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z(1gbkcT85Q|2c7T?}=j{x82U%vgMLci$bTSmv@q<_!*b@0}X7oru;7$*g}Xctf1=T H|K9`vEOuPi diff --git a/sections/tax_einordnung.tex b/sections/tax_einordnung.tex index 0c51af5..7a84097 100644 --- a/sections/tax_einordnung.tex +++ b/sections/tax_einordnung.tex @@ -64,7 +64,7 @@ Sind Überschneidungen der Arbeitsbereiche und Berührungen zwischen Mensch und \paragraph{Permanenter sicherer Betrieb} Die einfachste aber auch ineffizienteste Strategie ist ein permanenter sicherer Betrieb, indem der komplette Arbeitsbereich als eine Sicherheitszone definiert wird, was eine dauerhafte Beschränkung von Geschwindigkeit und Kraft und permanente Kollisionsvermeidung erfordert. -\subsubsection{Hindernisse} +\subsection{Hindernisse} Da das Ziel des Motion Planning das Erstellen einer kollisionsfreie Trajektorie ist, beschränken Hindernisse innerhalb des Arbeitsbereich maßgeblich die gültigen Pfade. Das Springer Handbook of Robotics~\cite[Kapitel 35.9]{siciliano_springer_2008} definiert eine Taxonomie der verschiedenen Darstellungsmöglichkeiten von Hindernissen und Algorithmen, diese zu vermeiden. Eine Visualisierung der Taxonomie ist in Abbildung~\ref{fig:obstacle_tax} dargestellt. Im folgenden Abschnitt werden diese Möglichkeiten kurz erläutert. @@ -77,18 +77,28 @@ Im folgenden Abschnitt werden diese Möglichkeiten kurz erläutert. \end{figure} -\paragraph{Ein-Schritt-Methoden} +\subsubsection{Ein-Schritt-Methoden} Ein-Schritt-Methoden sind Techniken zur Hindernisvermeidung, die Sensordaten direkt zur Bewegungssteuerung verwenden, ohne weitere Zwischenberechnungen durchzuführen. Dazu zählen unter anderem Methoden, die auf physikalischen Analogien basieren. Ein Beispiel für eine solche Analogie ist die Potentialfeldmethode, wo der Roboter als Partikel unter dem Einfluss eines Kräftefeldes angesehen wird. Die Zielposition übt eine anziehende Kraft auf das Partikel aus während es von Hindernissen abgestoßen wird. Die resultierende Bewegung ergibt sich aus der Summer der einwirkenden Kräfte. \textcolor{blue}{Heuristische Methoden} -\paragraph{Mehr-Schritt-Methoden} -Bei Mehr-Schritt-Methoden werden Zwischeninformationen berechnet, die verarbeitet werden müssen, um eine Bewegung zu erhalten. Diese Methoden sind zum einen solche, die eine Untermenge an Bewegungsrichtungen berechnen, wie das Vektor-Feld-Histogramm oder die Hindernis-Begrenzungs-Methode und solche, die eine Menge an Geschwindigkeitsreglungen berechnen, wie der dynamische Fensteransatz oder die Methode der Geschwindigkeitshindernisse. +\subsubsection{Mehr-Schritt-Methoden} +Bei Mehr-Schritt-Methoden werden Zwischeninformationen berechnet, die verarbeitet werden müssen, um eine Bewegung zu erhalten. Diese Methoden sind zum einen solche, die eine Untermenge an Bewegungsrichtungen berechnen, wie das Vektor-Feld-Histogramm oder die Hindernis-Begrenzungs-Methode und solche, die eine Menge an Geschwindigkeitsreglungen berechnen, wie der dynamische Fensteransatz oder die Methode der Geschwindigkeitshindernisse. Nachfolgend werden die Grundkonzepte dieser Methoden kurz dargestellt. -\textcolor{blue}{[Genauer auf die Beispiele eingehen]} +\paragraph{Vektor-Feld-Histogramm} +Die Welt werden vom Roboter ausgehen in Sektoren aufgeteilt. Den Sektoren wird anschließend die Dichte an Hindernissen zugeteilt, sodass ein Polarhistogramm entsteht. Die Sektoren mit der kleinsten Dichte, die gleichzeitig am nächsten zu dem Sektor sind, der das Ziel enthält, werden als Kandidaten ausgewählt. Liegt das Ziel innerhalb eines der Sektoren, wird dieser als Richtung gewählt. Liegt das Ziel außerhalb, wird der Sektor mit der geringsten Dichte gewählt. Da Hindernisse durch Wahrscheinlichkeitsdichten repräsentiert sind, eignet sich diese Methode gut bei Verwendung von Sensoren mit höherer Unsicherheit, wie zum Beispiel Ultraschallsensoren~\cite[Seite 841]{siciliano_springer_2008}. + +\paragraph{Hindernis-Begrenzungs-Methode} +Im ersten Schritt werden Zwischenziele definiert, wenn das eigentliche Ziel nicht auf direktem Wege erreichbar ist. Diese Zwischenziele liegen entweder zwischen Hindernissen oder auf der Kante eines Hindernisses. Das Zwischenziel mit dem geringsten Abstand zum Ziel wird als neues Ziel festgelegt. Für jedes Hindernis wird eine Menge an unerwünschten Richtungen berechnet, die für eine erfolgreiche Hindernisvermeidung ungeeignet wären. Im letzten Schritt wird ein Kompromiss berechnet, in dem aus den erlaubten Richtungen die ausgewählt wird, die sich dem Ziel annähert, gleichzeitig aber einen möglichst großen Abstand zu den Hindernissen hat. Da die Bewegungsgeschwindigkeit invers proportional zum Abstand zu den Hindernissen ist, wird diese dadurch ebenfalls optimiert. Als effektiv hat sich diese Methode vor allem in beengten Räumen gezeigt~\cite[Seite 842]{siciliano_springer_2008}. + +\paragraph{Dynamischer Fensteransatz} +Die Menge an Kandidaten-Geschwindigkeitsregelungen ist eine Teilmenge aller Regelungen, die noch ein Abbremsen ermöglichen, bevor es zu einer Kollision kommt, und die ihren Zielwert in vorgegebener Zeit erreichen können. Im zweiten Schritt wird die Regelung gewählt, die eine gewichtete Summe aus der Näherung an das Ziel, den Abstand zu Hindernissen und die ausführbare Geschwindigkeit maximiert. Der Dynamische Fensteransatz eignet sich vor allem für Roboter mit langsamen dynamischen Reaktionsmöglichkeiten oder für die Arbeit mit hohen Geschwindigkeiten~\cite[Kapitel 35.9.4 ]{siciliano_springer_2008}. + +\paragraph{Geschwindigkeitshindernisse} +Die Methode der Geschwindigkeitshindernisse folgt den selben Annahmen wie der dynamische Fensteransatz, mit dem Unterschied, dass auch die Geschwindigkeiten der Hindernisse berücksichtigt werden. Dadurch eignet sie sich besonders für dynamische Anwendungsfälle~\cite[Kapitel 35.9.5]{siciliano_springer_2008}. \paragraph{} -Eine allgemein optimale Methode lässt sich nicht festlegen. Diese hängt von den Anforderungen, der Geschwindigkeit des Roboters und der Hindernisse und die Unsicherheit über den Zustand der Welt. +Eine allgemein optimale Methode lässt sich nicht festlegen. Diese hängt von den Anforderungen, der Geschwindigkeit des Roboters und der Hindernisse und der Unsicherheit über den Zustand der Welt ab. \subsection{Teilpfade} In einigen Anwendungsfällen, wie beispielsweise dem Schweißen, ist es notwendig, dass der Endeffektor des Roboters zwischen Start- und Zielposition einen vorgegebenen Pfad abfährt. Befindet sich der Teilpfad vollständig innerhalb des stationären Arbeitsbereichs, können seine Punkte einfach als Zwischenziele im Motion Planning berücksichtigt werden. Beim Einsatz von mobilen Manipulatoren kann der zu folgende Teilpfad auch außerhalb des aktuellen Arbeitsbereichs sein, da sich dieser durch die Bewegung im Raum verändert~\cite{oriolo_motion_2005}. -- GitLab