In this paper we provide a method to generate a continuum of limit cycles using a single precomputed exponentially stable limit cycle designed within the Hybrid Zero Dynamics framework. Guarantees for existence and stability of these limit cycles are provided. We derive analytical constraints that ensure boundedness of the state under arbitrary switching among a finite set of limit cycles extracted from the continuum. These limit cycles are used for changing the speeds of an underactuated planar bipedal model while satisfying all modeling constraints such as saturation torque and coefficient of friction in a provably correct manner. A strongly connected directed graph of allowable limit cycle switches is built to obtain valid limit cycle transitions for speed changes within 0.42-0.81 m/s.
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机译：在本文中，我们提供了一种方法，可以使用在混合零动态框架内设计的单个预先计算的指数稳定的极限循环来生成限制循环的连续循环。提供了这些极限循环的存在的保证和稳定性。我们推出了分析约束，以确保在从连续体中提取的有限一组限制循环中任意切换下的状态的界限。这些极限循环用于改变欠锯平面BipeDal模型的速度，同时满足所有建模约束，例如饱和扭矩和摩擦系数以可透明的方式。构建了一个强连接的允许极限循环开关图以获得有效的限制周期转换，以便在0.42-0.81 m / s内变化。
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