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Lesson10/Lesson10.tex

+\section{Group 7}\label{group-7}
+
+\subsection{Lab Notebook - Lesson 10}\label{lab-notebook---lesson-10}
+
+\textbf{Date:} 21/05 2015
+
+\textbf{Group members participating:} Ivan Grujic, Lasse Brøsted
+Pedersen, Steffan Lildholdt, René Nilsson
+
+\textbf{Activity duration:} 5 hours
+
+\subsection{Goal}\label{goal}
+
+The goal of this exercise is to investigate how the method of odometry
+and the tachocounter can be used to keep track of position of a LEGO car
+with differential drive.
+
+\subsection{Plan}\label{plan}
+
+The plan is to follow the plan described in {[}1{]}.
+
+\subsection{Odometry}\label{odometry}
+
+For this exercise the standard base vehicle from Lesson 6 is used
+together with the PilotSquare.java program provided in this lesson. The
+parameters of the LEGO car in this program is defined as the following.
+
+\begin{longtable}[c]{@{}lc@{}}
+\toprule
+Parameter & Value\tabularnewline
+\midrule
+\endhead
+Left wheel diameter & 5.5 cm\tabularnewline
+Right wheel diameter & 5.5 cm\tabularnewline
+Track width & 16 cm\tabularnewline
+\bottomrule
+\end{longtable}
+
+The program makes the car drive 20 cm straight forward, turn 90 degrees
+to the left and repeat this 4 times in order to get back to the initial
+position. A special piece of paper with multiple grids on it is used to
+measure the accuracy of the system. This is shown in the following
+image.
+
+\begin{figure}[H]
+\centering
+\includegraphics{Lesson10/Images/Odometry.JPG}
+\caption{Measuring physical accuracy of the DifferentialPilot class}
+\end{figure}
+
+Optimally, the LEGO car should end up in the exact same position as
+prior to the execution of the program. However this is not the case due
+to both \textbf{systematic} and \textbf{non-systematic} errors. The
+result of the 3 test runs are summarized in the following table.
+
+\begin{longtable}[c]{@{}lcrrr@{}}
+\toprule
+Attempt & Measured x & Measured y & Calculated x & Calculated
+y\tabularnewline
+\midrule
+\endhead
+1 & -2.00 mm & -2.00 mm & 1.00 mm & -1.60 mm\tabularnewline
+2 & -2.00 mm & 2.00 mm & 0.40 mm & -0.60 mm\tabularnewline
+3 & -4.00 mm & 3.50 mm & 2.50 mm & -1.90 mm\tabularnewline
+\bottomrule
+\end{longtable}
+
+``Measured'' x and y is the physical error measured by a ruler and
+``Calculated'' x and y is computed error displayed in the LCD on the
+NXT.
+
+The \textbf{Non-systematic} involves variations in the surface and the
+internal uncertainty of \textasciitilde{}2\% {[}2{]}. These errors are
+difficult to cope with. However the \textbf{systematic} errors involves
+incorrect definition of the LEGO car parameters and these can be
+corrected by calibration which is described in the following.
+
+\subsection{Calibration of wheel diameter and the track
+width}\label{calibration-of-wheel-diameter-and-the-track-width}
+
+The wheels diameter is calibrated by letting the car drive 50 cm - using
+the ``travel()'' function of the DifferentialPilot with 50 as parameter
+- and then adjusting the diameter according to where the car stops.
+Similarly the track width is calibrated by letting the car spin 360
+degrees - using the ``rotate()'' function of the DifferentialPilot with
+360 as parameter - and again observing the stopping position and
+adjusting the track width accordingly. The calibration setup is shown in
+the following image.
+
+\begin{figure}[H]
+\centering
+\includegraphics[width = 200 pt]{Lesson10/Images/Calibration.JPG}
+\caption{Calibration of LEGO car parameters}
+\end{figure}
+
+We found out that it was necessary to set the right wheel diameter a
+little higher than the left in order to make the LEGO car drive
+straight. The calibrated values are shown in the following table.
+
+\begin{longtable}[c]{@{}lc@{}}
+\toprule
+Parameter & Value\tabularnewline
+\midrule
+\endhead
+Left wheel diameter & 5.539 cm\tabularnewline
+Right wheel diameter & 5.544 cm\tabularnewline
+Track width & 16.27 cm\tabularnewline
+\bottomrule
+\end{longtable}
+
+To validate the calibrated values we let the LEGO car drive in a 50 x 50
+cm square as shown in following image. The goal is, after the trip, to
+end back up in the starting position.
+
+\begin{figure}[H]
+\centering
+\includegraphics[width = 250 pt]{Lesson10/Images/PilotSquareLeftTurns.JPG}
+\caption{Validation of LEGO car parameters - Left turns}
+\end{figure}
+
+The result of 3 attempts are summarized in the following table.
+
+\begin{longtable}[c]{@{}lcrrr@{}}
+\toprule
+Attempt & Measured x & Measured y & Calculated x & Calculated
+y\tabularnewline
+\midrule
+\endhead
+1 & -10.00 mm & -13.00 mm & 1.30 mm & -1.30 mm\tabularnewline
+2 & -10.00 mm & -10.00 mm & 2.80 mm & -2.80 mm\tabularnewline
+3 & -13.00 mm & -15.00 mm & 3.00 mm & -1.80 mm\tabularnewline
+\bottomrule
+\end{longtable}
+
+Despite what we expected the LEGO car did not end up in the exact
+position as it started in. A clear sign of systematic errors is seen due
+to the x and y position always are negative. We then tried to calibrate
+the parameters of the LEGO car according to the 50 x 50 cm square and
+ended up with the following parameters.
+
+\begin{longtable}[c]{@{}lc@{}}
+\toprule
+Parameter & Value\tabularnewline
+\midrule
+\endhead
+Left wheel diameter & 5.539 cm\tabularnewline
+Right wheel diameter & 5.544 cm\tabularnewline
+Track width & 16.4 cm\tabularnewline
+\bottomrule
+\end{longtable}
+
+Apparently, it was only the track width that needed to be adjusted in
+order to correct for the systematic errors. The result after four runs
+with the updated parameters is shown in the following table.
+
+\begin{longtable}[c]{@{}lcrrr@{}}
+\toprule
+Attempt & Measured x & Measured y & Calculated x & Calculated
+y\tabularnewline
+\midrule
+\endhead
+1 & 5.00 mm & 5.00 mm & 0.60 mm & -0.60 mm\tabularnewline
+2 & -1.25 mm & -2.50 mm & 1.90 mm & -2.10 mm\tabularnewline
+3 & 2.00 mm & 3.00 mm & 6.30 mm & -1.80 mm\tabularnewline
+4 & -1.00 mm & 0.00 mm & 1.80 mm & -2.30 mm\tabularnewline
+\bottomrule
+\end{longtable}
+
+The measured x and y errors seem to be random with these parameters. To
+validate these results the car is programmed to drive the other way
+around as shown in the following image.
+
+\begin{figure}[H]
+\centering
+\includegraphics[width = 250 pt]{Lesson10/Images/PilotSquareRightTurns.JPG}
+\caption{Validation of LEGO car parameters - Right turns}
+\end{figure}
+
+In this setup the LEGO car performed poorly with much larger errors in
+the x and y direction.
+
+\begin{longtable}[c]{@{}lcrrr@{}}
+\toprule
+Attempt & Measured x & Measured y & Calculated x & Calculated
+y\tabularnewline
+\midrule
+\endhead
+1 & 30.00 mm & 40.00 mm & 1.30 mm & 2.30 mm\tabularnewline
+2 & -27.50 mm & -30.00 mm & 5.20 mm & 2.70 mm\tabularnewline
+\bottomrule
+\end{longtable}
+
+Due to these poor results the original calibrated parameter values are
+used.
+
+\begin{longtable}[c]{@{}lc@{}}
+\toprule
+Parameter & Value\tabularnewline
+\midrule
+\endhead
+Left wheel diameter & 5.539 cm\tabularnewline
+Right wheel diameter & 5.544 cm\tabularnewline
+Track width & 16.27 cm\tabularnewline
+\bottomrule
+\end{longtable}
+
+It seems like it is near impossible to calibrate the parameters so that
+the LEGO car is able to travel a given distance while performing a
+number of random turns. Multiple reason can cause this behavior. An
+obvious reason is the leJOS maximum precision of 2 \%. So no matter how
+much calibration is performed some error will always exist, even though
+this probably is non-systematic. Other factors like the position of the
+back wheel could also be part of the explanation. If the back wheel is
+not aligned with the driving direction the car can be drawn out of
+course when pulling the back wheel into the correct direction.
+
+\subsection{Position tracking by means of particle
+filters}\label{position-tracking-by-means-of-particle-filters}
+
+\subsubsection{Estimating the noise
+factors}\label{estimating-the-noise-factors}
+
+The tests to estimate the noise factors was performed at low speeds, on
+a wooden table covered by a single sheet of paper. The low speed reduces
+the noise factors because the wheel stops faster, and thus closer to the
+intended angle, also the low speed reduces the risk the wheel loosing
+grip of the surface. The wooden table covered by paper also reduces the
+noise factors, because the surface is homogeneously smooth, without any
+irregularities which could introduce errors.
+
+The distance noise factor was determined by having the robot perform
+multiple forward travels of 50 cm. The average distance from the target
+was \textasciitilde{}0.5 mm, thus the distance noise factor was
+estimated as: 0.5/500 = 0.001.
+
+The angle noise factor was determined by two tests, both performed
+multiple times. In the first test, the robot performed four 360 degrees
+rotation. The second test was similar, but reversed the direction of the
+2nd and 4th rotation. For both tests, the average deviation was 0.5
+degrees.
+
+\subsubsection{\texorpdfstring{Test with \texttt{PilotMonitor} and
+\texttt{PilotRoute}}{Test with PilotMonitor and PilotRoute}}\label{test-with-pilotmonitor-and-pilotroute}
+
+The \texttt{applyMove} function in the \texttt{Particle} class was
+initially corrected, so that the addition of the random error is not
+dependent of the coordinate system. In the snippet below, the old
+implementation is shown. Here the addition of noise depends on the
+distance traveled in the x or y direction, meaning that if the Lego car
+only moved in the y direction, no noise would be added to the
+x-coordinate. And vice versa.
+
+\begin{Shaded}
+\begin{Highlighting}[]
+\NormalTok{pose.}\FunctionTok{setLocation}\NormalTok{(}\KeywordTok{new} \NormalTok{Point(}
+    \NormalTok{(}\DataTypeTok{float}\NormalTok{) (pose.}\FunctionTok{getX}\NormalTok{() + xm + (distanceNoiseFactor * xm * rand.}\FunctionTok{nextGaussian}\NormalTok{())),}
+    \NormalTok{(}\DataTypeTok{float}\NormalTok{) (pose.}\FunctionTok{getY}\NormalTok{() + ym + (distanceNoiseFactor * ym * rand.}\FunctionTok{nextGaussian}\NormalTok{()))));}
+\end{Highlighting}
+\end{Shaded}
+
+In the snippet below the corrected implementation is shown. Instead of
+using the distance in the x and y direction, the total distance is used.
+In this way, the noise addition is independent of the coordinate system.
+
+\begin{Shaded}
+\begin{Highlighting}[]
+\NormalTok{pose.}\FunctionTok{setLocation}\NormalTok{(}\KeywordTok{new} \NormalTok{Point(}
+    \NormalTok{(}\DataTypeTok{float}\NormalTok{) (pose.}\FunctionTok{getX}\NormalTok{() + xm + (distanceNoiseFactor * move.}\FunctionTok{getDistanceTraveled}\NormalTok{() }
+            \NormalTok{* rand.}\FunctionTok{nextGaussian}\NormalTok{())),}
+    \NormalTok{(}\DataTypeTok{float}\NormalTok{) (pose.}\FunctionTok{getY}\NormalTok{() + ym + (distanceNoiseFactor * move.}\FunctionTok{getDistanceTraveled}\NormalTok{() }
+            \NormalTok{* rand.}\FunctionTok{nextGaussian}\NormalTok{()))));}
+\end{Highlighting}
+\end{Shaded}
+
+The particle filter was tested by making the car follow the track as
+shown in the picture below. By using the poster with distances it is
+possible to see how accurate the car is.
+
+\begin{figure}[H]
+\centering
+\includegraphics[width = 250 pt]{Lesson10/Images/PilotHorseShoe.jpg}
+\caption{Test of particle filter}
+\end{figure}
+
+The test was run with two different settings: 1. Speed = 5, distance
+noise factor = 0.001 and angle noise factor = 0.5. 2. Speed = 15,
+distance noise factor = 0.005 and angle noise factor = 2.5.
+
+Below is a picture of the test results.
+
+\begin{figure}[H]
+\centering
+\includegraphics[width = 200 pt]{Lesson10/Images/ParticleFilter.JPG}
+\caption{Test results with speed = 15, distance noise factor = 0.005 and
+angle noise factor = 2.5. The robot was supposed to stop with the black
+brick underneath the front pointing on the cross. It is approximately 4
+cm away. The PC shows the possible locations calculated using the
+particle filter.}
+\end{figure}
+
+\subsection{Position tracking while avoiding
+obstacles}\label{position-tracking-while-avoiding-obstacles}
+
+We have chosen to answer this exercise based on the exercise \emph{Make
+the robot stay within the robot arena} from lesson 11. The following
+image shows the setup used, with a sonar sensor, two light sensors, and
+a bumper and touch sensor mounted on the front of the vehicle.
+
+\begin{figure}[H]
+\centering
+\includegraphics[width = 250 pt]{Lesson10/Images/Sonar.JPG}
+\caption{Setup for tracking whilst avoiding obstacles}
+\end{figure}
+
+We used the bumper and touch sensor to detect obstacles as this was
+easier to test. Odometry was used to track the movements performed in
+the two behaviors \emph{Avoid obstacle} and \emph{Travel route}.
+
+\begin{figure}[H]
+\centering
+\includegraphics{Lesson10/Images/BehavioralControl.jpg}
+\caption{Behavioral control}
+\end{figure}
+
+Travel route was implemented to drive in a straight line to obtain a
+simple fixed route. The Avoid Obstacle behavior, which backs the car up
+10 cms and turns 90 degrees to the left, is activated by the touch
+sensor. Both behaviors use the \texttt{Travel()} and \texttt{Rotate()}
+methods of the \texttt{DifferentialPilot}. These methods are both called
+with the \texttt{ImmediateReturn} parameter set to true, in order to let
+the them be suppressed.
+
+We tested the tracking by placing the vehicle approximately 30 cm in
+front of an obstacle. When the car reached the obstacle, it backed up,
+turned to the left and continued forward. As can be seen in the video in
+{[}3{]}, the odometry was able to keep track of the car.
+
+\subsection{Conclusion}\label{conclusion}
+
+In this exercise we have performed experiments with odometry in a real
+world setting. For this to work a highly precise calibration of the
+wheel diameter and track width is required. We discovered that this is
+not a straight forward task when working with LEGO and the leJOS
+environment. The problems we encountered resulted in that we were not
+entirely able to remove systematic errors from the system. Many factors
+will affect the driving and we were therefore not able to determine the
+exact cause of the calibration errors. Our best estimate is that the
+orientation of the back wheel plays an important role and should be
+aligned precisely according to the direction of driving. When doing
+position tracking with the particle filter a distance and an angle noise
+factor needs to be determined in order to cope with the non-systematic
+errors. Here we found out that speed is a significant factor. When the
+speed is increased the different noise factors also needs to be
+increased due to a higher uncertainty of the end position.
+
+\subsection{References}\label{references}
+
+{[}1{]}
+http://legolab.cs.au.dk/DigitalControl.dir/NXT/Lesson10.dir/Lesson.html
+
+{[}2{]}
+http://lejos.sourceforge.net/nxt/nxj/tutorial/WheeledVehicles/WheeledVehicles.htm
+
+\subsubsection{Videos}\label{videos}
+
+{[}3{]} http://youtu.be/JOdNyQy-lQ4