Owing to their nonlinear structures and dynamics, bipedal walking robots are commonly used as appropriate case studies for nonlinear modeling and control. In this study, the dynamics of a point-feet 4-link biped robot having asymmetric structure is studied. This asymmetry appears on the robot’s legs such that one leg of the robot does have an active knee while the other is knee-less. In this way, the style and analysis of each step depends on which leg is the stance leg. Although the stable steady state behavior of the system is purely periodic, the gait cycle does consist of two sequential steps. Since each step includes a continuous phase followed by an impact phase, hence, we need to model the system as a multiphase (4-phase) hybrid system. The main purpose of this research is to find stable gating pattern and employ appropriate controller to make sure that the gating is accomplished in an asymptotically stable manner. A combination of feedback linearization and finite-time controllers is used to control the walking posture, and the stability of the whole behavior is investigated by analysis of a one-dimensional Poincaré map. Simulation results successfully support the modeling and control approach.

中文翻译：

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非对称结构双足机器人的动态行走分析

由于其非线性结构和动力学，双足步行机器人通常用作非线性建模和控制的适当案例研究。在这项研究中，研究了具有不对称结构的点英尺四连杆双足机器人的动力学。这种不对称出现在机器人的腿上，因此机器人的一条腿确实有活动的膝盖，而另一条腿没有膝盖。这样，每一步的风格和分析就取决于哪条腿是站姿腿。尽管系统的稳定稳态行为是纯周期性的，但步态周期确实由两个连续步骤组成。由于每个步骤都包括一个连续阶段和一个冲击阶段，因此，我们需要将系统建模为多相（4 相）混合系统。本研究的主要目的是找到稳定的门控模式并采用适当的控制器来确保门控以渐近稳定的方式完成。采用反馈线性化和有限时间控制器的组合来控制步行姿势，并通过分析一维庞加莱图来研究整个行为的稳定性。仿真结果成功地支持了建模和控制方法。