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letter-spacing: 0pt; font-size: 11pt;">對機器人進行動力學研宄的方法較多，其中，牛頓-歐拉法是利用運動（速度、加速 度）和力遞推建立數(shù)學模型方程，方程計算量會隨著機器人自由度的增加而急劇增加； </span><span id="tpnrxl7j" class="16" style="font-family: Georgia; letter-spacing: 0pt; font-size: 10.5pt;">Huston</span><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 11pt;">-</span><span id="tpnrxl7j" class="16" style="font-family: Georgia; letter-spacing: 0pt; font-size: 10.5pt;">Kane</span><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 11pt;">法是一種數(shù)值方法，該方法側(cè)重于矢量和標量對機器人動力學進行表達， 算法便于實現(xiàn)，但幾何意義不明確，難以理解和應用。利用李群李代數(shù)方法得到的機器 人動力學方程具有明確的幾何意義，計算復雜性低。拉格朗日法是利用系統(tǒng)能量建立數(shù) 學模型方程，屬于多體系統(tǒng)理論，當廣義坐標數(shù)很大時，方程將十分復雜</span><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 11pt; vertical-align: super;">[64]</span><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 11pt;">。在高等動 力學中，拉格朗日法是最為常用的方法，</span><span id="tpnrxl7j" class="16" style="font-family: Georgia; letter-spacing: 0pt; font-size: 10.5pt;">Delta</span><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 11pt;">機器人將采用拉格朗日法進行動力學研 宄，為了減小該方法的計算量，將對機器人的慣量矩陣進行簡化，簡化部分是該</span><span id="tpnrxl7j" class="16" style="font-family: Georgia; letter-spacing: 0pt; font-size: 10.5pt;">Delta </span><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 11pt;">機器人動力學計算中的次要量，對動力學的影響很小，簡化后的模型作為軌跡規(guī)劃中動 力學優(yōu)化的數(shù)學模型，在下一章節(jié)中，將會利用</span><span id="tpnrxl7j" class="16" style="font-family: Georgia; letter-spacing: 0pt; font-size: 10.5pt;">Delta</span><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 11pt;">機器人的上述運動學模型和該簡 化的動力學模型進行關節(jié)空間、工作空間和混合空間的軌跡規(guī)劃。</span></p> <p class="NewStyle18" style="margin-left: 0pt; text-indent: 18pt; line-height: 23.3pt;"> </p> <p class="NewStyle18" style="margin-left: 0pt; text-indent: 18pt; line-height: 23.3pt;"><span style="font-size:9.0pt;font-family:宋體;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman";mso-bidi-font-family: 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