Lie Group Forced Variational Integrator Networks for Learning and Control of Robot Systems
Lie Group Forced Variational Integrator Networks for Learning and Control of Robot Systems
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DOI：
10.48550/arxiv.2211.16006
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发表时间：
2022-11
期刊：
影响因子：
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通讯作者：
Valentin Duruisseaux;T. Duong;M. Leok;Nikolay A. Atanasov
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文献类型：
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作者：
Valentin Duruisseaux;T. Duong;M. Leok;Nikolay A. Atanasov
将物理定律和动力系统结构特性的先验知识引入深度学习架构的设计中，已被证明是提高其计算效率和泛化能力的强大技术。学习机器人动力学的精确模型对于安全和稳定的控制至关重要。自主移动的机器人，包括轮式、空中和水下机器人，可以建模为在矩阵李群上演化的受控拉格朗日或哈密顿刚体系统。在本文中，我们介绍了一种新的结构保持深度学习架构，李群强迫变分积分网络（LieFVIN），能够学习李群上的受控拉格朗日或哈密顿动力学，无论是从位置-速度数据还是仅从位置数据。通过设计，LieFVIN既保留了动力学演化的李群结构，又保留了感兴趣的汉密尔顿或拉格朗日系统的辛结构。所提出的架构学习代理离散时间流图，允许准确和快速的预测，而不需要数值积分器，神经ODE，或伴随技术，这是矢量场所需要的。此外，学习的离散时间动态可以与计算上可扩展的离散时间（最优）控制策略一起使用。
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.