calization
The Fuzzy controller is almost the same of the presented on 3.4.1. In this case an offset is added at the end of the controller’s output. The control’s structure of Fuzzy+ I + O f f set is shown in Figure 5.24.
Figure 3.24: Control loop of the visual servoing system with global localization. Fuzzy+ I + O f f set schema.
The offset component behaves like a feed-forward controller that offsets the effect of the change of the curvature of the circuit each time that a new mark has been detected. It is calculated theoretically using the equations of the Frenet- frame kinematic model of a car-like mobile robot (Siciliano and Khatib, 2008b). More detailed information about this control component is shown in (Sanchez- Lopez et al., 2012).
The Kiis reduced from 0.6, of the previous approach, to 0.3.
3.5.2.
Experiments
The behavior of the Fuzzy controller with the mark recognition has been checked with a set of tests in the real circuit. First is presented a set of step response. Secondly the system was tested covering a number of laps inside the circuit with a constant vehicle’s speed. Finally a set of tests are shown with speed variations.
Step response
As well as the previous approach the new approach was also tested against 50 pixels step perturbation. The most relevant tests are presented next.
Chapter 3. Fuzzy Logic Control for Ground Vehicles 37
Figure 3.25(a) shows the error measured when a +50 pixels step perturbation is applied to the system at 10 km/h. The resulting RSME value is 6.8402 cm. The angle of the steering wheel versus the controller commands is shown in Figure 3.25(b).
(a) Error measured (in pixels). (b) Evolution of the steering wheel angle ver- sus the controller commands.
Figure 3.25: Step response to a 50 pixels step at 10 km/h in straight with mark approach system. The Error measurement, and the steering wheel movements, and the Fuzzy controller output are shown. The value of the RMSE of the test is 6.8402 cm.
Figure 3.26 shows the results for a step perturbation test at 15 km/h in a straight way. For this test the value of the RMSE is 7.0592.
(a) Error measured (in pixels). (b) Evolution of the steering wheel angle ver- sus the controller commands.
Figure 3.26: Step response to a 50 pixels step at 15 km/h in straight with mark approach system. The Error measurement, and the steering wheel movements, and the Fuzzy controller output are shown. The RMSE value of the test is 6.719 cm.
To test the robustness of the controller against step perturbations similar tests have been done when the vehicle was inside a curve. Figure 3.27(a) shows the step command and the evolution of the error at 10 km/h. In this case the curve to
38 3.5. Autonomous Driving with Global Localization
the left and the step was done to the internal part of the curve (to the left). The action of the controller and the response of the steering are shown in Figure 3.27(b).
(a) Error measured (in pixels). (b) Evolution of the steering wheel angle ver- sus the controller commands.
Figure 3.27: Step response to a 50 pixels step at 10 km/h in curve with mark approach system. The Error measurement, and the steering wheel movements, and the Fuzzy controller output are shown. The value of the RMSE of the test is 5.1034 cm.
The test at 15 km/h inside the curve has been done applying a perturbation in the direction against the curve, trying to move the car out of the curve. Fig- ure 3.28(a) shows the evolution of this test comparing the step command and the error at each frame. As well as previous tests the Figure 3.28(b) shows a compar- ison between the commands sent by the Fuzzy controller and the steering wheel position frame by frame.
(a) Error measured (in pixels). (b) Evolution of the steering wheel angle ver- sus the controller commands.
Figure 3.28: Step response to a 50 pixels step at 15 km/h in curve with mark approach system. The Error measurement, and the steering wheel movements, and the Fuzzy controller output are shown. The value of the RMSE of the test is 5.5429 cm.
Chapter 3. Fuzzy Logic Control for Ground Vehicles 39
Table 3.4 shows the results of all the step perturbation’s tests. Comparing this table with the previous approach (Table 3.2) is possible to appreciated that the change of the integral’s gain (from 0.6 to 0.3) has a small effect in controller’s behavior. In curve tests the offset added in the second approach improves the controller behavior reducing the RMSE value.
Step size circuit speed RMSE (pixels) section (km/h) (cm) 50 straight 10 7.5051 50 straight 10 6.8402 50 straight 15 7.8274 50 straight 15 6.7190 50 curve 10 6.9561 50 curve 10 5.1034 50 curve 15 5.5429 50 curve 15 6.5174 50 curve 15 6.2648 50 curve 20 6.9676
Table 3.4: Results of the 50 pixels step perturbation for the system with mark detection.
Constant vehicle speed
As well as the previous approach a set of test were done to check the behavior of the controller when the system have to cover a long distance. Firstly a set of tests in which the speed is set to a constant value is presented. Then a set of tests is presented with variable vehicle’s speed.
In the first test the vehicle cover 9 laps on the circuit (Figure 3.29). The distance covered is almost 2 km. Figure 3.29(a) shows that the vehicle speed was set to 15 km/h for this test. Figure 3.29(b) shows the evolution of the car inside the circuit by the steering wheel’s movement. As previously shown in Figure 3.20 when the car is on the bigger radius curve the steering wheel is turned around 120 degrees. The steering wheel’s turn around 220 represents when the vehicle is on the short radius curve. Otherwise the car is on the circuit’s straights. Figure 3.29(c) shows the error during all the test. The RMSE value obtained in this test is 4.8270 cm.
In the second test the vehicle cover 13 laps on the circuit (Figure 3.30). The distance covered is almost 2 km. Figure 3.30(a) shows the vehicle speed set to 20 km/h with small variations. Figure 3.30(b) shows the error during all the test. The RMSE value obtained in this test is 3.5256 cm.
In the third test the vehicle cover 13 laps on the circuit (Figure 3.31). The distance covered is more than 2 km. Figure 3.31(a) shows the vehicle speed set to 15 km/h. Figure 3.31(b) shows the evolution of the car inside the circuit by
40 3.5. Autonomous Driving with Global Localization
(a) Vehicle speed.
(b) Evolution of the steering wheel.
(c) Error measured (in pixels). The value of RMSE for this test is 4.820 cm.
Figure 3.29: Evolution of the system during 9 laps inside the circuit with mark detection. Speed is set to 15 km/h.
(a) Vehicle speed. (b) Error measured in pixels
Figure 3.30: Evolution of the system during this test 13 laps inside the circuit with mark detection. Variable speed with an average of 20 km/h.
Chapter 3. Fuzzy Logic Control for Ground Vehicles 41
(a) Vehicle speed.
(b) Evolution of the steering wheel.
(c) Error measured (in pixels). The value of RMSE for this test is 5.8098 cm.
Figure 3.31: Evolution of the system during 13 laps inside the circuit with mark detection. Speed is set to 15 km/h.
the test. The RMSE value obtained in this test is 5.8098 cm.
In the fourth test the vehicle cover 21 laps on the circuit (Figure 3.32). The distance covered is more than 4 km. Figure 3.32(a) shows the vehicle speed set to 14 km/h. An emergency stop was tested here. After that the test was finished covering one lap more at 16 km/h. Figure 3.32(b) shows the evolution of the car inside the circuit by the movement of the steering wheel. Figure 3.32(c) shows the error during all the test. The RMSE value obtained in this test is 3.41006 cm.
Finally a long test of 30 laps on the circuit (Figure 3.33) was done. The distance covered is around 6 km. Figure 3.33(a) shows the vehicle speed set to 15 km/h. Figure 3.33(b) shows the evolution of the car inside the circuit by the movement of the steering wheel. Figure 3.33(c) shows the error during all the test. The RMSE value of this test is 3.6874 cm.
42 3.5. Autonomous Driving with Global Localization
(a) Vehicle speed.
(b) Evolution of the steering wheel.
(c) Error measured (in pixels). The value of RMSE for this test is 3.41006 cm.
Figure 3.32: Evolution of the system during 21 laps inside the circuit with mark detection. Speed is set to 14 km/h. An emergency stop was applied.
Variable vehicle speed
Next is presented a set of tests in which the speed is not set to a constant value. In this cases the speed was controlled by a human.
In the first one was tested the behavior of the controller against a big speed acceleration, and reduction and two stop and go tests inside curves (Figure 3.34). Here a top speed of 48 km/h was reached as is shown in Figure 3.34(a). After this, a strong reduction of the speed was applied. The vehicle cover 2 laps on the circuit. Figure 3.34(b) shows the evolution of the car inside the circuit by the movement of the steering wheel. Figure 3.34(c) shows the error during all the test. The RMSE value of this test is 3.0313 cm. The circuit length limitations implies to do a big acceleration to reach the top inner-city speed.
The second test shows the behavior the system covering 17 laps at different speeds (Figure 3.35). Vehicle speed changes from 15 to 25 km/h as is shown in Figure 3.35(a). Figure 3.35(b) shows the evolution of the car inside the circuit by the movement of the steering wheel. Figure 3.35(c) shows the error during all
Chapter 3. Fuzzy Logic Control for Ground Vehicles 43
(a) Vehicle speed.
(b) Evolution of the steering wheel.
(c) Error measured (in pixels). The value of RMSE for this test is 3.6874 cm.
Figure 3.33: Evolution of the system during 30 laps inside the circuit with mark detection. Speed is set to 15 km/h.
the test. The RMSE value of this test is 5.5535 cm.
The third test shows the behavior the system covering 4 laps with big speed changes (Figure 3.36). Here is also checked the robustness of the system af- ter line loss. Vehicle speed changes from 6 to 38 km/h as is shown in Figure 3.36(a). Figure 3.36(b) shows the evolution of the car inside the circuit by the movement of the steering wheel. Figure 3.36(c) shows the error during all the test. The RMSE value of this test is 8.6494 cm. The line loss are shown as an error constant value.
The fourth test shows the behavior the system covering 6 laps with big speed changes (Figure 3.37). Vehicle speed changes from 14 to 42 km/h as is shown in Figure 3.37(a). Figure 3.37(b) shows the evolution of the car inside the circuit by the movement of the steering wheel. Figure 3.37(c) shows the error during all the test. The RMSE value of this test is 10.7916 cm.
44 3.5. Autonomous Driving with Global Localization
(a) Vehicle speed. A top speed of 48km/h has been reached.
(b) Evolution of the steering wheel.
(c) Error measured (in pixels). The value of RMSE for this test is 3.0313cm.
Figure 3.34: Evolution of the system with mark detection and speed changes from 0 to 48 km/h.
The fifth test shows the behavior the system covering 4 laps with big speed changes (Figure 3.38). Vehicle speed changes from 14 to 42 km/h as is shown in Figure 3.38(a). Figure 3.38(b) shows the evolution of the car inside the circuit by the movement of the steering wheel. Figure 3.38(c) shows the error during all the test. The RMSE value of this test is 9.1397 cm.
The following test shows the behavior the system covering 14 laps at different speeds (Figure 3.39). Vehicle speed changes from 10 to 23 km/h as is shown in Figure 3.39(a). Figure 3.39(b) shows the evolution of the car inside the circuit by the movement of the steering wheel. Figure 3.39(c) shows the error during all the test. The RMSE value of this test is 7.5486 cm.
The last test shows the behavior the system covering 6 laps at different speeds (Figure 3.40). Vehicle speed changes from 14 to 24 km/h as is shown in Figure 3.40(a). Figure 3.40(b) shows the evolution of the car inside the circuit by the movement of the steering wheel. Figure 3.40(c) shows the error during all the test. The RMSE value of this test is 8.4839 cm.
Chapter 3. Fuzzy Logic Control for Ground Vehicles 45
(a) Vehicle speed. A top speed of 25km/h has been reached.
(b) Evolution of the steering wheel.
(c) Error measured (in pixels). The value of RMSE for this test is 5.5535cm.
Figure 3.35: Evolution of the system during 17 laps inside the circuit with mark detection. Speed changes from 15 to 25 km/h.
Number Min Speed Top Speed RMSE
of Laps (km/h) (km/h) (cm) 9 15 15 4.8270 13 20 20 3.5256 13 15 15 5.8098 21 14 14 3.4100 30 15 15 3.6874 17 15 25 5.5535 4 6 38 8.6494 6 14 42 10.7916 4 14 42 9.1397 14 10 23 7.5486 6 14 24 8.4839 2 10 48 3.0313
46 3.5. Autonomous Driving with Global Localization
(a) Vehicle speed. A top speed of 38km/h has been reached.
(b) Evolution of the steering wheel.
(c) Error measured (in pixels). The value of RMSE for this test is 8.6494cm.
Figure 3.36: Evolution of the system during 4 laps inside the circuit with mark detection. Speed changes from 6 to 38 km/h.
tests.
Chapter 3. Fuzzy Logic Control for Ground Vehicles 47
(a) Vehicle speed. A top speed of 42km/h has been reached.
(b) Evolution of the steering wheel.
(c) Error measured (in pixels). The value of RMSE for this test is 10.7916cm.
Figure 3.37: Evolution of the system during 6 laps inside the circuit with mark detection. Speed changes from 14 to 42 km/h.
48 3.5. Autonomous Driving with Global Localization
(a) Vehicle speed. A top speed of 42km/h has been reached.
(b) Evolution of the steering wheel.
(c) Error measured (in pixels). The value of RMSE for this test is 9.1397cm.
Figure 3.38: Evolution of the system during 4 laps inside the circuit with mark detection. Speed changes from 14 to 42 km/h.
Chapter 3. Fuzzy Logic Control for Ground Vehicles 49
(a) Vehicle speed. A top speed of 23km/h has been reached.
(b) Evolution of the steering wheel.
(c) Error measured (in pixels). The value of RMSE for this test is 7.5486cm.
Figure 3.39: Evolution of the system during 14 laps inside the circuit with mark detection. Speed changes from 10 to 23 km/h.
50 3.5. Autonomous Driving with Global Localization
(a) Speed car during the first test. A top speed of 24km/h has been reached.
(b) Evolution of the steering wheel.
(c) Error measured (in pixels). The value of RMSE for this test is 8.4839cm.
Figure 3.40: Evolution of the system during 17 laps inside the circuit with mark detection. Speed changes from 14 to 24 km/h.
Chapter 3. Fuzzy Logic Control for Ground Vehicles 51