Raspberry Pi Robotics Projects (2nd Edition) by Richard Grimmett

By Richard Grimmett

This booklet is for fanatics who are looking to use the Raspberry Pi to construct complicated robotics tasks. due to the step by step directions during this booklet, you could build complicated robotics tasks that may stream, speak, pay attention, see, swim, or fly.

No earlier Raspberry Pi robotics event is believed, yet even specialists will locate unforeseen and fascinating info.

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41). 0 c3 c3 = 43 0 − 23 1 Durch fortlaufende Aktualisierung der rechten Seite haben wir bei der Elimination Lc = f gel¨ost. Die Vorw¨artselimination hat f in c verwandelt. Anschließend liefert das R¨uckw¨artseinsetzen schnell u = (3, 2, 1). Es mag Ihnen aufgefallen sein, dass wir bei dieser Berechnung nirgends inverse ” Matrizen“ verwendet haben. Die Inverse der Matrix K wird nicht ben¨otigt. Gute Software f¨ur lineare Algebra (die LAPACK-Bibliothek ist public domain) unterteilt das Eliminationsverfahren von Gauß in einen Schritt, der auf K arbeitet, und einen L¨osungsschritt, der auf f arbeitet: Schritt 1.

Der Fehler ist h(1 − x)/2. Der Vollst¨andigkeit halber k¨onnen wir noch Tn u = h2 ones(n, 1) f¨ur alle n l¨osen: ⎡ ⎤⎡ ⎤ 1 0 1 −1 ⎢ −1 1 0 ⎥ ⎢ 0 1 −1 ⎥ ⎢ ⎥⎢ ⎥ −vorw¨arts) = ⎢ ¨ arts)(− . 33) T n = (ruckw¨ ⎥ ⎢ . . .. 0 ⎦⎣ . . −1 ⎥ ⎣ ⎦ −1 1 0 1 Die Inversen dieser Matrizen der ersten Differenzen sind Summenmatrizen (Dreiecksmatrizen mit den Elementen 1). Die Inverse der Matrix Tn ist das Produkt aus einer oberen Dreiecksmatrix und einer unteren Dreiecksmatrix: 24 1 Angewandte lineare Algebra ⎡ ⎤⎡ ⎤⎡ ⎤ ..

In unserem ersten Schritt war der Multiplikator − 12 (der Quotient aus −1 und 2). Der Schritt bestand darin, Zeile 1 mit 12 zu multiplizieren und zu Zeile 2 zu addieren. Das ist dasselbe, wie Zeile 1 mit − 12 zu multiplizieren und von Zeile 2 abzuziehen. Subtrahiere i j mal die Zeile mit dem Pivotelement j von Zeile i . Dann ist das Element an der Stelle i , j null. Das Element an der Stelle 3, 1 in der unteren linken Ecke war bereits null. Folglich musste nichts eliminiert werden und der Multiplikator 31 war gleich null.

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