Self-Correcting Projectile Launcher: - Rensselaer Polytechnic Institute

Self-Correcting Projectile Launcher:
Progress Report for ECSE-4460 Control Systems Design
Josh Schuster
Yena Park
Diana Mirabello
Ryan Kindle
March 30, 2005
Rensselaer Polytechnic Institute

ABSTRACT
The design of a Self-Correcting Projectile Launcher was motivated by the desire
to improve the accuracy existing launchers without the use of extensive sensor networks,
and to demonstrate the viability of an iterative learning algorithm for disturbance
rejection. The goal is to fire a disc from a commercially available toy gun at a target, and
have its accuracy improve with each subsequent shot until the target is struck precisely.
As the disc strikes the touch screen, the error in the trajectory will be calculated based on
the difference between the target and impact site, and the orientation of the launcher will
be adjusted to compensate using a pan and tilt mechanism.
ii

TABLE OF CONTENTS
1. Introduction 1
2. Preliminary Results 3
2.1 Friction Identification. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3
2.2 Model Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15
2.4 Learning Algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21
2.5 Subsystem Development. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .28
3. Summary of Progress 31
3.1 Plan. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2 Schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3 Cost. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.4 Unanticipated Challenges. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.5 Forecast. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4. Bibliography 36
5. Statement of Contribution 37
Appendix A: MATLAB Code 38
iii

LIST OF FIGURES
2.1 Identification Simulink Model File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3
2.2 Velocity Diagram without Filter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.3 Velocity Diagram after Implementation of Second Filter. . . . . . . . . . . . . . . . . .5
2.4 Velocity Diagram after Implementation of Third Filter for Tilt Axis. . . . . . . . .5
2.5 Velocity Diagram after Implementation of Third Filter for Pan Axis. . . . . . . . .6
2.6 Diagram of Torque vs. Steady State Velocity of Tilt Axis. . . . . . . . . . . . . . . . . 7
2.7 Diagram of Torque vs. Steady State Velocity for Pan Axis. . . . . . . . . . . . . . . . 8
2.8 Simulink Model File for the Parameter Equations. . . . . . . . . . . . . . . . . . . . . . . 9
2.9 Angular Velocity Measured from the Tilt Motor. . . . . . . . . . . . . . . . . . . . . . . . 11
2.10 Tilt Angular Velocity Simulated from the Model. . . . . . . . . . . . . . . . . . . . . . . .11
2.11 Angular Velocity Measured from the Pan Motor. . . . . . . . . . . . . . . . . . . . . . . . 12
2.12 Pan Angular Velocity Simulated from the Model. . . . . . . . . . . . . . . . . . . . . . . .12
2.13 Parameter Equation Verification with Noise Consideration. . . . . . . . . . . . . . . .13
2.14 Launcher Testing Procedure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15
2.15 2 nd Launcher Testing Procedure. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . .16
2.16 Plot of Short Range Trajectory Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18
2.17 Average Vertical Displacement vs. Distance from Launcher to Target. . . . . . . 19
2.18 Target Cones Resulting from Different Position Errors. . . . . . . . . . . . . . . . . . . 20
2.19 Error Correction for Unusual Cases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.20 Distance to Edges of Touchpad. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.21 Learning Algorithm Chart. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.22 Aluminum Mounting Base. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27
2.23 Disc Launcher. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.24 Automated Firing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.25 Mounting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
iv

LIST OF TABLES
1.1 System Specifications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2
2.1 Coulomb and Viscous Friction for Pan and Tilt Axes. . . . . . . . . . . . . . . . . . . . . 7
2.2 Parameters for Pan and Tilt Axes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10
2.3 Variation of the Parameters with respect to noise. . . . . . . . . . . . . . . . . . . . . . . . 13
2.4 Disc Shooter Accuracy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15
2.5 Preliminary Trajectory Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16
2.6 Short Range Trajectory Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.7 Average Short Range Trajectory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.8 Effect of Distance Change Due to Angle Change (x-direction) . . . . . . . . . . . . . 24
2.9 Effect of Distance Change Due to Angle Change (y-direction). . . . . . . . . . . . . .24
3.1 Pan and Tilt Mechanism Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2 Additional Parts Needed for System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.3 Labor Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.4 Lab Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.5 Total System Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.6 Actual Cost of System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
v

1. INTRODUCTION
The world is an unpredictable place, and when it comes to projectile motion the
unknowns one must take into account are numerous and complex. The purpose of the
project proposed in this paper is to create a prototype Self-Correcting Projectile
Launcher. Instead of rejecting disturbances in advance to improve the chance of striking
a target in a single shot, the system will fire repeatedly at a target and learn from its errors
to strike more accurately with subsequent shots. The motivation for the project was to
create a launcher that was capable of high accuracy but without the extensive sensor
setup required to predict disturbances. The creation of such a system would be an
economical solution for any number of applications, as well as a significantly more
portable system.
A trajectory may be altered by the varying currents, density, and stresses found in
any given medium. While some of these may be measured and accounted for in advance,
the variable nature of the environment dictates that no disturbance will be completely
rejected. The measurements and computations to achieve such an incomplete error
reduction would also require a significant investment in equipment. If an iterative
learning approach were utilized instead, all that would be required to reject an error is the
ability to sense to actual impact’s location relative to the target and extra projectiles.
The design of projectile launchers is hardly a new endeavor; everything from
batting cages to artillery has attempted to accurately hit a target. While small consumer
systems such as a ping pong machine or batting cage lack sensory capabilities and rely
instead on calibration, military applications are usually far more sophisticated. However,
while guided artillery batteries are capable of rejecting disturbances through sensors and
computers, smaller launchers such as mortars are not. The same desire for compactness
and economy is what drives commercial applications to rely simply on calibration to
ensure accuracy. Both commercial enterprises that market projectile launchers requiring
accuracy as well as the military would benefit from a small cost-effective trajectory
correction system.
Since the purpose of the prototype is simply to demonstrate the viability of such a
system, the most significant functional requirement is accuracy. The firing system must
be above all be capable of consistently striking the same location when locked into a
position, else the iterative learning algorithm will be unable to calculate corrections.
Also, the pan and tilt mechanism used to aim the launcher must be able to accurately
adjust and detect its orientation, and the controller must ensure that steady-state position
error is near zero and that noise tolerance is high. To ensure that any error in the
orientation is insignificant, the rise time, fall time and settling time of the control system
should be low; the percent overshoot should be small but this is not a critical factor.
Beyond the control system, the rotational velocity of the launcher is not a significant
factor and as such will be kept low to allow for increased accuracy. The range of motion
for the launcher will be sufficient to strike any target within range. The payload for the
pan and tilt mechanism, specifically the launcher and its mounting apparatus, will be
vi

made of plastic and aluminum and hence lightweight. The cost of the system will be low
enough to allow for its widespread adaptation to the various low-cost applications
discussed previously. Quantitative specifications are described in Table 1.1, with
justification in the Preliminary Results section.
Range of Motion (Pan) -180° to +180°
Range of Motion (Tilt) -45° to +45°
Rotational Accuracy ±0.1°
Rotational Velocity 30° / s
Steady State Error < 2%
Noise Tolerance 98%
Rise Time < 0.1 s
Settling Time < 0.1 s
Percent Overshoot < 15%
Payload < 2 lbs
Table 1.1: System Specifications
The scope of effort required to realize the project proposed here is significant and
diverse. The initial design and control of the pan and tilt mechanism require knowledge
of control theory and modeling. Once that is accomplished, the implementation of the
disturbance rejection system will integrate algorithm design skills, sensor development
and trajectory planning. Beyond the control design, mechanical design skills will be used
to create the mounting apparatus for the launcher, as well as to automate the firing of a
projectile. Nonetheless, the project goal is attainable within the allocated timeframe.
The preliminary results of the project show that model development is nearing
completion, requiring only a few recalibrations once the launcher has been mounted. The
automation of the firing system has been designed, and is ready to be implemented in the
next week. The mount by which the system will be affixed to the pan and tilt mechanism
has been designed and machined. Preliminary testing and calculation indicates that the
system will be able to meet all of its specifications, and the transition into control design
should begin shortly.
Currently the project is slightly behind schedule. The delay is due in part to the
break in the semester, during which less work than anticipated was accomplished, and the
unavailability of necessary components. That has been the greatest setback to date, in
that a cable to connect a laptop to the digital ports of the microcontroller, which will be
used to automate firing, and the touch screen controller used in the previous year both
required purchase. That set back the development and testing of the touch screen and
learning algorithm, and may result in less time to test the system. Fortunately, it is not
believed that these setbacks will affect the overall goal of the project beyond making the
integration of the IR sensor an optional enhancement. The primary goal of using a
learning algorithm to correct the trajectory of an object in flight should still be achievable
within the remaining timeframe.
vii

2. PRELIMINARY RESULTS
2.1 Friction Identification
Testing Procedure
The purpose of the following Simulink model file shown in Figure 2.1 is to obtain
necessary data for estimating Coulomb frictions and viscous frictions for tilt axis. The
corresponding MATLAB code is located in Appendix A. For pan axis, the two inputs to
the PCIM-DAS1602 16 block have to be swapped. PCI-QUAD04 has one output port
that needs to be multiplied by 2π/(2048*4) to acquire theta which is the angle that motor
points to after the command. Theta1 and thetadot1 corresponds to angle and the speed of
tilt motor. Since the amount of torque that is required to start the system moving is
greater than the torque required to keep the system moving in motion once it is already
moving, an impulse was inputted 0.3 seconds after the simulation started with a pulse
width of 0.01 seconds to break the static friction. Input voltage was incremented
automatically with the ‘for loop’ from the script.
Figure 2.1: Friction Identification Simulink Model File
Some filtering was necessary because the velocity collected from a single
simulation was fluctuating up and down. Figure 2.2 shows the raw data before the filter
is applied. Filtering was implemented in three steps. First step was taking average from
five runs for each voltage steps. And during second step, it took the average of the twenty
five adjacent data points, from the data set that was calculated from first step. And
viii

finally, the impulse spikes were eliminated. The data plot from Figure 2.3 is after first
step of the filtering.
For both pan and tilt axis, all velocities with input voltage greater than -0.5 volts
and less than 0.5 volts saturated to zero. And velocities with input voltage greater than 1
Volts or less than -1 volts all saturated to 9.3143 rad/s and -9.0014 rad/s for tilt axis,
9.4629 rad/s and -9.1584 rad/s respectively for pan axis. The velocity diagrams for pan
and tilt axis after all of the filtering was complete are shown in Figure 2.4 and 2.5.
Figure 2.2: Velocity Diagram without Filter
ix

Figure 2.3: Velocity Diagram after Implementation of Second Filter
Figure 2.4: Velocity Diagram After Implementation of Third Filter for Tilt Axis
x

Figure 2.5: Velocity Diagram After Implementation of Third Filter for Pan Axis
Torque was calculated using following equation:
Torque = Voltage * N * Nm * Kt*Ka
Voltage = Input Voltage (-1~1 Volts)
N = External Gear Ratio (2.47)
Nm = Internal Gear Ratio (19.5)
Kt = Motor Torque Constant (4.36e-2Nm)
Ka = Amplifier Gain Constant (.1A)
From Figure 2.6 and Figure 2.7, the Coulomb frictions and the viscous frictions
are obtained. The Coulomb frictions are the two end points of the line where steady state
velocity is zero, and the viscous frictions are the velocity of the line where it connects the
maximum velocity to zero. From this fact, for the tilt axis, the negative Coulomb friction
came out to be -0.1365Nm, and the positive Coulomb friction came out to be 0.115Nm.
The negative viscous friction and positive viscous friction are 0.0082NmS/rad and
0.0150NmS/rad respectively. These values are calculated using script attached in the
back. Also for pan axis, negative Coulomb friction and positive Coulomb friction came
out to be -0.0945Nm, and negative Coulomb friction came out to be 0.0735Nm. The
negative viscous friction and positive viscous friction are 0.0218NmS/rad and
0.0582NmS/rad as displayed in Table 2.1.
xi

Axis
Coulomb Friction (Nm)
negative positive
Viscous Friction (NmS/rad)
negative positive
Tilt Axis -0.1365 0.115 0.0082 0.0150
Pan Axis -0.0945 0.0735 0.0218 0.0582
Table 2.1: Coulomb and Viscous Friction for Pan and Tilt Axis
Figure 2.6: Diagram of Torque vs. Steady State Velocity of Tilt Axis
xii

Figure 2.7: Diagram of Torque vs. Steady State Velocity for Pan Axis
Tolerance Analysis
The data captured from the above procedure will not be in our project for two
reasons. First because only the pan and tilt mechanism was tested without the firing
mechanism since mounting the firing mechanism has not been done yet. The second
reason is because the testing was done before the pulse width for impulse was given. The
testing was done with the pulse width of 0.01 seconds when the suggested pulse width for
impulse is 0.25 seconds. Further testing will be done using the impulse of 0.25 seconds
to determine if it yields better results. Therefore, more accurate friction testing should be
done once the mechanism is complete with the right value of pulse width.
xiii

2.2 Model Development
Friction Parameters
θ + a
1 θ L + a sgn(
2 θ L ) = a3V
+ a4
sinθ
L
Equation 2.1
The equation above was provided during the class lecture and the Simulink model
file shown in Figure 2.8 is driven from it. The corresponding MATLAB code can be
found in Appendix A. The chirp was used as input voltage which is a sinusoidal wave
and it has frequency that increases from 0.1Hz to 10Hz in 20 seconds.
Figure 2.8: Simulink Model File for the Parameter Equations
Through some integrations and simplifications, matrices were developed in terms
of θ , θ , V, sample time, and parameter a1, a2, a3, and a4.
⎡−
( 2 2
θ +
0 θ ) ∆t
− ( θ +
0 θ1
) ∆t
1
2V0
( θ1
−θ
) − −
0
⎤
⎢ 2 2
A =
⎢−
( θ1
+ θ 2 ) ∆t
− ( θ +
1 θ ) ∆t
2V
2
1(
θ 2 −θ
) − −
⎥
1
⎥
⎢
⎢
⎥
⎥
2 2
⎢⎣
− ( θ N −1
+ θ N ) ∆t
− ( θ + θ ) ∆t
2VN
−1(
θ N −θ
N −1)
− − − ⎦ ) cos
(cos 2
2(cosθ1
cosθ
0 )
2(cosθ
2 cosθ1
)
θ N θ N 1
N − 1
N
xiv

⎡ 2 2
θ − ⎤
1 θ 0
⎡a1
⎤
⎢ ⎥
⎢ 2 2
θ −
⎢ ⎥
2 θ1
⎥
b = ⎢ ⎥ a = ⎢
a2
⎥
a = pinv(A)*b
⎢
⎢a
⎥ 3
⎥
⎢ ⎥
⎢ 2 2 ⎥
⎣θ
N − θ N −1
⎦
⎣a4
⎦
The data which was achieved when the parameters, a1, a2, a3, and a4 were set to be
random numbers, 1, 2, 3, and 4 respectively, was again used to calculate parameters using
above method. a1 was calculated and came out to be 1.0053, a2 came out to be 1.7730, a3
came out to be 2.8580, and a4 was came out to be 4.0053. All four parameters were very
close to their original values. This proves that the above method is valid.
With chirp input that was described in advance, thetas and angular velocities were
obtained from pan and tilt mechanism. With this data, the parameters, a1 through a4
were calculated for both pan and tilt axes.
a1 a2 a3 a4
tilt 128.9306 -566.2103 898.5276 121.5573
pan 43 -23656 -12418 0
Table 2.2: Parameters for pan and tilt axes
Figures 2.9 through 2.12 below are the actual angular velocity and the angular
velocity generated from modeling. The actual angular velocities are filtered in the same
way as they were in friction identification through three filtering steps.
xv

Figure 2.9: Angular velocity measured from the tilt motor
Figure 2.10: Tilt Angular velocity simulated from the model
xvi

Figure 2.11: Angular velocity measured from the pan motor
Figure 2.12: Pan Angular velocity simulated from the model
xvii

To consider the noise, random input was added to the theta. Results seemed to be
close enough to the original value when the noise was less than 0.000001. Figure 2.13
shows the Simulink diagram used.
Figure 2.13: Parameter equation verification with noise consideration
The table below shows how much the noise effects the parameters. The error is
Parametermeasured − Parameteractual
calculated using
equation.
Parameter
actual
noise gain a1 a2 a3 a4 error
0.1 7 -1558 2952 -26884 -6513
0.01 5.1 -138.5 205.1 2285.7 571.6416
0.001 -48.7 -19.1 -63 -1281.5 -403.625
0.0001 -132.732 -16.6409 -18.2091 -266.7625 -217.8127
0.00001 -0.3162 1.3461 2.7369 0.7359 -2.546875
0.000001 1.0444 1.9809 3.0036 4.0307 0.043725
Table 2.3: Variation of the parameters with respect to noise
xviii

Tolerance Analysis
Even though it was very time consuming and difficult to finish, the actual data
and the results from modeling do not match too well. There can be many factors that
could contribute to the failure. Thus, the solution would be to collect the data until the
most reasonable set is found. Moreover, noise should be considered after realistic
parameters are found.
xix

2.3 Validation
Launcher Verification
To verify that the toy disc shooter obtained would be consistent and accurate
enough to be viable for use in our system a few tests were run. The first test was a simple
test to determine consistency. Holding the gun on a level surface and aiming it at a pint
glass on the same level surface, the gun was fired 5 times at a set distance. A diagram of
this testing procedure can be seen in figure 2.14.
Figure 2.14: Launcher Testing Procedure
This was repeated for three trials for each distance. The number of times the disc
hit the glass was recorded and the percent of that number out of 5 was put in the table.
The Total Accuracy of the disc shooter at that set distance was then averaged from the
averages obtained from the three trials. The results of this experiment are listed in Table
2.4.
Distance Try 1 Try 2 Try 3 Total Accuracy
3ft 0.9m 100% 100% 100% 100%
5ft 1.5m 80% 100% 100% 93.33%
7ft 2.1m 80% 80% 80% 80%
9ft 2.75m 80% 60% 80% 73.33%
11ft 3.35m 80% 100% 80% 86.67%
13ft 4m 60% 60% 40% 53%
Table 2.4: Disc Shooter Accuracy
xx

Finding the results of this first experiment satisfactory, it was decided that the disc
shooter would be used. To obtain a more accurate understanding of how the disc is fired
and how it travels a second test was designed to determine the trajectory of the disc after
being launched from the toy gun. This experiment was set up very similarly to the
previous one. The gun was held on a level surface and now aimed at a piece of paper
with a graph drawn on it. This graph had marks for each centimeter vertically and
horizontally away from the origin and was taped to the wall so that the origin was on the
same level surface as that of the barrel of the toy gun. This experiment is diagrammed in
figure 2.15
Figure 2.15: 2 nd Launcher Testing Procedure
The gun was fired 10 times at a set distance and the x and y coordinates where the
disc hit were recorded for each shot. The gun was then moved to another set distance and
theexperiment was repeated. The results of this experiment are listed in Table 2.5.
x position
in cm
from
origin
0.5 m 1.0 m 1.5 m 2.0m
y position
in cm
from
origin
x position
in cm
from
origin
y position
in cm
from
origin
x position
in cm
from
origin
y position
in cm
from
origin
x position
in cm
from
origin
y position
in cm
from
origin
Shot
#
1 -2 -1 0 -6 0 -10 X X
2 -2 -1 0 -3 -1 -11 X X
3 0 -1 1 -5 5 -9 X X
4 -2 -2 -3 -5 2 -11 X X
5 -1 -2 1 -5 1 -9 X X
6 1 -1 -2 -5 -1 -10 X X
7 -1 0 -3 -5 -1 -10 -1 -13
8 -2 0 2 -4 2 -9 X X
9 -2 0 0 -6 -2 -11 X X
10 0 0 -2 -5 -2 -11 X X
• x means the disc hit lower than -14cm and could not be recorded
Table 2.5: Preliminary Trajectory Results
The conclusion drawn from this experiment was that the trajectory should be
determined from data collected between 0.5 and 1.5 meters. Anything before 0.5 meters
will be fired at a negative angle and anything after 1.5 meters will be fired at a positive
xxi

angle relative to the horizon. This led to the next experiment that was done in the exact
same matter as above. The result of the trajectory experiment with data from 0.5 to 1.5
meters is shown in Table 2.6. The experiment is graphed in Figure 2.16.
0.5 m
(x
position
in cm
from
origin)
0.5 m
(y
position
in cm
from
origin)
0.7 m
(x
position
in cm
from
origin)
0.7 m
(y
position
in cm
from
origin)
0.9 m
(x
position
in cm
from
origin)
0.9 m
(y
position
in cm
from
origin)
Shot
#
1 -2 -1 1 -2 0 -4
2 -2 -1 0 -2 2 -3
3 0 -1 2 -2 -1 -5
4 -2 -2 -2 -2 -2 -4
5 -1 -2 4 -1 0 -3
6 1 -1 3 -2 -1 -4
7 -1 0 -2 -1 -1 -5
8 -2 0 -2 -1 1 -3
9 -2 0 -1 -2 3 -2
10 0 0 3 0 0 -2
1.0 m (x
position
in cm
from
origin)
1.0 m (y
position
in cm
from
origin)
1.1 m (x
position
in cm
from
origin)
1.1 m (y
position
in cm
from
origin)
1.3 m (x
position
in cm
from
origin)
1.3 m (y
position
in cm
from
origin)
1.5 m (x
position
in cm
from
origin)
1.5 m (y
position
in cm
from
origin)
0 -6 0 -5 0 -6 0 -10
0 -3 -2 -6 -1 -7 -1 -11
1 -5 -1 -6 -5 -6 5 -9
-3 -5 -2 -8 -3 -10 2 -11
1 -5 0 -5 -5 -10 1 -9
-2 -5 0 -6 1 -5 -1 -10
-3 -5 0 -6 2 -6 -1 -10
2 -4 -1 -8 0 -8 2 -9
0 -6 2 -7 2 -5 -2 -11
-2 -5 -2 -7 -2 -9 -2 -11
Table 2.6: Short Range Trajectory Results
xxii

y-position (cm)
Position of each individual trial disc at target from given distance
4
2
0
-6 -4 -2 0 2 4 6
-2
-4
-6
-8
-10
-12
x-position (cm)
Figure 2.16: Plot of Short Range Trajectory Results
From 0.5 meters
From 0.7 meters
From 0.9 meters
From 1.0 meters
From 1.1 meters
From 1.3 meters
From 1.5 meters
A summary of this experiment can be seen in the Table 2.7, which shows the
average x and y positions at each distance in cm.
0.5 m (x 0.5 m (y 0.7 m (x 0.7 m (y 0.9 m (x 0.9 m (y
position) position) position) position) position) position)
-1.1 -0.8 0.6 -1.5 0.1 -3.5
1.0 m (x 1.0 m (y 1.1 m (x 1.1 m (y 1.3 m (x 1.3 m (y 1.5 m (x 1.5 m (y
position) position) position) position) position) position) position) position)
-0.6 -4.9 -0.6 -6.4 -1.1 -7.2 0.3 -10.1
Table 2.7: Average Short Range Trajectory
From this data, it can be concluded that the horizontal position of the disc stays
relatively close to straight with a maximum of 1 cm average deviation from the origin. It
can also be seen that as the distance from the target increases, the vertical position that
the disc strikes the target also decreases. A plot of distance from target (in meters) vs.
vertical position relative to the horizontal (in centimeters) is shown in Figure 2.17.
xxiii

Average Vertical Displacement (cm)
4
2
0
-2
-4
-6
-8
-10
-12
Average Vertical Displacement vs. Distance from launcher to target
0.5 0.7 0.9 1 1.1 1.3 1.5
Distance from launcher to target (meters)
Average
Standard Deviation
Figure 2.17: Average Vertical Displacement vs Distance from launcher to target
Fitting a best-fit line to this data, the equation is found to be: Y = -9.5X +
4.58571429, where X is the distance from the gun barrel to the target and Y would be the
vertical displacement where the disc would hit the target. This equation is a good
estimation of the trajectory of the disc knowing the distance to the target between 0.5 and
1.5 meters. This equation can be used to estimate the vertical position at which the disc
will strike the target if the distance from the launcher barrel to the target is known. This
equation can also be used to estimate the distance the launcher is from the target given
the vertical displacement of the striking area of the disc. A final use for this equation
comes into the learning algorithm where knowing both the distance from the launcher to
the target and the vertical displacement of the disc at the target, the algorithm can check
the accuracy of the shot by comparing it with this model. This will later be expanded to
range from zero to three meters after the disc launcher has been mounted and angled tests
can be done.
The size of the target will dictate the required accuracy for the system. The initial
expectation is that the firing system be able to consistently hit within a 7.5 cm diameter
circle at a maximum range of 1.5m, when at a zero degree tilt. Through simple
trigonometry, it can be deduced that ensuring an impact within 3.25 cm of center at 1.5 m
requires that the rotational position be within ±1.24 degrees. Taking into account the
standard deviation of the horizontal deviations shown in Table 2.7 and Figure 2.17, the
largest standard deviation was 2.60 cm, with the deviation at 1.5m being 2.21 cm. By
subtracting the standard deviation from the allowable error, a circle of approximately 1
cm radius is left, resulting in a maximum position error of ±0.382 degrees. The specified
error of ±0.1 degrees falls well within the tolerable error, and should allow for the desired
target to be hit at an even greater range with consistency. The mechanism itself should
xxiv

have no difficulty achieving this low error, as the encoder allows for accuracy within
0.0439 degrees since it has a 2048 bit quadrature reading on the output shaft. Figure 2.18
shows the offset resulting from the possible position errors discussed above. Since the
current trajectory of vertical motion is a best-fit line, it can be assumed that the same
values will hold true for the tilt axis. These are likely to differ once a more precise
trajectory can be calculated experimentally; however it appears that a ±0.1 degree error
will supply the necessary accuracy and feasibility for the project.
0.04
0.03
0.02
0.01
0
-0.01
X: 1.5
Y: 0.01
X: 1.5
Y: -0.002618
-0.02
Target Cone
Target Cone
-0.03
Allowable Error
Allowable Error
Desired Error
Desired Error
X: 1.5
Y: -0.03246
-0.04
0 0.5 1 1.5
Figure 2.18: Target Cones Resulting from Different Position Errors
Since the control design has not yet been completed, it is not possible to do any
tests on the rise time, settling time, steady state error, or percent overshoot. As such, the
temporary values for those in the specification have been taken from the previous year’s
project [1], as the application of the system is fairly similar, and for the time being, will
serve our purposes until we can obtain more accurate values. Fortunately, the main
criteria for the system is rotational accuracy, so any minor discrepancies in the actual
specifications beyond that should be tolerable.
xxv

2.4 Learning Algorithm
Since it is not expected that the disc will hit the touchpad exactly on target the first time,
an iterative learning algorithm is being developed in order to correct for any error that
occurs. The learning algorithm is to be developed using MATLAB and Simulink
software. It works by taking the touchpad data regarding the positional error and
calculating new pan and tilt angles to reduce the error and hopefully hit the target on the
next launch. If the disc does not hit the target on the next launch, the process is repeated
with the error becoming smaller and smaller each time until the disc successfully hits the
target.
A learning algorithm requires that the launcher be repeatable. Unfortunately,
initial testing results proved that the launcher used in this system is not perfectly
repeatable. According to the initial launcher testing, there was some deviation of the
point of impact when the launch was repeated under identical conditions. Even though
that error occurs, it was determined that the launcher is a valid option for this project.
Occasionally a disc will behave very irregularly when launched and will not follow a
normal trajectory. This can cause a major problem when implementing a learning
algorithm that assumes repeatability. If a normal trajectory at a specified pan and tilt
angle would miss the target by two centimeters to the left, the correct action regarding
error correction would be to correct for an error of two centimeters to the right along the
x-axis. If, for example the disc were slightly bent, and curved more than usual because of
this, then the same pan and tilt angle could end up yielding an error of ten centimeters to
the left, even though the predicted trajectory would hit only two centimeters to the left. If
that error of ten centimeters were corrected, there would be a large amount of overshoot
in the correction. Assuming the next disc launches properly, it would hit the touchpad
somewhere around 8 centimeters to the right of the target. The diagram in Figure 2.19
should illustrate this more clearly.
xxvi

Figure 2.19: Error Correction for Unusual Cases
In order to compensate for this problem, the learning algorithm will check for
accuracy so that it can be determined whether or not the particular launch is an unusual
case. Once the gun is mounted, more extensive testing of the launcher should be possible
and advanced trajectory equations will be obtained. With more testing once the launcher
is mounted, an advanced trajectory system can be obtained. The advanced trajectory
equations should be able to predict a point of impact for a disc launched at any given
distance and pan and tilt angle. This predicted point of impact will not be completely
accurate since the launcher is not perfectly repeatable, however, it should yield a good
estimate of where the disc should hit the touchpad. The actual point of impact is
compared to the point predicted by the advanced trajectory to determine if that particular
launch is within the range of accuracy. If the point of impact is found to be outside the
range of accuracy, then the launch will be considered inaccurate and no error correction
will occur. After the initial testing, it was determined that the range of accuracy will be
within a 6 cm of the projected point of impact in both the x and the y direction.
According to the initial launcher testing results shown in Table 2.6 in the launcher
verification section, the maximum distance between observed points of impact at any
distance was 6 cm. Once the gun is mounted and the touchpad controller is obtained,
more additional testing will be needed to confirm that 6 cm is a suitable accuracy range.
If the launch is outside that radius, no error correction will occur and another disc will be
launched at that pan and tilt angle.
xxvii

If a launch is determined to be accurate, the learning algorithm will then use the
data from the touchpad regarding the Cartesian Coordinates of the point of impact and the
center of the target to calculate the error in the x and y direction. Inverse kinematics are
then used to transform the distance from the point of impact to the center of the target
into a desired pan and tilt angle. The distance in Cartesian Coordinates in the X direction
will be converted into a desired pan angle and the distance in the Y direction will be
converted to a desired tilt angle.
A potential problem is the fact that the distance will change slightly as the pan or
tilt angle changes due to the fact that the touchpad is flat. Figure 2.20 shows that the
distance will be slightly greater when aiming at a point nearer to the edge of the touchpad
since the equilibrium position will be pointed directly at the center of the touchpad. The
principle is the same for the x-direction and the y-direction.
Figure 2.20: Distance to Edge of Touchpad
The touchpad is 30 centimeters wide and therefore the maximum distance from
the center in the x direction is positive or negative 15 cm. It is 20 cm high and therefore
the maximum change in vertical distance is positive or negative 10 cm. Table 2.8 shows
the positional changes in point of impact that would be predicted as a result of the slight
changes in distance due to pointing at the edge of the touchpad. Calculations were only
done for the points at the very edges of the touchpad because those points give the
maximum change that would occur. The original values for the deviation from x = 0 and
y = 0 at the equilibrium angle were taken from Table 2.7 in the launcher verification
section.
xxviii

Effects of Aiming at the Edges of the Touchpad (x-direction)
Dist. From pad (equillibrium)
(in m)
Pan angle require to point at 15
0.5 0.7 0.9 1.0 1.1 m 1.3 1.5
cm in x-direction (degrees)
Distance from pad (pointed at 15
16.700 12.094 9.462 8.531 7.765 6.582 5.711
cm) (in m)
Deviation y = 0 at 0 degrees
0.522 0.716 0.912 1.011 1.110 1.309 1.507
(equilibrium) (in meters) -0.008 -0.015 -0.035 -0.049 -0.064 -0.072 -0.101
Deviation y = 0 at the pan angle
- -
required to point at 15 cm (in m) -0.0085 0.0155 0.0357 -0.0498 -0.0649 -0.0727 -0.1017
Difference (m)
Deviation from x = 0 at 0 degree
..0005 0.0005 0.0007 0.0008 0.0009 0.0007 0.0007
pan angle (in meters)
Deviation x = 0 at the pan angle
-0.011 0.006 0.001 -0.006 -0.006 -0.011 0.003
required to point at 15 cm (in m) -0.0117 0.0062 0.001 -0.0061 -0.0061 -0.011 0.003
Difference 0.0007 0.0002 0 0.0001 0.0001 0 0
Table 2.8: Effect of Distance Change due to Angle Change(x-direction)
Effects of Aiming at the Edges of the Touchpad (x-direction)
Dist. From pad (equillibrium)
(in m)
Tilt angle require to point at 10
0.5 0.7 0.9 1.0 1.1 m 1.3 1.5
cm in y-direction (degrees)
Distance from pad (pointed at 10
11.310 8.130 6.340 5.711 5.194 4.399 3.814
cm) (in m)
Deviation y = 0 at 0 degrees
0.510 0.707 0.906 1.005 1.105 1.304 1.503
(equilibrium) (in meters) -0.008 -0.015 -0.035 -0.049 -0.064 -0.072 -0.101
Deviation y = 0 at the pan angle
- -
required to point at 15 cm (in m) -0.0084 0.0153 0.0356 -0.0498 -0.0647 -0.0726 -0.1017
Difference (m)
Deviation from x = 0 at 0 degree
..0004 0.0003 0.0006 0.0008 0.0007 0.0006 0.0007
pan angle (in meters)
Deviation x = 0 at the pan angle
-0.011 0.006 0.001 -0.006 -0.006 -0.011 0.003
required to point at 15 cm (in m) -0.0115 0.0061 0.001 -0.0061 -0.0061 -0.011 0.003
Difference 0.0005 0.0001 0 0.0001 0.0001 0 0
Table 2.9: Effect of Distance Change due to Angle Change(y-direction)
The changes in predicted point of impact due to changes in distance to touchpad
resulting from a change in angle are on the order of 10^-4 and are therefore negligible
since they are very small compared to the deviations from x = 0 and y = 0. Therefore, the
change in distance to the touchpad need not be taken into account.
xxix

A flow chart depicting the learning algorithm is displayed in Figure 2.21
Figure 2.21: Learning Algorithm Chart
In summary, the learning algorithm will work as follows. The initial disc will be
launched at the touchpad. Using the advanced trajectory models, the projected point of
impact for the given distance and angles will be calculated in Cartesian coordinates.
When the disc hits the touch pad, the touchpad will give back data regarding the actual
point of impact, and the location of the target. First the actual point of impact will be
compared to the projected point of impact. If the actual point of impact is greater then
xxx

6 cm away from the projected point of impact in either the x or the y direction, the launch
will be considered an unusual case and determined inaccurate and another launch will
take place. If the point of impact is within the range of accuracy then the error is
computed using the data from the touchpad. The error will be given in terms of Cartesian
Coordinates and therefore has to be transformed into a desired pan and tilt angle using
inverse kinematics. Once the desired pan and tilt angle is reached, another disc is
launched. If this next disc hits the target, then the process is complete. If the disc does not
hit the target, the process repeats itself until a launch successfully hits the target.
xxxi

2.5 Subsystem Development
Mounting and Automated Firing
To mount the launcher to the pan and tilt mechanism and allowing for automated
firing required a whole new look at out system. First a way to mount the launcher to a flat
surface that could pan and tilt was necessary. The design in Figure 2.22 illustrates the
solution to this problem.
Figure 2.22: Aluminum Mounting Base
We’ve since acquired a proper sized piece aluminum stock and cut and drilled it
to specifications. The drilled hole in the bottom is where the shaft of the tilt axis will slide
through and be set-screwed securely on. Once this is in place, a flat surface perpendicular
to the tilt shaft is now available to mount the launcher on.
Next we reduced the launcher to only it’s necessary components for firing discs.
An illustration of this piece can be seen in Figure 2.23. By simply connecting the disc
spinning motor to a power source, the launcher can now fire discs as before with less
weight, drag, and a now flat and easily mountable surface.
xxxii

Figure 2.23: Disc Launcher
This reduction of the launcher removed our trigger, but this actually aided in the
mounting process. Now, by simply connecting a DC motor to the gear on the bottom of
our launcher, the motor will turn a set distance, which will turn the gear, which will then
push the disc into the launching chamber causing it to fire when it meets the spinning
wheel powered by the motor on the launcher. See figure 2.24. By simply reversing the
voltage on the DC motor for the same set time, the gun can reload also.
Figure 2.24: Automated Firing
Now to fit the motor in between the base and launcher simple screws, nuts, and
washers will be all that is needed. The motor will screw into position on the base. Then
the launcher will be placed above it and the gear on the motor aligned with the gear on
the launcher arm. This will be then screwed into the base, using the screws to suspend the
xxxiii

launcher in the air while holding it firmly onto the base, the long screw length acting as
spacers for the motor. Figure 2.25 demonstrates the mounting of our launching system on
the pan and tilt mechanism.
Figure 2.25: Mounting of System
xxxiv

3. SUMMARY OF PROGRESS
3.1 Plan
For the most part, the initial plan has remained unchanged. When complete, the
system should be able to successfully launch a disc at a touchpad and implement a
learning algorithm to correct for the error; eventually having the foam disc hit the target.
Other than delays in needed components of the system, the project seems to be
moving along well. Though this has slowed progress down and pushed the schedule back,
no more setbacks of this nature are expected. An anticipated change to the original plan
of action may be the removal of the IR sensor since, at this point, it is not looking like
there will be sufficient time to complete it. The IR sensor is an added component that will
only be utilized if time permits. Though we may have to play catch-up in the next couple
of weeks, completion of our project on time is still very feasible.
3.2 Schedule
Thus far the plan of action has been followed very closely and seems to be
working out well for the most part. Unfortunately a few tasks are slightly behind
schedule and this has held up progress on some aspects of this project somewhat. The
mounting and automatic firing of the disc launcher is behind due to slow retrieval of
necessary materials such as the aluminum stock and DC motor. This will be finished this
week, about 2 weeks late. The advanced trajectory model will then be next; it depends on
the mounting of the gun so therefore cannot be started until the mounting is completely
finished. The modeling and simulation has been continually progressing and is still
advancing according to schedule. The learning algorithm is in the process of being
developed and is currently progressing according to schedule. At this point, all of the
necessary parts for the system have been obtained except a controller for the touchpad.
The original plan was to use the touchpad controller used by the group that worked with
the touchpad last year, however this was unable to be found. Due to this, touchpad
testing and development will be delayed about a week.
For our modeling and simulation, Yena and Diana have completed some more
friction identification and parameter identification. They have also begun work on the
modeling of the pan and tilt mechanism. Ryan has begun calibration and kinematics and
is learning about employing the touchpad. Josh has begun physical modeling and has
created and obtained all necessary parts for the mounting and automatic firing of the disc
launcher. These are all necessary initial phases in our plan of action. We are currently
working on completing these and have even begun some work in the next phase of our
plan of action. We have obtained the touchpad and are seeking a controller for it and we
have begun to design and develop the learning algorithm.
xxxv

3.3 Cost
As for cost of the system, our analysis was quite accurate. The touchpad cost us a
total of $25.00, off .05 from our $24.95 estimate. Also, our DC motor only cost us $3.00,
a savings of $2.50 off our original estimate. However, having to purchase a controller for
our touchpad now seems highly probable. This is an extra cost we did not budget for and
is now estimated to cost us $40. The updated cost of the assembled pan and tilt system
used as the basis of this project has been itemized and calculated as follows in Table 3.2.
Item
Motor
Timing Belt
Part Number Price ($) Quantity Total ($)
GM8724S017 192.86 [1] 2 385.72
A6Z16-C01806 1.86 [1] 2 2.70
Encoder
S1 & S2 Optical Shaft 49.00 [3]
Encoders
2 98.00
Gear
A6A6-75NF01812 15.15 [1] 2 30.30
A6A6-25DF01806 7.76 [1] 2 15.52
Total 532.24
Table 3.1: Pan and Tilt Mechanism Cost
The costs of additional parts and programs needed for our complete system
beyond those of the assembled pan and tilt mechanism are listed in Table 3.3.
xxxvi

Item
Toy Disc Shooter and Discs
Touchpad
Touchpad Controller
Wires (spool)
Programs:
SolidWorks
MATLAB 7
Simulink 6
Motor [6]
Gears [6]
Sensors:
Infrared LED [5]
Infrared Detector [5]
Clamps (for Mounting)
TOTAL
Price ($) Quantity Total
4.97 2 9.94
24.95 [4]
40.00
1 24.95
40.00
4.00 1 4.00
64.98 [7]
1900.00[2]
2800.00[7]
3.00
2.25
0.60
2.75
1
4
4
1
1
2
1
64.98
7,600.00
11,200.00
3.00
2.25
1.20
2.75
8.95 1 8.95
Table 3.3: Additional Parts Needed for System
18,962.03
The labor cost of designing, building, testing and operating the system among the
four members of this group project are listed in Table 3.4.
Laborer Salary ($/hr) Hours/Week Weeks Total ($)
Ryan Kindle
25 10 10 2,500
Diana Mirabello
Yena Park
Josh Schuster
Total for 4 Employees ($)
25 10 10 2,500
25 10 10 2,500
25 10 10 2,500
Table 3.4: Labor Costs
10,000
xxxvii

The use of different labs to build and test our system has been assumed to cost as
follows in Table 3.5 and the total system costs are listed in Table 3.6.
Lab Rate ($/day) Use (days) Total ($)
Control Systems Lab 50 30 3,000
Engineering Lab
50 4 200
Total 3,200
Table 3.5: Lab Usage
Pan and Tilt
Mechanism
$532.24
Additional Parts Needed for
System
Labor Costs Lab Use Total
$18,922.02 $10,000 $3,200 $32,694.26
Table 3.6: Total System Costs
Seeing as many of the components, programs, labs and equipment are provided
free of charge, along with the fact that there is no labor cost, the actual cost to our group
can be calculated and are displayed in Table 3.7.
Pan and Tilt
Mechanism
$0
Additional Parts Needed for
System
Labor Costs Lab Use Total
$97.04 $0 $0 $97.04
3.4 Unanticipated Challenges
Table 3.7: Actual Cost of System
During the development of the system, a few unanticipated challenges have come
up. The first was with the touchpad control. It was expected that the touchpad controller
from last year’s team could be used, however that controller has yet to be found. This
caused some delay in obtaining a controller because now it has to be ordered and
researched. Another challenge was in the mounting of the system. A chunk of aluminum
stock was needed to make the base for the launcher to sit on, however there was some
difficulty in obtaining this because the machine shop did not have it readily available.
Another challenge encountered was with the automated firing of the mechanism. There
has been some difficulty in hooking the DC motor up to the xpc target so that it can be
controlled through MATLAB and Simulink .
xxxviii

3.5 Forecast
For the remainder of the project, we consider it reasonable to predict that we will
have a working automated disc launcher by the end of the semester. We will be able to
automate the firing and implement the learning algorithm. We currently do not believe
that we will be able to complete the IR sensor for initial sensing of the location of the
touchpad and therefore the first launch will most likely be aimed manually. Since there
have been a few setbacks with some aspects of this project, we feel that it is in our best
interest to concentrate on catching up with our original schedule and successfully
completing all of parts of the project which we consider to be the most important. It is
reasonable for us to predict that we will get all of the other aspects of the project done
successfully.
xxxix

4. BIBLIOGRAPHY
[1] Bowen, Luke, Cieloszyk, Matt and Gillette, Rob. “Team 5 Proposal.” Team 5
Proposal. 2/22/2004.
http://www.cat.rpi.edu/~wen/ECSE4962S04/proposal/team5proposal.pdf
[2] Strassberg, Dan. “Math, simulation updates offer new programming tools, faster
development.” EDN.com. 6/10/2004. http://www.edn.com/article/CA421495.html
[3] Wen, John. “S1 & S2 Optical Shaft Encoders.” Encoder Datasheet. 9/26/02.
http://www.cat.rpi.edu/~wen/ECSE4962S03/encoder_datasheet.pdf
[4] “Action Solutions.” Action Solutions. 2004.
http://www.actionsolutions.com/subcat.asp?departmentid=74
[5] “High Power Infrared LEDs.” Reynolds Electronics. 2000.
http://www.rentron.com/Products/Electronic-Components.htm
[6] “Motors, Servos, Wheels and H-Bridges Section.” Hobby Engineering. 2/28/2005.
http://www.hobbyengineering.com/SectionM.html
[7] “SolidWorks Student Edition 2004-2005.” JourneyEd.com. 2004.
http://www.journeyed.com/itemDetail.asp?GEN0=01&GEN1=01&GEN2=SOLI
DWORKS&GEN3=JEM&T1=36785643FS6
xl

5. Statement of Contribution
Here is the breakdown for who wrote the various sections of this report
Introduction Ryan Kindle
Friction Identification Yena Park
Model Development Yena Park
Validation Josh Schuster
Ryan Kindle
Learning Algorithm Diana Mirabello
Subsystem Development Josh Schuster
Summary of Progress Josh Schuster
Compiling and Editing Diana Mirabello
______________________________
Josh Schuster
______________________________
Yena Park
______________________________
Diana Mirabello
______________________________
Ryan Kindle
xli

Appendix A
MATLAB Code
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%friction_param_setup.m
%02/26/05
%By Yena Park
%set the initial values for friction_param.mdl
%put the logs on the signals
%subsystem under friction_param.mdl needs to be selected before running this file
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
ts = 0.001; %sample time
const_voltage = 1;
peak_voltage =10;
handles = get_param(gcb, 'porthandles');
outputports = handles.Outport;
for i = 1 :length(outputports)
set_param(outputports(i), 'DataLogging', 'on');
set_param(outputports(i), 'TestPoint', 'on');
end
set_param(outputports(1), 'Name', 'theta1_log');
set_param(outputports(2), 'Name', 'thetadot1_log');
set_param(outputports(3), 'Name', 'theta2_log');
set_param(outputports(4), 'Name', 'thetadot2_log');
set_param(outputports(5), 'Name', 'voltage_log');
xlii

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%friction_param_save.m
%02/26/05
%By Yena Park
%run friction_param.mdl in a for loop
%collect the data and plot it
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
voltage_range = [-1:.05:1];
times = [0:0.001:5];
for k = 1:length(voltage_range)
voltage_range(k)
for i = 1 : 5
setparam(tg, 28, voltage_range(k));
i
if voltage_range(k)==0
else
if voltage_range(k)>0
setparam(tg, 27, 10);
setparam(tg, 24, 10);
else
setparam(tg, 27, -10);
setparam(tg, 24, -10);
end
start(tg);
pause(5);
stop(tg);
outputlog = tg.OutputLog;
theta_1(i, :) = outputlog(:, 1);
theta_dot_1(i, :) = outputlog(:, 2);
voltage_out(i, :) = outputlog(:, 5);
pause(.5);
end
end
%first filtering
thetadot_ave_temp(k, :) = (theta_dot_1(1, :)+theta_dot_1(2, :)+theta_dot_1(3,
:)+theta_dot_1(4, :)+theta_dot_1(5, :))/5;
%second filtering
xliii

for j = 1 : length(thetadot_ave_temp(k, :)) - 25
sum = 0;
for ii = 0 : 24
sum = sum + thetadot_ave_temp(k, j+ii);
end
thetadot_ave(k,j) = sum/25;
end
end
%third filtering
for i = 1 : 41
for j = 1 : 4975
if abs(thetadot_ave(i, j) - thetadot_ave(i, j+1))>1
thetadot_ave(i, j +1) = (thetadot_ave(i, j) + thetadot_ave(i, j + 2))/2;
end
end
end
for i = 1 : 25
plot(times(1:4976), thetadot_ave(i, :));
hold on;
end
ylabel('thetadot');
xlabel('second');
title('Tilt Axis');
save tilt_axis.mat thetadot_ave_temp thetadot_ave
xliv

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%steady_state1.m
%2/27/05
%By Yena Park
%calculate steady state velocity
%calculate torque
%plot torque vs. velocity
%calculate frictions
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
voltage = [-1:.05:1];
%calculate Torque
N1 = 2.47; %External Gear Ratio
Nm1 = 19.5; %Internal Gear Ratio
Kt = 4.36e-2; %motor torque constant
Ka = .1; %amplifier gain constant
torque = voltage .* N1 * Nm1 * Kt * Ka;
k = 1;
positive = 0;
viscous_friction_negative_sum = 0;
viscous_friction_positive_sum = 0;
negative_count = 0;
positive_count = 0;
for i = 1 : 22
thetadot1_ss(i) = 0;
for j = 4976-1000:4976
thetadot1_ss(i) = thetadot1_ss(i) + thetadot1_ave(i, j)/1000;
end
if abs(thetadot1_ss(i)) < 0.0001
save_torque(k) = torque(i);
k = k + 1;
positive = 1;
elseif i ~= 1 && abs(thetadot1_ss(i) - thetadot1_ss(i-1))>0.05
if positive ==0
viscous_friction_negative_sum = viscous_friction_negative_sum + (torque(i)torque(i-1))/(thetadot1_ss(i)-thetadot1_ss(i-1));
negative_count = negative_count + 1;
else
xlv

viscous_friction_positive_sum = viscous_friction_positive_sum + (torque(i)torque(i-1))/(thetadot1_ss(i)-thetadot1_ss(i-1));
positive_count = positive_count + 1;
end
end
end
coulomb_friction_negative_tilt = save_torque(1);
coulomb_friction_positive_tilt = save_torque(k-1);
viscous_friction_negative_tilt = viscous_friction_negative_sum/negative_count;
viscous_friction_positive_tilt = viscous_friction_positive_sum/positive_count;
plot(thetadot1_ss, torque)
xlabel('steady state velocity')
ylabel('torque');
title('Tilt Axis');
xlvi

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%param_save_tilt.m
%3/25/05
%By Yena Park
%to obtain the theta, thetadot, and inputvoltage
%to filter the thetadot
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear theta2 thetadot2 voltage_in voltage_in_sum theta2_sum thetadot2_sum
voltage_in_ave theta2_ave thetadot2_ave
times = [0:0.001:20];
for k = 1:10
start(tg);
pause(20);
stop(tg);
outputlog = tg.OutputLog;
theta1(k,:) = outputlog(:, 1);
thetadot1(k, :) = outputlog(:, 2);
voltage_in(k, :) = outputlog(:, 5);
pause(0.5);
end
voltage_in_sum(1:14285) = 0;
theta1_sum(1:14285) = 0;
thetadot1_sum(1:14285) = 0;
for i = 1 : 10
voltage_in_sum = voltage_in_sum + voltage_in(i, :);
theta1_sum = theta1_sum + theta1(i, :);
thetadot1_sum = thetadot1_sum + thetadot1(i, :);
end
voltage_in_ave = voltage_in_sum / 10;
theta1_ave = theta1_sum/10;
thetadot1_ave = thetadot1_sum/10;
xlvii

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%param_calculation.m
%3/26/05
%By Yena Park
%to get the parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
theta = logsout.theta;
theta_Data = theta.Data;
voltage = logsout.voltage;
voltage = voltage.Data;
ts = 0.001;
for j = 1 : length(theta_Data)-1
thetadot_Data(j) = (theta_Data(j+1) - theta_Data(j))/ts;
end
for i = 1 : length(theta_Data)-2
col1 = -(thetadot_Data(i)^2 + thetadot_Data(i+1)^2)*ts;
col2 = -(abs(thetadot_Data(i)) + abs(thetadot_Data(i+1)))*ts;
col3 = 2*voltage(i)*(theta_Data(i+1) - theta_Data(i));
col4 = -2*(cos(theta_Data(i+1)) - cos(theta_Data(i)));
A(i, :) = [col1 col2 col3 col4];
b(i) = thetadot_Data(i+1)^2 - thetadot_Data(i)^2;
end
a = pinv(A)*b'
xlviii