Embodying Rather Than Encoding: Undulation with Binary Input

Undulation is the most common gait generated by legless creatures, which enables their robust and efficient locomotion in various environments. Such advantages inspired the control design of many kinds of locomotion robots. Despite their technical details, most of them realize the undulation gait via tracking predetermined trajectories called serpenoid curves, which are a group of sinusoidal waveforms with specified phase differences. This technique, however, sounds quite redundant in terms of sensing and control. Here, we investigate the research question: whether the sinusoidal waveform is necessary to be encoded in the control signal to make the whole body an "Sshape"? We use a 4-link rigid body dynamics model as a simple example, by which numerical simulations are conducted. Together with theoretical analysis, we show that undulation gait emerges naturally based on embodied position controller and filter, where binary actuation torques are required only. Our results not only discover locomotion mechanisms for significantly reducing the sensing and control requirement of generating artificial undulation gait, but also provide additional understandings for biological systems from the mechanical engineering point of view.