Pareto Design of State Feedback Tracking Control of a Biped Robot via Multiobjective PSO in Comparison with Sigma Method and Genetic Algorithms: Modified NSGAII and MATLAB’s Toolbox

<table>The desired trajectory of <svg height="16.450001" id="M151" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 14.925 16.450001" width="14.925" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path d="M475 507q0 -83 -20 -172t-56 -167.5t-93.5 -129t-125.5 -50.5q-157 0 -157 227q0 78 21.5 164t59 161t96.5 123.5t126 48.5q79 0 114 -58t35 -147zM391 522q0 155 -81 155q-62 0 -111 -82.5t-73 -200.5h253q12 81 12 128zM373 346h-255q-12 -91 -12 -150q0 -72 20 -123
t63 -51q34 0 64 28.5t52.5 77t39 103t28.5 115.5z" id="x1D703"></path></g>
<g transform="matrix(.012,-0,0,-.012,8.525,16.25)"><path d="M285 378v-2q65 -13 102 -54.5t37 -97.5q0 -57 -30.5 -104.5t-74 -75t-85.5 -42t-72 -14.5q-31 0 -59.5 11t-40.5 23q-19 18 -16 36q1 16 23 33q13 10 24 0q58 -51 124 -51q55 0 88 40t33 112q0 64 -39 96.5t-88 32.5q-29 0 -64 -11l-6 29q77 25 118 57.5t41 84.5
q0 45 -26.5 69.5t-68.5 24.5q-67 0 -120 -79l-20 20l43 63q51 56 127 56h1q66 0 107 -37t41 -95q0 -42 -31 -71q-22 -23 -68 -54z" id="x33"></path></g>
</svg> and its tracking trajectory for the optimum design points A, B, and C shown in the Pareto front.</table>

The Scientific World Journal

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Figure 5

Figure 5: Pareto Design of State Feedback Tracking Control of a Biped Robot via Multiobjective PSO in Comparison with Sigma Method and Genetic Algorithms: Modified NSGAII and MATLAB’s Toolbox 

Figure 5 | Pareto Design of State Feedback Tracking Control of a Biped Robot via Multiobjective PSO in Comparison with Sigma Method and Genetic Algorithms: Modified NSGAII and MATLAB’s Toolbox 