Resonant hopping of a robot controlled by an artificial neural oscillator

The bouncing gaits of terrestrial animals (hopping, running, trotting) can be modeled as a hybrid dynamic system, with spring-mass dynamics during stance and ballistic motion during the aerial phase. We used a simple hopping robot controlled by an artificial neural oscillator to test the ability of the neural oscillator to adaptively drive this hybrid dynamic system. The robot had a single joint, actuated by an artificial pneumatic muscle in series with a tendon spring. We examined how the oscillator-robot system responded to variation in two neural control parameters: descending neural drive and neuromuscular gain. We also tested the ability of the oscillator-robot system to adapt to variations in mechanical properties by changing the series and parallel spring stiffnesses. Across a 100-fold variation in both supraspinal gain and muscle gain, hopping frequency changed by less than 10%. The neural oscillator consistently drove the system at the resonant half-period for the stance phase, and adapted to a new resonant half-period when the muscle series and parallel stiffnesses were altered. Passive cycling of elastic energy in the tendon accounted for 70-79% of the mechanical work done during each hop cycle. Our results demonstrate that hopping dynamics were largely determined by the intrinsic properties of the mechanical system, not the specific choice of neural oscillator parameters. The findings provide the first evidence that an artificial neural oscillator will drive a hybrid dynamic system at partial resonance.