A New Real-Time Path Planning Method Based on the Belief Space

<table>The sketch map of S-DSE at time <svg height="10.3875" id="M132" style="vertical-align:-0.11285pt" version="1.1" viewbox="0 0 5.9250002 10.3875" width="5.9250002" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.125)"><path d="M324 430l-26 -36l-112 -4l-55 -265q-13 -66 7 -66q13 0 44.5 20t50.5 40l17 -24q-38 -40 -85.5 -73.5t-87.5 -33.5q-50 0 -21 138l55 262h-80l-2 8l25 34h66l25 99l78 63l10 -9l-37 -153h128z" id="x1D461"></path></g>
</svg>: DSE points set is <svg height="23.6" id="M133" style="vertical-align:-2.26974pt" version="1.1" viewbox="0 0 23.6625 23.6" width="23.6625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,20.662)"><path d="M293 -169q-145 0 -145 128q0 35 4 106t3 104q0 17 -2 28t-10 25.5t-28 23t-51 10.5v29q31 2 51 10.5t28 23t10 25.5t2 28q0 31 -4 101t-3 104q0 132 145 132v-28q-51 -7 -67.5 -30t-16.5 -63q0 -32 6.5 -99.5t6.5 -100.5q0 -97 -83 -115v-4q83 -20 83 -117
q0 -34 -6.5 -99.5t-6.5 -96.5q0 -41 16.5 -65.5t67.5 -31.5v-28z" id="x7B"></path></g><g transform="matrix(.017,-0,0,-.017,5.961,20.662)"><path d="M452 333q0 -82 -46 -164t-116 -128q-81 -53 -158 -53q-26 0 -51 13t-37 32q-26 41 -6 134l91 431q7 40 2.5 47t-34.5 7h-33l2 25q36 4 72.5 13t58.5 15.5t28 6.5q10 0 4 -29l-91 -391h2q65 77 130 116.5t105 39.5q36 0 56.5 -32t20.5 -83zM365 316q0 76 -35 76
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<g transform="matrix(.008,-0,0,-.008,13.937,6.8)"><path d="M227 744l-123 -338l-31 15l73 368q12 3 41.5 -8t36.5 -20z" id="x2032"></path></g>
<g transform="matrix(.017,-0,0,-.017,17.7,20.662)"><path d="M283 255q-31 -2 -51 -10.5t-28 -23.5t-10 -27t-2 -30q0 -28 4 -97.5t4 -107.5q0 -128 -146 -128v28q50 7 67.5 31t17.5 63q0 33 -7 100t-7 98q0 96 84 117v4q-84 20 -84 115q0 34 7 102.5t7 98.5q0 40 -17.5 63t-67.5 30v28q28 0 50 -4t45.5 -16.5t37 -40t13.5 -68.5
q0 -37 -4 -106.5t-4 -98.5q0 -18 2 -30t10 -27t28 -23.5t51 -10.5v-29z" id="x7D"></path></g>
</svg>, safe distance set is <svg height="23.6" id="M134" style="vertical-align:-2.26974pt" version="1.1" viewbox="0 0 37.075001 23.6" width="37.075001" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,20.662)"><path d="M293 -169q-145 0 -145 128q0 35 4 106t3 104q0 17 -2 28t-10 25.5t-28 23t-51 10.5v29q31 2 51 10.5t28 23t10 25.5t2 28q0 31 -4 101t-3 104q0 132 145 132v-28q-51 -7 -67.5 -30t-16.5 -63q0 -32 6.5 -99.5t6.5 -100.5q0 -97 -83 -115v-4q83 -20 83 -117
q0 -34 -6.5 -99.5t-6.5 -96.5q0 -41 16.5 -65.5t67.5 -31.5v-28z" id="x7B"></path></g><g transform="matrix(.017,-0,0,-.017,5.961,20.662)"><path d="M766 88q-40 -45 -83.5 -72.5t-63.5 -27.5q-39 0 -16 103l49 224q15 68 -10 68q-36 0 -112.5 -78.5t-105.5 -133.5q-27 -101 -38 -165q-35 -4 -77 -18l-6 6q42 153 70 288q12 55 10 78t-19 23q-38 0 -114 -80.5t-101 -131.5q-24 -68 -41 -165q-36 -3 -76 -18l-8 6
q56 202 87 347q7 33 -3 33q-8 0 -31.5 -17.5t-41.5 -35.5l-12 28q42 45 84 72t63 27q44 0 10 -124l-20 -75h2q92 121 193 178q36 21 64 21q62 0 28 -159l-8 -37h2q50 67 103.5 112t94.5 65q39 19 62 19q60 0 23 -156l-45 -189q-9 -39 2 -39q17 0 71 49z" id="x1D45A"></path></g><g transform="matrix(.017,-0,0,-.017,19.373,20.662)"><path d="M452 333q0 -82 -46 -164t-116 -128q-81 -53 -158 -53q-26 0 -51 13t-37 32q-26 41 -6 134l91 431q7 40 2.5 47t-34.5 7h-33l2 25q36 4 72.5 13t58.5 15.5t28 6.5q10 0 4 -29l-91 -391h2q65 77 130 116.5t105 39.5q36 0 56.5 -32t20.5 -83zM365 316q0 76 -35 76
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<g transform="matrix(.008,-0,0,-.008,27.35,6.8)"><path d="M227 744l-123 -338l-31 15l73 368q12 3 41.5 -8t36.5 -20z" id="x2032"></path></g>
<g transform="matrix(.017,-0,0,-.017,31.112,20.662)"><path d="M283 255q-31 -2 -51 -10.5t-28 -23.5t-10 -27t-2 -30q0 -28 4 -97.5t4 -107.5q0 -128 -146 -128v28q50 7 67.5 31t17.5 63q0 33 -7 100t-7 98q0 96 84 117v4q-84 20 -84 115q0 34 7 102.5t7 98.5q0 40 -17.5 63t-67.5 30v28q28 0 50 -4t45.5 -16.5t37 -40t13.5 -68.5
q0 -37 -4 -106.5t-4 -98.5q0 -18 2 -30t10 -27t28 -23.5t51 -10.5v-29z" id="x7D"></path></g>
</svg>, and safe distance set is <svg height="13.3" id="M135" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 18.1625 13.3" width="18.1625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,8.863)"><path d="M445 282q0 -64 -27.5 -125t-80.5 -104q-80 -65 -168 -65q-73 0 -109.5 46.5t-36.5 116.5q0 92 46.5 163t119.5 104q66 30 108 30q67 0 107.5 -43.5t40.5 -122.5zM355 280q0 62 -26.5 94.5t-64.5 32.5q-26 0 -44 -8q-39 -18 -74 -82t-35 -163q0 -57 25.5 -90.5t70.5 -33.5
q22 0 36 6q46 20 79 89t33 155z" id="x1D45C"></path></g><g transform="matrix(.017,-0,0,-.017,8.018,8.863)"><path d="M570 304q0 -108 -87 -199q-40 -42 -94.5 -74t-105.5 -43q-41 0 -65 11l-29 -141q-9 -45 -1.5 -58t45.5 -16l26 -2l-5 -29l-241 -10l4 26q51 10 67.5 24t26.5 60l113 520q-54 -20 -89 -41l-7 26q38 28 105 53l11 49q20 25 77 58l8 -7l-17 -77q39 14 102 14q82 0 119 -36
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</svg>.</table>

Abstract and Applied Analysis

A New Real-Time Path Planning Method Based on the Belief Space

Figure 8