The single-step recovery predictions for 2 scenarii from [11] with and without upper-body inertia against the experimental results.

<p>The single-step recovery predictions for 2 scenarii from [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151166#pone.0151166.ref011" target="_blank">11</a>] with and without upper-body inertia against the experimental results.</p

Stride length results for multiple-step recovery scenario from [32].

<p>The 3^<i>rd</i> stride, reported by [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151166#pone.0151166.ref032" target="_blank">32</a>] but not predicted by our model, was only observed for 2 out of 28 subjects.</p

The basic principle of Model Predictive Control.

<p>At any time instant <i>t</i> the most recent mechanical system state <i>x</i>(<i>t</i>) is sampled and fed to the controller. The control is computed minimizing the cost <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151166#pone.0151166.e003" target="_blank">function 2</a> to bring the internal model to a standstill posture.The computed control vector <i>u</i>, consisting of the CoM and flywheel jerks and the future step positions, is then applied back to the mechanical system.</p

Effect of varying weight coefficients w₂ and w₃ on the resulting predicted single step length and duration for the inclination of 21.6° from vertical.

<p>Effect of varying weight coefficients w₂ and w₃ on the resulting predicted single step length and duration for the inclination of 21.6° from vertical.</p

Effect of varying weight coefficients w₄ and w₅ on the resulting predicted single step length and duration for the inclination of 21.6° from vertical.

<p>Effect of varying weight coefficients w₄ and w₅ on the resulting predicted single step length and duration for the inclination of 21.6° from vertical.</p

Model Parameters.

<p>Model Parameters.</p

Peak of flywheel torque achieved during the recovery scenarii from [6] and corresponding recovery postures at the instant of stepping.

<p>The filled area represents the flywheel rotation angle.</p

The two representations used of the human body.

<p>Left: <i>Mechanical</i> system: simple inverted pendulum + flywheel model, i.e. the CoM follows a circular arc. Right: <i>Internal</i> model: linearized inverted pendulum + flywheel model, i.e. the CoM travels at a constant height <i>h</i>.</p