08:09Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.