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11pt;">1.3.4</span><span class="18" style="line-height: 11pt; text-indent: 0pt; font-family: 宋体; letter-spacing: 1pt; font-size: 11pt;">轨迹规划</span></p> <p class="NewStyle20" style="margin-left: 0pt; text-indent: 18pt; line-height: 23.05pt;"><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">轨迹规划是机器人运动学逆解、正解的实际工程应用，分析机器人的轨迹特点及其 应用场合，对机器人进行合理的轨迹规划是机器人运动控制的基础。因此，轨迹规划算 法的好坏直接影响了机器人的动力学性能</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt; vertical-align: super;">[44</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">_</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt; vertical-align: super;">45]</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">，轨迹规划在非线性系统的控制设计中占 有不可替代的作用</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt; vertical-align: super;">[46</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">_</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt; vertical-align: super;">47]</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">。一方面，轨迹规划结果可以作为前馈项与反馈控制一起构成两 自由度控制，从而获得更好地运动控制性能；另一方面，最优轨迹规划与最优控制具有 一致性，借助最优的轨迹规划结果，可以实现满足各种约束并具有特定优化指标的运动 控制。</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;"><o:p></o:p></span></p> <p class="NewStyle20" style="margin-left: 0pt; text-indent: 18pt; line-height: 23.05pt;"><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">在轨迹规划样条函数的开发与应用上，</span><span class="16" style="font-family: Georgia; letter-spacing: 0pt; font-size: 10.5pt;">B-Spline</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;"> </span><span class="16" style="font-family: Georgia; letter-spacing: 0pt; font-size: 10.5pt;">(Basic</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;"> </span><span class="16" style="font-family: Georgia; letter-spacing: 0pt; font-size: 10.5pt;">Spline</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">) </span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt; vertical-align: super;">[48</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">_</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt; vertical-align: super;">49]</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">、多项式样条函数以及</span><span class="16" style="font-family: Georgia; letter-spacing: 0pt; font-size: 10.5pt;">PH</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;"> </span><span class="16" style="font-family: Georgia; letter-spacing: 0pt; font-size: 10.5pt;">(Pythagorean</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;"> </span><span class="16" style="font-family: Georgia; letter-spacing: 0pt; font-size: 10.5pt;">Hodograph</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">速端螺旋线）</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt; vertical-align: super;">[5(5]</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">样条函数等被广泛采纳与应用， 例如，简单的三次样条函数因其算法简单易懂、可控性好而被广泛应用在通用控制器上</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;"><o:p></o:p></span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">。但是，在大多数情况下，采用三次样条函数进行轨迹规划得到的加速度曲线不连续，</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;"><o:p></o:p></span></p> <p class="NewStyle20" style="margin-left: 0pt; text-indent: 0pt; line-height: 23.3pt;"><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">由此产生的理论上无穷大的加加速度</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">（</span><span class="16" style="font-family: Georgia; letter-spacing: 0pt; font-size: 10.5pt;">Jerk</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">)</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">对于系统的整体性能和元器件都有较大影 响。对于现有的各种样条函数，国内外学者做了许多探索与研究，例如</span><span class="16" style="font-family: Georgia; letter-spacing: 0pt; font-size: 10.5pt;">Gasparetto</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt; vertical-align: super;">[52</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">^ </span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">用了五次</span><span class="16" style="font-family: Georgia; letter-spacing: 0pt; font-size: 10.5pt;">B</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">-</span><span class="16" style="font-family: Georgia; letter-spacing: 0pt; font-size: 10.5pt;">Spline</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">, </span><span class="16" style="font-family: Georgia; letter-spacing: 0pt; font-size: 10.5pt;">Liu</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;"> </span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt; vertical-align: super;">[53]</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">采用了七次</span><span class="16" style="font-family: Georgia; letter-spacing: 0pt; font-size: 10.5pt;">B</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">-</span><span class="16" style="font-family: Georgia; letter-spacing: 0pt; font-size: 10.5pt;">Spline</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">。</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">其中高次多项式</span><span class="16" style="font-family: Georgia; letter-spacing: 0pt; font-size: 10.5pt;">B</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">-</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">样条函数轨迹规划 应用最为广泛。例如，陈伟华等</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt; vertical-align: super;">[54]</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">、李万莉等</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt; vertical-align: super;">[55]</span><span style="font-family: 宋体; letter-spacing: 0pt; font-size: 11pt;">均采用五次样条函数对机器人进行轨迹 规划。陈伟华等在笛卡尔空间内对机器人的连续曲线路径进行规划，采用五次多项式对 曲线的拐角处在关节空间内进行规划；李万莉等采用五次多项式对机器人进行轨迹规划, 根据不同运动方式选取相应的边界条件，单段运动时，起始点速度和加速度一般设为零， 对于多段的连续运动，对其赋值，使机器人以一定速度和加速度通过中间点，以使动作 连贯。</span></p> <p class="NewStyle20" style="margin-left: 0pt; text-indent: 0pt; line-height: 23.3pt;"> </p> <p class="NewStyle20" style="margin-left: 0pt; text-indent: 0pt; line-height: 23.3pt;"><span style="font-size:9.0pt;font-family:宋体;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman";mso-font-kerning:1.0pt;mso-ansi-language:EN-US;mso-fareast-language: ZH-CN;mso-bidi-language:AR-SA">本文采摘自“高速并联工业机械手臂分析设计与实现”，因为编辑困难导致有些函数、表格、图片、内容无法显示，有需要者可以在网络中查找相关文章！本文由伯特利数控整理发表文章均来自网络仅供学习参考，转载请注明！</span></p> <p class="NewStyle20" 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