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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN" "http://www.w3.org/TR/html4/strict.dtd"> <html> <head> <title>page_36</title> <link rel="stylesheet" href="reset.css" type="text/css" media="all"> <meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /> </head> <body> <table summary="top nav" border="0" width="100%"> <tr> <td align="left" width="30%" style="background: #EEF3E2"><a style="color: blue; font-size: 120%; font-weight: bold; text-decoration: none; font-family: verdana;" href="page_35.html">< previous page</a></td> <td id="ebook_previous" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_36</strong></td> <td align="right" width="30%" style="background: #EEF3E2"><a style="color: blue; font-size: 120%; font-weight: bold; text-decoration: none; font-family: verdana;" href="page_37.html">next page ></a></td> </tr> <tr> <td id="ebook_page" align="left" colspan="3" style="background: #ffffff; padding: 20px;"> <table border="0" width="100%" cellpadding="0"><tr><td align="center"> <table border="0" cellpadding="2" cellspacing="0" width="100%"><tr><td align="left"></td> <td align="right"></td> </tr></table></td></tr><tr><td align="left"><p></p><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="right"><font face="Times New Roman, Times, Serif" size="2" color="#FF0000">Page 36</font></td></tr></table><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td align="center"><font face="Times New Roman, Times, Serif" size="3"><img src="30f8821660e4b510f5410bcef3650ada.gif" border="0" alt="0036-01.GIF" width="248" height="157" /></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td align="center"><font face="Times New Roman, Times, Serif" size="2">Figure聽2.8<br />Relation聽between聽vehicle聽and聽tangent-plane<br />coordinate聽systems.</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">2.4.1.2<br />Vehicle-to-Tangent-Plane Transformations</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">Consider the situation shown in Fig. 2.8, which depicts two coordinate systems. The first coordinate system can be thought of as a local tangent plane. The second coordinate system is attached to a moving vehicle that is at an arbitrary orientation relative to the tangent plane.</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">The relation between points and vectors in the vehicle and the tangent-plane coordinate systems can be completely described by the position <img src="7e3f156d6d17c87b64b68b5588c164e9.gif" border="0" alt="C0036-01.GIF" width="71" height="21" /> of the vehicle-frame origin in tangent-plane coordinates and the rotation matrix Rb2t. This rotation matrix can be defined by a series of three plane rotations involving the Euler angles (</font><font face="Symbol" size="3"><i>f</i></font><i><font face="Times New Roman, Times, Serif" size="3">, </font><font face="Symbol" size="3">q</font><font face="Times New Roman, Times, Serif" size="3">, </font><font face="Symbol" size="3">y</font></i><font face="Symbol" size="3"></font><font face="Times New Roman, Times, Serif" size="3">) = (roll, pitch, and heading)</font><font face="Times New Roman, Times, Serif" size="2"><sup>**</sup></font><font face="Times New Roman, Times, Serif" size="3">.</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">The first rotation, as shown in Fig. 2.9, rotates the tangent-plane coordinate system by </font><font face="Symbol" size="3"><i>y</i></font><font face="Times New Roman, Times, Serif" size="3"> radians about the <i>z</i> axis. This rotation aligns the new <i>x</i></font><font face="Symbol" size="3">垄</font><font face="Times New Roman, Times, Serif" size="3"> axis with the projection of the vehicle <i>u</i> axis into the tangent plane. The plane rotation for this operation is described as</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3"><img src="ec9b421cb26adef89e43e8e97141ec19.gif" border="0" alt="0036-02.GIF" width="363" height="57" /></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">The second rotation, as shown in Fig. 2.10, rotates the coordinate system that resulted from the previous yaw rotation by </font><font face="Symbol" size="3"><i>q</i></font><font face="Times New Roman, Times, Serif" size="3"> radians about the <i>y</i></font><font face="Symbol" size="3">垄</font><font face="Times New Roman, Times, Serif" size="3"> axis. This rotation aligns the new <i>x</i></font><font face="Symbol" size="3">垄垄</font><font face="Times New Roman, Times, Serif" size="3"> axis with the vehicle <i>u</i> axis. The plane rotation</font><font face="Times New Roman, Times, Serif" size="3" color="#FFFF00"></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td align="center"><font face="Times New Roman, Times, Serif" size="3"><img src="8358638d0ed99d726181da6c79e9d07a.gif" border="0" alt="0036-03.GIF" width="115" height="135" /></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td align="center"><font face="Times New Roman, Times, Serif" size="2">Figure聽2.9<br />Result聽of聽yaw聽rotation.</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td rowspan="5"><img src="f7703d30723feae8ee39d997c6419c20.gif" border="0" width="24" height="1" alt="f7703d30723feae8ee39d997c6419c20.gif" /></td> <td colspan="3" height="12"></td> <td rowspan="5"><img src="f7703d30723feae8ee39d997c6419c20.gif" border="0" width="24" height="1" alt="f7703d30723feae8ee39d997c6419c20.gif" /></td></tr><tr><td colspan="3" height="1"><table cellpadding="0" cellspacing="0" border="0"><tr><td></td></tr></table></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="2"><sup>**</sup>Although represented as a three-tuple, (</font><font face="Symbol" size="2">f</font><font face="Times New Roman, Times, Serif" size="2">, </font><font face="Symbol" size="2">q</font><font face="Times New Roman, Times, Serif" size="2">, </font><font face="Symbol" size="2">y</font><font face="Times New Roman, Times, Serif" size="2">) is not a true vector. For example, the addition of Euler angles is not commutative.</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table></td></tr></table><p><font size="0"></font></p>聽 </td> </tr> <tr> <td align="left" width="30%" style="background: #EEF3E2"><a style="color: blue; font-size: 120%; font-weight: bold; text-decoration: none; font-family: verdana;" href="page_35.html">< previous page</a></td> <td id="ebook_next" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_36</strong></td> <td align="right" width="30%" style="background: #EEF3E2"><a style="color: blue; font-size: 120%; font-weight: bold; text-decoration: none; font-family: verdana;" href="page_37.html">next page ></a></td> </tr> </table> </body> </html>⌨️ 快捷键说明
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