Stability Analysis and Variational Integrator for Real-Time Formation Based on Potential Field

<table>Formation of three vehicles in obstacle environment with <svg height="17.575001" id="M273" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 65.675003 17.575001" width="65.675003" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g><g transform="matrix(.017,-0,0,-.017,56.895,12.725)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
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</svg> N/m. The out circles are safe bounds, stepping in which will cause obstacle forces.</table>

Mathematical Problems in Engineering

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Figure 5

Figure 5: Stability Analysis and Variational Integrator for Real-Time Formation Based on Potential Field 