Necessary condition for simple oscillatory neural control of robotic yoyo

Open-loop unstable rhythmic tasks, like yoyo playing, require proper phase locking to stabilize. Given the phase-locking property of coupled oscillators and their successful application to open-loop control of rhythmic motion, we investigate their application to closed-loop control of a yoyo. In particular, we focus on pulse coupling, where the yoyo sends a feedback pulse upon reaching the bottom of the string and the onset of the oscillatory cycle is used to trigger the movement. A necessary condition for stable control is derived and applied to disqualify the simply-coupled stand-alone leaky integrate-and-fire oscillator. In contrast, an alternative circuit-level oscillator, known as a phase-locked loop, is proposed. The results are verified by numerical simulations and demonstrate that the proposed pulse-coupled oscillatory control provides a model-free control strategy that operates with an easy-to-measure low-rate feedback