Experiments

In this subsection are presented the obtained results. First, we present the system behavior’s results against step perturbations. These reference changes were applied at different velocities and circuit curvatures. Subsequently, results for the tests with an autonomous driving inside the circuit are presented.

Step perturbation test series.

First of all it must be taken into account that the car has 0.4 seconds or 11 frames of response delay. This is the elapsed time from the moment that the controller sent the command until the wheels reach the commanded angle. This relation is shown in Figure 3.14.

Figure 3.14: Representation of the steering wheel response. The delay from the command sent to the steering wheel reach the commanded angle position is 0.4 seconds.

In order to measure how good the fuzzy controller is, a set of step tests was made. The step value is 50 pixels, equivalent to 6.85 cm (1 pixels = 0.137 cm). The step was applied by adding a reference of 50 pixels to the current error value. For this reason the red line that represents the step applied not always is on −50 or 50 pixels line. In order to obtain a good representation of the response of the fuzzy controller a set of tests at different speeds and at different parts of the circuit were done (straights and curves).

Figure 3.15(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 7.166 cm. At it is shown, the system corrects the error in just 27 frames, which is about 1 second for an average rate of 28 frames per second during the test. The angle of the steering wheel versus the controller commands is shown in Figure 3.15(b). The previously mentioned delay of 11 frames in the steering wheel action may be noticed. Ignoring this delay, the system correct the error in 17 frames or 0.6 seconds.

Figure 3.16 shows the results for a step perturbation test at 15 km/h in a straight way. This test had a RMSE value equal to 7.0592. The settling time is less than half second (25 − 11 frames).

30 3.4. Autonomous Driving with Local Localization

(a) Error measured (in pixels). (b) Evolution of the steering wheel angle ver- sus the controller commands.

Figure 3.15: Step response to a 50 pixels step at 10 km/h in straight. The Er- ror measurement, and the steering wheel movements, and the Fuzzy controller output are shown. The value of the RMSE of the test is 7.1666 cm.

(a) Error measured (in pixels). (b) Evolution of the steering wheel angle ver- sus the controller commands.

Figure 3.16: Step response to a 50 pixels step at 15 km/h in straight. The Er- ror measurement, and the steering wheel movements, and the Fuzzy controller output are shown. The value of the RMSE of the test is 7.0592 cm.

To test the robustness of the controller against step perturbations similar tests have been done when the vehicle was inside a curve. Figure 3.17(a) shows the step command and the evolution of the error at 10 km/h. In this case the curve to 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 3.17(b).

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 3.18(a) shows the evolution of this test comparing the step command and the error at each frame. As well as previous tests the Figure 3.18(b) shows a compar- ison between the commands sent by the Fuzzy controller and the steering wheel

Chapter 3. Fuzzy Logic Control for Ground Vehicles 31

(a) Error measured (in pixels). (b) Evolution of the steering wheel angle ver- sus the controller commands.

Figure 3.17: Step response to a 50 pixels step at 10 km/h in curve. The Er- ror measurement, and the steering wheel movements, and the Fuzzy controller output are shown. The value of the RMSE of the test is 7.8007 cm.

(a) Error measured (in pixels). (b) Evolution of the steering wheel angle ver- sus the controller commands.

Figure 3.18: Step response to a 50 pixels step at 15 km/h in curve. The Er- ror measurement, and the steering wheel movements, and the Fuzzy controller output are shown. The value of the RMSE of the test is 7.2187 cm.

position frame by frame.

Table 3.2 shows the results of all the step perturbation’s tests.

In all the step tests done the response of the controller was around 1 second. Taking into account the response delay of the system and the complexity of this non-linear system, the controller behavior is better than the initial expectations.

Constant vehicle speed

Next are presented two tests of the car covering a long distance inside the circuit. The first one was done with a constant vehicle’s speed and the second one was done changing the speed during the test.

32 3.4. Autonomous Driving with Local Localization Step size circuit speed RMSE

(pixels) section (km/h) (cm) 50 straight 10 7.1666 50 straight 10 7.4257 50 straight 10 8.3321 50 straight 15 6.9314 50 straight 15 7.0592 50 curve 10 7.8007 50 curve 15 6.8574 50 curve 20 7.2187

Table 3.2: Results of the 50 pixels step perturbation.

Figure 3.19 shows the evolution of the vehicle and the controller in this test. In Figure 3.19(b) the measured error during the whole test is shown. In this case, the RMSE value is 5.0068 cm. Figure 3.19(c) shows the comparison between the controller commands and the measured angle of the steering wheel. In the Fig- ure, the changes between straight lines and curves could be appreciated. In the straight lines, the steering wheel stays around 0 degrees, while it turns between −100 and −150 degrees in the first curve, and between −150 and −300 in the second one. It is easily appreciates in Figure 3.20, in which the plot is scaled to show only one lap. The evolution of the vehicle speed is depicted in Figure 3.19(a), which covers speeds between 12 and 13 km/h.

(a) Vehicle’s speed. (b) Error measured. The value of RMSE for this test is 5.0015 cm.

(c) Steering wheel versus the Fuzzy con- troller’s commands.

Figure 3.19: Evolution of the system during 18 laps inside the circuit without mark detection. Constant speed was applied.

Chapter 3. Fuzzy Logic Control for Ground Vehicles 33

Figure 3.20: Zoom to one lap of the circuit.

In Figure 3.19(b) large error peak of even 170 pixels appear at every curvature change. However, they are decreased in a few frames by the controller. This errors appear because the circuit was not designed with clothoids. Therefore, curvature discontinuities happen when changing from straight line to curve and vice-versa. Figure 3.21 shows a zoom of one of this instants in which a peak of −171 pixels occurs. The evolution of the error is plotted in Figure 3.21(a), while the output of the controller and the steering wheel angle are in Figure 3.21(b).

(a) Zoom of the error (b) Zoom of the steering wheel angle and con- troller commands

Figure 3.21: Zoom of 170 pixels step at the beginning of the second curve.

Variable vehicle speed

Here are presented some tests in with the vehicle speed is not fixed to a con- stant value. First, a test to check the robustness of the system against emergency stops an big speed changes is presented. Then a test of continuous autonomous driving of the system inside the system covering some laps is shown.

In this test is presented how the system response against big speed changes. In order to check this behavior an emergency stop was applied to the vehicle as is shown in Figure 3.22. Figure 3.22(a) shows the speed of the vehicle during this test. At the end of this Figure is shown the radical step from 10 to 0 km/h. Figure 3.22(b) shows the evolution of the error during this test. To increase the complexity of the test the speed reduction has been done when the vehicle was inside a curve. At the beginning of the test the vehicle was located in a straight, gong inside a curve at the end of test. The transition from straight to curve is appreciable at the interval between the frames 280 to 420. The response of the

34 3.4. Autonomous Driving with Local Localization

controller and the evolution of the steering wheel have been shown in Figure 3.22(c).

(a) Vehicle’s speed during the emergency stop’s test.

(b) Error measured during the emergency stop’s test.

(c) Comparison between the steering wheel and the commands sent by the Fuzzy controller during the emergency stop’s test.

Figure 3.22: Evolution of the system during the emergency stop’s test. Another test has been done to check the correct behavior of the controller when the speed is not fixed (Figure 3.23). In this case is appreciated some peaks of 25 km/h. These speed changes are shown in Figure 3.23(a). The evolution of the error is shown in Figure 3.23(b) with a RMSE value of 5.8328 cm. In this Figure also is appreciated the changes between straight and curve and vice- verse when the error peaks appears. These transitions are appreciated too, in the variations of the steering wheel value in Figure 3.23(c) as has been explained in the previous Figure 3.20.

Chapter 3. Fuzzy Logic Control for Ground Vehicles 35

(a) Vehicle’s speed. (b) Error measured. The RMSE during this test was 5.8328

(c) Measure of the steering wheel of the vehi- cle during the 4 laps test with speed variations.

Figure 3.23: Evolution of the system during 4 laps inside the circuit without mark detection. Variable speed was applied.

Number Kms Min Speed Top Speed RMSE

of Laps (km/h) (km/h) (cm)

18 3.5 13 13 5.0068

4 1 11 26 5.8328

Table 3.3: Results obtained with the driveless car without mark detection.