Entrainment of central pattern generators to natural oscillations of collocated mechanical systems

Rhythmic movements during animal locomotion are controlled by the neuronal circuits called central pattern generators (CPGs). The intrinsic frequency of a CPG in isolation is often different from that of observed movements, but appears to entrain to a natural mode of body oscillation through sensory feedback to achieve efficient locomotion. The objective of this paper is to reveal the feedback control mechanism underlying the entrainment of CPGs. Motivated by musculo-skeletal biomechanics, we consider the class of mechanical systems for which actuators, sensors, springs and dampers, are all collocated. Our main result provides a condition under which a CPG-based controller approximately achieves a selected mode of natural oscillation with a bound on the entrainment error.