Energy management that generates terrain following versus apex-preserving hopping in man and machine

While hopping, 12 subjects experienced a sudden step down of 5 or 10 cm. Results revealed that the hopping style was "terrain following". It means that the subjects pursued to keep the distance between maximum hopping height (apex) and ground profile constant. The spring-loaded inverse pendulum (SLIP) model, however, which is currently considered as template for stable legged locomotion would predict apex-preserving hopping, by which the absolute maximal hopping height is kept constant regardless of changes of the ground level. To get more insight into the physics of hopping, we outlined two concepts of energy management: "constant energy supply", by which in each bounce--regardless of perturbations--the same amount of mechanical energy is injected, and "lost energy supply", by which the mechanical energy that is going to be dissipated in the current cycle is assessed and replenished. When tested by simulations and on a robot testbed capable of hopping, constant energy supply generated stable and robust terrain following hopping, whereas lost energy supply led to something like apex-preserving hopping, which, however, lacks stability as well as robustness. Comparing simulated and machine hopping with human hopping suggests that constant energy supply has a good chance to be used by humans to generate hopping.