This work considers the periodic gait planning of a 3-D bipedal robot with two underactuated DOFs. Instead of planning a periodic gait by a traditional direct parameter optimization search, which is usually time-consuming, we present a novel modification-based periodic motion planning method, which consists of two steps. Firstly, an initial gait is obtained by relaxing the periodicity constraints in the optimization search. Then, the initial gait is modified to be a periodic one. To achieve a successful gait modification, the gait modification theory is firstly presented, and a gait modification strategy is then proposed. Finally, the presented method is illustrated on the underactuated 3-D biped, and a comparative simulation study is provided. It is shown that, compared with the traditional method, the time cost in the presented method is significantly reduced.

中文翻译：

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具有两个欠驱动自由度的 3-D 双足机器人的基于修改的周期性步态规划

这项工作考虑了具有两个欠驱动自由度的 3-D 双足机器人的周期性步态规划。我们不是通过传统的直接参数优化搜索来规划周期性步态，这通常很耗时，而是提出了一种新颖的基于修改的周期性运动规划方法，该方法由两个步骤组成。首先，通过放宽优化搜索中的周期性约束来获得初始步态。然后，初始步态被修改为周期性步态。为实现步态矫正的成功，首先提出了步态矫正理论，然后提出了步态矫正策略。最后，在欠驱动 3-D Biped 上说明了所提出的方法，并提供了比较模拟研究。结果表明，与传统方法相比，