Multiobjective Trajectory Optimization and Adaptive Backstepping Control for Rubber Unstacking Robot Based on RFWNN Method

<table class="table-group" id="tab3"><tr><td><table class="table"><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr class="thead"><td class="align_left" rowspan="2">NMSE (×10<sup>−3</sup>)</td><td class="align_center" colspan="3">Case  1 (rad)</td><td class="align_center" colspan="3">Case  2 (rad)</td></tr><tr class="thead"><td class="align_center">Joint 1</td><td class="align_center">Joint 2</td><td class="align_center">Joint 3</td><td class="align_center">Joint 1</td><td class="align_center">Joint 2</td><td class="align_center">Joint 3</td></tr><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr><td class="align_left">PID</td><td class="align_center">0.842</td><td class="align_center">4.387</td><td class="align_center">5.224</td><td class="align_center">2.517</td><td class="align_center">7.848</td><td class="align_center">6.042</td></tr><tr><td class="align_left">PD synchronic</td><td class="align_center">0.955</td><td class="align_center">2.282</td><td class="align_center">2.897</td><td class="align_center">1.338</td><td class="align_center">3.635</td><td class="align_center">4.055</td></tr><tr><td class="align_left">Adaptive backstepping</td><td class="align_center">0.225</td><td class="align_center">1.512</td><td class="align_center">2.199</td><td class="align_center">0.301</td><td class="align_center">2.167</td><td class="align_center">2.552</td></tr><tr class="table-tr"><td colspan="7"><hr class="tbody-hr"/></td></tr></table></td></tr><tr class="table-fn"><td><svg height="22.7523pt" id="M287" style="vertical-align:-6.7393pt" version="1.1" viewbox="-0.0498162 -16.013 189.067 22.7523" width="189.067pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M719 650H483V622C553 619 576 606 581 560C585 532 588 487 588 394V148H585L167 650H20V622C67 618 88 610 109 585C127 562 129 557 129 484V264C129 173 126 124 123 93C118 44 92 31 35 28V0H272V28C204 32 181 44 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NMSE comparison of each joint in different control strategies.

Mathematical Problems in Engineering

tab3

Table 3

Table 3: Multiobjective Trajectory Optimization and Adaptive Backstepping Control for Rubber Unstacking Robot Based on RFWNN Method 