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This paper presents a systematic approach to exponentially stabilize theperiodic orbits of multi-domain hybrid systems arising from 3D bipedal walking.Firstly, the method of Poincare sections is extended to the hybrid systems withmultiple domains. Then, based on the properties of the Poincare maps, acontinuous piecewise feedback control strategy is presented, and three methodsare furthermore given to design the controller parameters based on thedeveloped theorems. By those design methods, the controller parameters in eachcontinuous phase can be designed independently, which allows the strategy to beapplied to hybrid systems with multiple domains. Finally, the proposed strategyis illustrated by a simulation example. To show that the proposed strategy isnot limited to bipedal robots with left-right symmetry property which isassumed in some previous works, an underactuated 3D bipedal robot withasymmetric walking gait is considered.

Exponentially Stabilizing Continuous-Time Controllers for multi-domain hybrid systems with application to 3D bipdeal walking