Integration of Controllers for Filter Algorithms for Construction Machine Guidance Alexander Beetz & Volker Schwieger Institute for Applications of Geodesy to Engineering, Universität Stuttgart
June 24-26, 2008 ETH Zurich
Structure 1. 2. 3 3. 4. 5. 6. 7.
Simulator for construction machine guidance PID – controller Implemented closed closed-loop loop system s stem Anticipated computation point Test drives Results Conclusion
June 24-26, 2008 ETH Zurich
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Simulator for construction machine guidance Remote control Laptop Position of tachymeter
A/D
.
Control signals over A/D-converter
Hardware Driving direction v = const. Vehicle with 360°- reflector in the center of gravity
- Leica TCRP1201 - Laptop with A/D Converter - Remote R t control t l - Model truck (1:14) Software - LabView©
June 24-26, 2008 ETH Zurich
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Implemented closed-loop system
June 24-26, 2008 ETH Zurich
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PID - controller ⎛ 1 e(t ) ⎞ ⎟ u (t ) PID = K P ⋅ ⎜⎜ e(t ) + ∫ e(t )dt + Tv ⋅ T dt ⎟⎠ n ⎝ Kp… Tn… Tv…
Gain for proportional controller (P-Control) Integrate time for I-Control Derivative time for D-Control
Step response of a PID-controller
June 24-26, 2008 ETH Zurich
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Anticipated computation point (a.c.p.) X
Ya.c. p. = Yc.o. g . + sin(θ ) ⋅ d X
X a.c. p. = X c.o. g . + cos(θ ) ⋅ d
Given trajectory . Orientation θ
Lateral deviation Moving direction
Vehicle d Center of gravity (c.o.g.)
Anticipated computation point (a.c.p.)
Y
June 24-26, 2008 ETH Zurich
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Anticipated computation point (a.c.p.) Computing the lateral deviation to center of gravity
Computing the lateral deviation to anticipated computation point
Vehicle Center of gravity Anticipated computation point
Given trajectory
June 24-26, 2008 ETH Zurich
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Anticipated computation point (a.c.p.) Computing the lateral deviation to center of gravity
Computing the lateral deviation to anticipated computation point
Vehicle Center of gravity Anticipated computation point
Given trajectory
June 24-26, 2008 ETH Zurich
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Anticipated computation point (a.c.p.) Computing the lateral deviation to center of gravity
Computing the lateral deviation to anticipated computation point
Vehicle Center of gravity Anticipated computation point
Given trajectory
June 24-26, 2008 ETH Zurich
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Anticipated computation point (a.c.p.) Computing the lateral deviation to center of gravity
Computing the lateral deviation to anticipated computation point
Vehicle Center of gravity Anticipated computation point
Given trajectory
June 24-26, 2008 ETH Zurich
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Anticipated computation point (a.c.p.) Computing the lateral deviation to center of gravity
Computing the lateral deviation to anticipated computation point
Vehicle Center of gravity Anticipated computation point
Faster reaction
Given trajectory
Moment of the steer angle in the opposite direction
June 24-26, 2008 ETH Zurich
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Anticipated computation point (a.c.p.) Computing the lateral deviation to center of gravity
Computing the lateral deviation to anticipated computation point
Vehicle Center of gravity Anticipated computation point
Given trajectory
Delayed y reaction Moment of the steer angle in the opposite direction
June 24-26, 2008 ETH Zurich
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Anticipated computation point (a.c.p.) Starting of the steering for the curve drive with a pre-control
Delayed starting of steering
Optimal distance between c.o.g. and a.c.p. = delay
Correct starting of steering
Problem: Distance between c.o.g. and a.c.p. > delay Î Starting of steering is too early
Center of Gravity (c.o.g.) Anticipated computation Point (a.c.p)
June 24-26, 2008 ETH Zurich
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Anticipated computation point (a.c.p.)
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Anticipated computation point (a.c.p.) Transient oscillation with different a.c.p.s
June 24-26, 2008 ETH Zurich
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Anticipated computation point (a.c.p.) Simulated transient oscillation using LabVIEW©:
distance between c.o.g. and a.c.p. = half of lateral deviation (25 cm)
June 24-26, 2008 ETH Zurich
difference between c.o.g. and a.c.p. = lateral deviation (50 cm)
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Test drives Constant parameters for the test drives: • starting point (middle of the straight line Æ nearly no lateral deviation) • velocity (8-10 cm/s) • position of the tachymeter • parameters of the Kalman filter • 4 laps for each controller without a stop • the first lap will be deleted due to errors of transient g g of the drive oscillation at the beginning • the a.c.p. is 2 cm in front of the c.o.g. (optimum for guiding behaviour)
June 24-26, 2008 ETH Zurich
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Results RMS 3-point-controller
[m]
RMS line [m]
RMS clot [m]
RMS curve [m]
Lap
gon, buffer = 0.001 m a.c. = 5 g
0.0038
0.0041
0.0020
0.0036
2
a.c. = 5 gon, buffer = 0.001 m
0.0033
0.0038
0.0032
0.0031
3
a.c. = 5 gon, buffer = 0.001 m
0.0024
0.0032
0.0020
0.0019
4
Arithmetic mean
0.0032
0.0037
0.0024
0.0029
KP =12.3
0.0032
0.0032
0.0030
0.0031
2
KP =12.3
0.0042
0.0053
0.0040
0.0032
3
KP =12.3
0.0034
0.0041
0.0035
0.0026
4
Arithmetic mean
0.0036
0.0042
0.0035
0.0030
P-controller
June 24-26, 2008 ETH Zurich
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Results RMS
RMS clot [m]
RMS curve [m]
Lap
PI
[m]
RMS line [m]
KP =12.140,, Tn =0.478
0.0030
0.0030
0.0027
0.0031
2
KP =12.140, Tn =0.478
0.0036
0.0030
0.0042
0.0036
3 4
KP =12.140, Tn =0.478
0.0032
0.0029
0.0034
0.0032
Arithmetic mean
0.0033
0.0030
0.0034
0.0033
KP=25.000, Tn=0.150, Tv=0.001
0.0027
0.0030
0.0026
0.0023
2
KP=25.000, Tn=0.150, Tv=0.001
0.0021
0.0016
0.0026
0.0023
3
KP=25.000, Tn=0.150, Tv=0.001
0.0023
0.0022
0.0028
0.0023
4
Arithmetic mean
0.0024
0.0023
0.0027
0.0023
PID
June 24-26, 2008 ETH Zurich
Results PID-controller
June 24-26, 2008 ETH Zurich
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Results PID-controller without Kalman filter
June 24-26, 2008 ETH Zurich
Results 3-point-controller
June 24-26, 2008 ETH Zurich
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Conclusion • • • •
A control quality of approx. 2.4 mm is achievable (TCRP1201, v=0.08 m/s, range 5-9m). The simulator works in real-time with different controllers in combination with the Kalman filter. The implementation of an anticipated computation point makes the whole system more stable . The anticipated computation point enhances the transient oscillation of the vehicle for lateral controlling.
Next steps • • •
Reduction of the systematic oscillation. Implementation of a dynamic anticipated computation point. point Integration of height control and longitudinal control for a real 3Dsimulator.
June 24-26, 2008 ETH Zurich
Thank you very much for your attention !!!
Contact: Dipl.-Ing. Alexander Beetz / PD Dr.-Ing. Volker Schwieger Institut für Anwendungen der Geodäsie im Bauwesen Institute for Applications of Geodesy to Engineering Universität Stuttgart Geschwister Scholl Str 24 D Geschwister-Scholl-Str. 70174 Stuttgart Phone: Fax: Email:
+49-711-685-84042 / -84064 +49-711-685-84044
[email protected] /
[email protected]
June 24-26, 2008 ETH Zurich
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Test drives Determination of value Kp Steering angle:
u (t ) = K p ⋅ e (t ) Resulting radius:
R=
l u (t )
l… Wheelbase of model truck
June 24-26, 2008 ETH Zurich
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