This paper presents a combined sliding-mode control and subspace stabilization methodology for orbital stabilization of periodic trajectories in underactuated mechanical systems with one degree of underactuation. The approach starts with partial feedback linearization and stabilization. Then, transverse linearization along the reference orbit is computed, resulting in a periodic linear time-varying system with a stable subspace. Sliding-mode control drives trajectories toward this subspace. The proposed design avoids solving computationally intensive periodic LQR problems and improves robustness to matched disturbances. The methodology is validated through experiments on the Butterfly robot.

翻译：本文提出了一种结合滑模控制与子空间镇定的方法，用于具有一个欠驱动自由度的欠驱动机械系统中周期轨迹的轨道镇定。该方法首先进行部分反馈线性化与镇定，随后沿参考轨道计算横向线性化，得到一个具有稳定子空间的周期线性时变系统。滑模控制驱动轨迹趋向该子空间。所提出的设计避免了计算密集的周期LQR问题求解，并增强了对匹配扰动的鲁棒性。该方法通过在蝴蝶机器人上的实验进行了验证。