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

Abstract

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.

Locomotor Sub-functions for Control of Assistive Wearable Robots

“…In studies on MARCO-Hopper, the motor torque was simulating either a linear leg spring (based on SLIP model) or a muscle-reflex system. For stable hopping, significant energy supply was required after mid-stance, achieved by enhancing leg stiffness (Kalveram et al, 2012 ) or by continuously applying positive force feedback (Seyfarth et al, 2007 ). In Oehlke et al ( 2016 ), we have implemented the SLIP-based stance leg control on the MARCO-Hopper-II robot to mimic human hopping in place.…”

“…In Oehlke et al ( 2016 ), we have implemented the SLIP-based stance leg control on the MARCO-Hopper-II robot to mimic human hopping in place. The virtual model control (VMC) (Pratt et al, 2001 ) and energy-management (Kalveram et al, 2012 ) were two approaches to implement this control strategy on the robot. Stable hopping with similar features to human hopping was achieved using SLIP as the template for control.…”

Information processing via physical soft body

“…If the dynamics of the reservoir involve enough nonlinearity and memory, emulating complex, nonlinear dynamical systems only requires adding a linear, static readout from the high-dimensional state space of the reservoir. A number of different implementations for reservoirs have been proposed, such as abstract dynamical systems for echo state networks 7 8 or models of neurons for liquid state machines 9 , the surface of water in a laminar state 14 , and nonlinear mass spring systems 15 16 17 18 19 . Lately, electronic and optical implementations have also been reported 20 21 22 23 .…”

The Benefit of Combining Neuronal Feedback and Feed-Forward Control for Robustness in Step Down Perturbations of Simulated Human Walking Depends on the Muscle Function

“…One key function of these muscles is to counteract the gravitational force and reversing the body's vertical motion in stance. Although, overall, legs behave similar to elastic springs in steady running and walking (Blickhan, 1989 ; McMahon and Cheng, 1990 ; Geyer et al, 2006 ; Lipfert, 2010 ), a drop in ground level results in an increased impact velocity and additional kinetic energy (Müller and Blickhan, 2010 , e.g., in running) that has to be dissipated or redirected by the muscles in the leg (Kalveram et al, 2012 ). As demonstrated for hopping in section 2.1), a feed-forward control for an anti-gravity muscle can ensure a rising stimulation in anticipation of a larger impact due to the drop in ground level.…”