为高维机械系统设计了可保证稳定性的结构化降阶控制方法。
Reduced-order Control and Geometric Structure of Learned Lagrangian Latent Dynamics
- 基于黎曼几何的降阶模型，保留拉格朗日系统的物理结构。
- 理论证明了控制器在真实与仿真系统中均能稳定跟踪轨迹。
- 适合需要安全控制的软体机器人、变形体等复杂系统研究者。
基于模型的控制器依赖物理准确的动力学模型，能提供强稳定的收敛保证，但对高维机械系统（如可变形物体或软体机器人）通常不可用。尽管神经网络可近似复杂动力学，却常受限于低维系统，或因缺乏嵌入式物理结构而难以提供形式化控制保证。本文提出一种基于学习的结构保持降阶动力学的隐空间控制框架，推导出全驱动系统的降阶跟踪律，并从黎曼几何视角分析投影式模型降阶后的隐空间与投影闭环动力学。通过量化建模误差来源，导出了可解释的稳定性和收敛条件。进一步通过引入学习的执行模式，将该控制器与分析扩展至欠驱动系统。在模拟与真实系统上的实验验证了理论分析的有效性及控制器的准确性。
原文摘要 · Abstract (English)
Model-based controllers can offer strong guarantees on stability and convergence by relying on physically accurate dynamic models. However, these are rarely available for high-dimensional mechanical systems such as deformable objects or soft robots. While neural architectures can learn to approximate complex dynamics, they are either limited to low-dimensional systems or provide only limited formal control guarantees due to a lack of embedded physical structure. This paper introduces a latent control framework based on learned structure-preserving reduced-order dynamics for high-dimensional Lagrangian systems. We derive a reduced tracking law for fully actuated systems and adopt a Riemannian perspective on projection-based model-order reduction to study the resulting latent and projected closed-loop dynamics. By quantifying the sources of modeling error, we derive interpretable conditions for stability and convergence. We extend the proposed controller and analysis to underactuated systems by introducing learned actuation patterns. Experimental results on simulated and real-world systems validate our theoretical investigation and the accuracy of our controllers.
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