Energy consumption optimization and stumbling corrective response for bipedal walking gait.




When we look at the animal kingdom, we can agree our robotic technology is far from being able to cope with unpredictable environments as animals do. Animals manage to move in any environment with an astonishing fuidity. What are the key elements which allow a biological system to move in a given environment? The answer to this question is unfortunately far from being complete, and we will bring below only a little piece of the whole puzzle.

Early creatures which evolved limbs to cope with a terrestrial environment, rather than an aquatic one, needed a stable controller able to deal with unpredictable terrains. Such controllers for legged locomotion seem very complex indeed, since it is easier to make a wheel roll than a legged machine walk. And if natural wheels does not emerge from evolution, how can a controller for legs emerge despite its supposed high complexity?

Maybe the complexity operates at another level, like on the intrinsic properties of the legs. Could legs have intrinsic properties which help them to be stable? It is obvious the properties of materials used to build an arti

About this master project

In the present master project, we will reproduce this walking model with a small modi


Experiment 1

In this experiment, we are interested to see if we can obtain a stable walking gait by generating random feedback parameter sets.

We can obtain 1 good parameter set every 375 trials with a probability of 95%. Below are shown different parameter sets which give different gaits and are stable (they all do not look natural):

Parameter set 1: download movie

Parameter set 2: download movie

Parameter set 7: download movie

Parameter set 8: download movie

Parameter set 12: download movie

 Experiment 2, 3, 4, 5, 6

Here, we optimize the feedback parameter sets with two different algorithms:

  • Home made optimization algorithm

Starting from the initial parameter sets obtained in experiment 1, we optimize the energy consumption in muscles. We observe the final gaits are smoother and look more natural than in experiment 1, however the algorithm is slow.

Experiment 2, parameter set 8: download movie

Experiment 3, parameter set 6: download movie

  • PSO algorithm

Using the particle swarm optimization algorithm, we optimize again the energy consumption in muscles. This algorithm is faster than the previous one. In experiment 4 and 5, we observe the algorithm efficiently minimize the energy consumption of the walking gait, however the final results lack stability in experiment 4 and do not look natural in experiment 5.

Therefore, in experiment 6 we add a signal dependant noise (SDN) in the muscle activation. This final experiment shows that energy consumption optimization coupled with SDN converge to a smoother and more natural gait than in the previous experiments.

Experiment 4, parameter set 3: download movie

Experiment 5, parameter set 1: download movie

Experiment 5, parameter set 3: download movie

Experiment 6, parameter set 4: download movie

Stumbling corrective response

In this experiment, we implemented the stumbling corrective response. The humanoid avoid falling in 95% of the case its foot hit the obstacle (10 cm height) between 50% to 77% of the stride.

In the control experiment, we show the humanoid fall if no SCR reflexe are implemented. The figures below show exemples of early and mid stance SCR.

Control experiment: without SCR reflexe: download movie

SCR in early swing: download movie

SCR in mid-swing: download movie




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[2] H.Geyer, A.Seyfarth, R.Blickhan, Positive force feedback in bouncing gaits?, The Royal Society, 270, pp.2173-2183, 2003

[3] H.Geyer, H.Herr, A muscle-reflex model that encodes principles of legged mechanics produces human walking dynamics and muscle activities, IEEE transaction on neural systems and rehabilitation engineering, vol.18,N°3, pp263-273, 2010

[4] F.C. Anderson, M.G.Pandy, Dynamic optimization of human walking, Journal of biomechanical engineering, Vol 123, pp. 381-390, 2001.

[5] Kelvin E. Jones, Antonia D. de C. Hamilton, Daniel M. Wolpert, Sources of signal-dependent noise during isometric force production, Journal of neurophysiology, 88, pp 1533-1544, 2002.