Inelastic collision between oscillatory robots drive collective synchronization

Movement in biology and robotics arises from oscillatory motions of appendages and bodies. When groups of organisms and robots move in close proximity they may collide with each other yet the influence of collisions on collective oscillatory dynamics are unknown. We study a representative colliding oscillatory system: pairwise interactions between two robots oscillating as phase oscillators. We vary the separation distance between robots to study how proximity affects their phase dynamics. We observe three behaviors in colliding oscillators: 1) in-phase synchronization at close separation, 2) compatible oscillations in which a stationary phase mismatch persists when at intermediate separation, and 3) anti-phase synchronization which leads to repeated high-impact collisions at large separation. We develop a phase-oscillator model and calculate the stability of these behaviors dependent on the instantaneous phase difference. To understand how contact interactions influence oscillatory dynamics of larger groups of animals or robots we study an oscillator lattice with contact interactions as a function of density. At high density the group synchronizes with long range phase correlation however at lower densities the system enters an asynchronous state with continuous collisions.