Robotic vehicles inspired by animal locomotion are propelled by interactive forces from the environment resulting from periodic body movements. The pattern of body oscillation (gait) can be mimicked from animals, but understanding the principles underlying the gait generation would allow for flexible and broad applications to match and go beyond the performance of the nature's design. We hypothesize that the traveling-wave oscillations, often observed in undulatory locomotion, can be characterized as a natural oscillation of the locomotion dynamics, and propose a formal definition of the natural gait for locomotion systems. We first identify the dynamics essential to undulatory locomotion, and define the mode shape of natural oscillation by the free response of an idealized system. We then use bodyenvironment resonance to define the amplitude and frequency of the oscillations. Explicit formulas for the natural gait are derived to provide insight into the mechanisms underlying undulatory locomotion. An example of leech swimming illustrates how undulatory gaits similar to those observed can be produced as the natural gait, and how they can be modulated to achieve a variety of swim speeds.

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