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2026-04-29 15:17:43 +02:00
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18 changed files with 9083 additions and 147 deletions
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@@ -8,12 +8,12 @@
\usepackage{graphicx}
% Deutsche Sprache (Datum, Trennungen, etc.)
\usepackage[ngerman]{babel}
%\usepackage[ngerman]{babel}
% Optional: bessere Schrift
\usepackage{lmodern}
\title{How to get a robot position from video image}
\title{How to get a robot position from video images}
\author{Christoph Kendel}
\date{\today}
@@ -21,32 +21,49 @@
\maketitle
\section{Intro}
\begin{center}
\begin{minipage}{0.89\linewidth}
\section{Info}
My Robot-Arm does not have homing switches. I want to use WebCams and Aruco--Markers to get the position of each joint. This way
I can get the position as well as double--check the position while working under load.
My Robot-Arm does not have homing switches. I use WebCams to get the position of each joint. This way
I can get the initial position without movement as well as contiuously check the position while working under load.
I work with Arucos. With my low resolution WebCam I can get reliable positions (when using two cams). But the angle resolution is not usable.
So I have to calculate the angle of each element from the relative positions of the markers.
\vspace{2mm}
\hspace{5mm}
I work with Aruco markers. With budget low resolution WebCams I can get reliable positions (when using two cams). But the angular recognizion of the markers turned out
not to be reliable. Thus
I have to calculate the angle of each element from the relative positions of the markers. Here I explain how I these calculations are done.
\end{minipage}
\end{center}
\pagebreak
\section{Angles}
The linear $x$ Position is easy to get: the markers 201, 204, 200, 198, 229, 243 have all a fixed relative $x$ position. Thus the average
can be taken, wich is saved as $x_{242}$ the x-position of the hand-rotation-joint.
All the other values are the angles {\tt y, z, a, b, c} and {\tt e}. % (e for the opening-of the hand).
\subsection{Bizeps {\bf \tt y}}
To find the angle of the bizeps (upper arm) there are different options, depending on the angle-of-view and which
ArUcos are visable.
\vspace{2mm}
\noindent
\begin{figure}[h!]
\includegraphics[width=\linewidth]{pic/robot_image_a.png}
\caption{Video Capture with recognized Aruco markers}
\end{figure}
\vspace{2mm}
\noindent
The calculation is based on two approaches: Position of the Markers 243 etc on the one hand, and relative position 198 $\leftrightarrow$ 229 on the other hand.
\vspace{2mm}
\noindent
\begin{minipage}{0.39\linewidth}
Several ways to calculate {\tt y}:
@@ -79,11 +96,11 @@ At the ellbow there is a motor that turns the forearm arround. Depending on whic
%
the
{\tt y} and {\tt z} position of 223 etc can't be used, as it depends on the angle of the forearm and the angle of the bizeps. Thus is it less reliable. (Although it would be a nice
thing to use as a double--check). With the $x_{223}$ compared to the $x_{242}$ i can calculate the ellbow turning {\tt a} value:
thing to use as a double--check). With the $x_{223}$ compared to the $x_{226}$ i can calculate the ellbow turning {\tt a} value:
$$
\sin({\tt a} + \alpha_{\rm }) = \frac{\Delta x}{35\,\rm mm} = \frac{x_{223} - x_{242}}{35\,\rm mm}
\sin({\tt a} + \alpha_{\rm }) = \frac{\Delta x}{35\,\rm mm} = \frac{x_{223} - x_{226}}{35\,\rm mm}
$$
@@ -92,14 +109,12 @@ as I know the angle $\alpha$ (yellow triangle) from the printed geometry of the
sled and bizeps, as their markers are fixed in $x$ position. This $\alpha$ is calculated for all markers of the forearm.
\vspace{2mm}
\noindent
\includegraphics[height=0.3\linewidth]{pic/robot_frontView_forearm.pdf}\hspace{3mm}
\begin{figure}[h!]
\hspace*{-4.5mm}
\includegraphics[height=0.3\linewidth]{pic/robot_frontView_forearm.pdf}\hspace{6mm}
\includegraphics[height=0.3\linewidth]{pic/robot_sideView_forearm.pdf}
\vspace{2mm}
\caption{Front view and sideview of the forearm with calculation variables.}
\end{figure}
\noindent
As the rotation {\tt a} may change for different markers, the median is taken.
@@ -107,10 +122,57 @@ As the rotation {\tt a} may change for different markers, the median is taken.
\subsection{Forearm}
With the
The position of the forearm motor (controlling motor in the bizeps) can be calculated from the difference between the bizeps
position $y$ and the angle of the forearm. Thus we need the forearm--angle. That can be calculated in two ways
%
%
\begin{itemize}
\item relative position of two markers on the forearm, that are on one line.
\item relative $y, z$ position of one marker on the forearm and one marker on the ellbow, e.g. 242 or 222.
\end{itemize}
%
Again:
As I might get different results, I have to find a median value.
\vspace{2mm}
\hfill $\Rightarrow$ Hand-Joint $P$ is known.
\subsection{Hand}
To get the hand position, the easiest way I see is to calculate the middle position between both finger-markers%
\footnote{The
other way to calculate the hand position without the markers orientation would be: calculate the middle-hand-plane from
the forearm rotation, with the distance of the finger-point to that plane, you'd also get the finger-opening and the projectet position of the finger-marker
to that plane, you'd get the angle.}
($F_1$, $F_2$ here shown in green).
The direction $P \to M$ in combination with the forearm-direction results in the angle {\tt b}.
\begin{figure}[h!]
\hfill
\includegraphics[height=0.3\linewidth]{pic/robot_hand_sideView.pdf}
\hfill
\includegraphics[height=0.26\linewidth]{pic/robot_hand_topView.pdf}
\hfill {}
\caption{\small Hand with points to calculate the values for {\tt b, c, e}.}
\end{figure}
\noindent
The Distance between the hand markers is a result of the opening of the fingers {\tt e}.
So I can calculate {\tt e} from that distance.
Furthermore the direction of the distance between the grippers gives me the rotation of the hand {\tt c}.
\paragraph{Limitations with the Hand:} The results depend heavily on the accuracy of $P$ and $M$. Both are never measured directly. So have to
double check if they make sense. Only if the distance $\overline {PM}$ checks up to be the mechanical correct, that can be used to evaluate the correctnes of $P$ and $M$.
And only if the point $M$ lies in the plane of the rotation {\tt a} arround the forearm.
\section{Program}
The NodeJS Program calculates the angles and checks, if they are the ones at the moment represented by the system.
\end{document}