ABSTRACT
This chapter introduces zero dynamics and virtual constraints via two examples. The first example uses a Single-input single-output linear system with a single zero and two poles to develop the notion of zero dynamics. The second example uses a pendulum evolving in a horizontal plane to develop the notion of virtual constraints. The chapter identifies swing phase zero dynamics for a particular class of outputs that has proven useful in constructing feedback controllers for bipedal walkers. It considers the impact model into the notion of the maximal internal dynamics compatible with the output being identically zero, to obtain a zero dynamics of the complete model of the bipedal walker. The hybrid zero dynamics is a particular case of the hybrid restriction dynamics defined in, corresponding to the case that the invariant manifold arises from a set of virtual constraints. Fixed points of the Poincare return map of the hybrid zero dynamics correspond to periodic orbits of the hybrid zero dynamics.
