Power-continuous synchronisation of oscillators: A novel, energy-free way to synchronise dynamical systems

Synchronisation is an essential part of many controlled dynamical systems, in particular in the limb motion of legged robots. In this paper we introduce a novel control strategy that allows synchronisation of two oscillators without using any external power, but by modulating the power flow between the two oscillators. We then derive a separate energy-level controller that regulates the oscillation amplitude, again without changing the system's total energy. Finally, we show that the strategy works on a realistic mechanical system, by synchronising the phase difference and apex height of two bouncing masses.