Kinematics estimation of straddled movements on high bar from a limited number of skin markers using a chain model

To reduce the effects of skin movement artefacts and apparent joint dislocations in the kinematics of whole body movement derived from marker locations, global optimisation procedures with a chain model have been developed. These procedures can also be used to reduce the number of markers when self-occlusions are hard to avoid. This paper assesses the kinematics precision of three marker sets: 16, 11 and 7 markers, for movements on high bar with straddled piked posture. A three-dimensional person-specific chain model was defined with 9 parameters and 12 degrees of freedom and an iterative procedure optimised the gymnast posture for each frame of the three marker sets. The time histories of joint angles obtained from the reduced marker sets were compared with those from the 16 marker set by means of a root mean square difference measure. Occlusions of medial markers fixed on the lower limb occurred when the legs were together and the pelvis markers disappeared primarily during the piked posture. Despite these occlusions, reconstruction was possible with 16, 11 and 7 markers. The time histories of joint angles were similar; the main differences were for the thigh mediolateral rotation and the knee flexion because the knee was close to full extension. When five markers were removed, the average angles difference was about 3◦. This difference increased to 9◦ for the seven marker set. It is concluded that kinematics of sports movement can be reconstructed using a chain model and a global optimisation procedure for a reduced number of markers

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 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

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