足式运动的分层控制视角：通过混合零动力学嵌入降阶模型
A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics
AI总结：
针对足式机器人降阶模型步态合成缺乏形式化保证的问题，提出分层控制框架，通过合成零动力学流形建立ROM与全阶模型混合零动力学的稳定性关联，并经仿真验证。
摘要：
降阶模型（ROMs）为足式机器人合成动态行走步态提供了有力手段。然而，该方法缺乏利用全阶模型（FOM）进行步态合成的方法（如混合零动力学）所具备的形式化保证。本文旨在通过分层控制视角统一这两类方法。具体而言，我们确立了足式运动的ROM可在全阶混合动力学上实现稳定行走的条件。为得到该结果，针对给定的ROM，我们合成一个编码ROM行为的零动力学流形——可合成控制器将FOM驱动至该曲面，从而产生混合零动力学。我们证明，ROM中的稳定周期轨道意味着FOM的混合零动力学存在输入-状态稳定周期轨道，进而FOM动力学也存在该轨道。该结果在基于线性倒立摆ROM和5连杆平面行走FOM的仿真中得到了验证。
英文摘要：
Reduced-order models (ROMs) provide a powerful means of synthesizing dynamic walking gaits on legged robots. Yet this approach lacks the formal guarantees enjoyed by methods that utilize the full-order model (FOM) for gait synthesis, e.g., hybrid zero dynamics. This paper aims to unify these approaches through a layered control perspective. In particular, we establish conditions on when a ROM of locomotion yields stable walking on the full-order hybrid dynamics. To achieve this result, given an ROM we synthesize a zero dynamics manifold encoding the behavior of the ROM -- controllers can be synthesized that drive the FOM to this surface, yielding hybrid zero dynamics. We prove that a stable periodic orbit in the ROM implies an input-to-state stable periodic orbit of the FOM's hybrid zero dynamics, and hence the FOM dynamics. This result is demonstrated in simulation on a linear inverted pendulum ROM and a 5-link planar walking FOM.
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