Nonholonomic Hybrid Zero Dynamics for the Stabilization of Periodic Orbits: Application to Underactuated Robotic Walking
Nonholonomic Hybrid Zero Dynamics for the Stabilization of Periodic Orbits: Application to Underactuated Robotic Walking
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DOI：
10.1109/tcst.2019.2947874
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发表时间：
2020-11-01
影响因子：
4.8
通讯作者：
Ames, Aaron D.
中科院分区：
文献类型：
--
作者：
Akbari Hamed, Kaveh;Ames, Aaron D.
本简介讨论了与相对一阶和二阶非完整输出相关的零动力学，以实现双足运动混合模型的给定周期轨道的指数稳定性。构造零动力学流形以包含轨道，同时在连续和离散时间动力学下保持不变。相关的限制动态称为混合零动态 (HZD)。 HZD 的先前结果主要依赖于完整输出的输入输出线性化，被称为完整 HZD (H-HZD)。本简介介绍了与非完整输出函数（称为非完整 HZD (NH-HZD)）相关的 HZD 降阶表达式。本简介系统地综合了 NH-HZD 控制器，以基于降阶稳定性分析来稳定周期轨道。提出了 H-HZD 和 NH-HZD 的综合研究。结果表明，NH-HZD 可以稳定传统 H-HZD 无法稳定的更广泛的步行步态。最终通过数值模拟在双足机器人的混合模型上说明了分析结果的力量。
This brief addresses zero dynamics associated with relative degree one and two nonholonomic outputs for exponential stabilization of given periodic orbits for hybrid models of bipedal locomotion. Zero dynamics manifolds are constructed to contain the orbit while being invariant under both the continuous- and discrete-time dynamics. The associated restriction dynamics are termed the hybrid zero dynamics (HZD). Prior results on the HZD have mainly relied on input-output linearization of holonomic outputs and are referred to as holonomic HZD (H-HZD). This brief presents reduced-order expressions for the HZD associated with nonholonomic output functions referred to as nonholonomic HZD (NH-HZD). This brief systematically synthesizes NH-HZD controllers to stabilize periodic orbits based on a reduced-order stability analysis. A comprehensive study of H-HZD and NH-HZD is presented. It is shown that NH-HZD can stabilize a broader range of walking gaits that are not stabilizable through traditional H-HZD. The power of the analytical results is finally illustrated on a hybrid model of a bipedal robot through numerical simulations.