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Oscillations are often observed in nature at multiple levels, and form a basis for sustained operation of various functionalities. The objective of this plenary lecture is to introduce biological principles for coordinated oscillations to the control engineering community, and to provide a tutorial overview of recent developments on the analysis and design of dynamical mechanisms for oscillations, inspired by biological control systems. A particular focus will be placed on rhythmic body movements observed in animal locomotion, controlled by neuronal circuits called central pattern generators. We will discuss what periodic body motion (or gait) achieves efficient locomotion, and how neuronal interconnections can be designed to yield a given oscillation pattern as a stable limit cycle. In a more general context, the results will contribute to understanding of the mechanisms underlying global pattern formation of multiple agents through local interactions, and form a basis for developing a distributed feedback control theory to achieve coordinated oscillations.