In this article, we present a new controller for stable and robust walking control of ATRIAS, an underactuated bipedal robot designed based on the spring-loaded inverted pendulum (SLIP) model. We propose a forced-oscillation scheme for control of vertical motion, which we prove to be stable and contractive. Moreover, we prove that, through some mild assumptions, the dynamics of the system can be written in a hierarchical form that decouples the stability analyses of the horizontal and vertical directions. We leverage these properties to find a stabilizing class of functions for foot placement. The torso control is also proved to be decoupled using singular perturbation theory and is stabilized through a feedback linearization controller. We also take advantage of the proposed framework’s flexibility and extend it to include a new reflex-based uneven-terrain walking control scheme. We test the controller for various desired walking speeds (0 to 2.5 m/s), for stepping up and down unexpected obstacles (15 cm), and for high-speed walking on a random uneven terrain (up to 10 cm of step-ups and step-downs and up to 1.8 m/s). The results show successful performance of the controller and its stability and robustness against various perturbations.

中文翻译：

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三个维度的 ATRIAS 控制：作为强迫振荡问题的步行

在本文中，我们提出了一种新的控制器，可用于 ATRIAS 的稳定和稳健的步行控制，ATRIAS 是一种基于弹簧加载倒立摆 (SLIP) 模型设计的欠驱动双足机器人。我们提出了一种控制垂直运动的强制振荡方案，我们证明它是稳定和收缩的。此外，我们证明，通过一些温和的假设，系统的动力学可以写成分层形式，将水平和垂直方向的稳定性分析解耦。我们利用这些特性来寻找稳定的足部放置功能。躯干控制也被证明是使用奇异扰动理论解耦的，并通过反馈线性化控制器稳定。我们还利用所提出框架的灵活性并将其扩展为包括新的基于反射的不平坦地形行走控制方案。我们测试控制器的各种所需步行速度（0 到 2.5 m/s）、上下意外障碍物（15 厘米）以及在随机不平坦地形上的高速步行（最多 10 厘米的台阶）和降压和高达 1.8 m/s）。结果表明控制器的成功性能及其对各种扰动的稳定性和鲁棒性。