  This paper presents a systematic approach to exponentially stabilize the
periodic orbits of multi-domain hybrid systems arising from 3D bipedal walking.
Firstly, the method of Poincare sections is extended to the hybrid systems with
multiple domains. Then, based on the properties of the Poincare maps, a
continuous piecewise feedback control strategy is presented, and three methods
are furthermore given to design the controller parameters based on the
developed theorems. By those design methods, the controller parameters in each
continuous phase can be designed independently, which allows the strategy to be
applied to hybrid systems with multiple domains. Finally, the proposed strategy
is illustrated by a simulation example. To show that the proposed strategy is
not limited to bipedal robots with left-right symmetry property which is
assumed in some previous works, an underactuated 3D bipedal robot with
asymmetric walking gait is considered.
