Synthesis of controllers for exact entrainment to natural oscillation

For a biologically inspired mechanical system consisting of multiple segments, its natural oscillation is defined as a periodic body movement pattern conforming to the dynamics inherent to the body-environment interaction, leading to an effective locomotion of the system. In the literature, a central pattern generator based controller has been designed to approximately achieve entrainment to a natural oscillation. This paper further refines the previous result by proposing a controller that achieves exact entrainment, as well as a rigorous stability analysis which leads to a complete solution to the problem of entrainment to natural oscillation.