用机器人数据训练不稳定的特征函数，实现更精准的双足平衡控制。
Koopman DCM: Unstable Eigenfunctions as Data-driven Representations for Legged Balancing
- 将运动不稳定性转化为数据驱动的特征函数，突破传统模型限制。
- 一小时真实机器人数据训练后，行走轨迹跟踪精度显著提升。
- 可与模型预测控制结合，为复杂动作提供状态可行性约束。
在双足运动中，发散运动分量（DCM）已成为平衡控制的典型状态。它们分离了系统的不稳定动态模式，但现有方法仅适用于简化模型（如线性倒立摆）。本文揭示了如何将DCM一般化为柯普曼特征函数。不同于通常关注接近零的特征值以捕捉守恒或缓慢变化量的柯普曼分析，本研究主动寻找具有大特征值的不稳定特征对。由此得到的柯普曼-DCM是仅基于真实机器人数据训练的数据驱动可观测量。在真实双足机器人上，仅使用一小时的实机数据学习到的DCM，显著提升了参考行走模式的跟踪性能。进一步表明，学习到的DCM可与模型预测控制结合，提供基于状态的可行性约束。
原文摘要 · Abstract (English)
In legged locomotion, divergent components of motion (DCMs) have emerged as characteristic states for balance control. They isolate the unstable mode of the dynamics but, in existing formulations, apply only to reduced models such as the linear inverted pendulum. In this study, we show how DCMs can be more generally formulated as Koopman eigenfunctions. Whereas Koopman analysis typically targets eigenvalues near zero, which capture conserved or slowly varying quantities, our investigation leads us to deliberately search for unstable eigenpairs with large eigenvalues. The resulting Koopman DCMs are data-driven observables trained using only real-robot data. On a real biped, DCMs learned from one hour of robot data improve tracking of reference walking patterns. We further show how learned DCMs provide state-based viability constraints when combined with model predictive control.
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