Homework 2: Car Steering

Autonomous Line Following Racecar
Homework 2: Car Steering
EE192 
1 Steering Simulation - Proportional Control
With pure position control, δ = kpya, we chose a fixed speed V = 1.25 m/s and a kp = 500.0 which allowed
the car to successfully complete the track without hitting any of the cones. The worst-case overshoot was
0.3049 m or 3.049 cm, and is indicated as a point in Fig. 1 and a red-highlighted path in Fig. 2. A
comparison between the lateral error and the actual position of the car is shown in Fig. 3.
Figure 1: Time Plots of the Lateral Error and Steering Angle
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Figure 2: Actual x vs. y Position of Car
Figure 3: Lateral Error and Actual Position Plots for Comparison
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2 Steering Simulation - Proportional & Derivative Control
With PD control, δ = kpya + kdy˙a, we chose a fixed speed V = 2.2 m/s (almost double our earlier speed),
a kp = 500.0, and a kd = 50.0 which allowed the car to successfully complete the track without hitting any
of the cones. The worst-case overshoot was 0.1766 m or 1.766 cm, and is indicated as a point in Fig. 4 and
a red-highlighted path in Fig. 5. A comparison between the lateral error and the actual position of the car
is shown in Fig. 6. PD control was much better at following the line, ”swayed” significantly less (i.e. the
derivative control reduced the overshoot), and was able to handle higher speeds as a result.
We also tried PD control with a fixed speed V = 3.75 m/s (more than triple our first speed), a kp = 500.0,
, a kp = 500.0, and a kd = 200.0 which allowed the car to successfully complete the track without hitting any
of the cones (though it came close). The worst-case overshoot was 0.3855 m or 3.855 cm, and is indicated
as a point in Fig. 7 and a red-highlighted path in Fig. 8. A comparison between the lateral error and the
actual position of the car is shown in Fig. 9. In this case, the overshoot is similar to our first run with only
position control, but at a much faster speed.
Figure 4: Time Plots of the Lateral Error and Steering Angle
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Figure 5: Actual x vs. y Position of Car
Figure 6: Lateral Error and Actual Position Plots for Comparison
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Figure 7: Time Plots of the Lateral Error and Steering Angle
Figure 8: Actual x vs. y Position of Car
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Figure 9: Lateral Error and Actual Position Plots for Comparison
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3 Steering Servo Speed Limit
With PD control and a more reasonable steering servo, we chose a fixed speed V = 3.15 m/s (almost double
our earlier speed), a kp = 500.0, and a kd = 150.0 which allowed the car to successfully complete the track
without hitting any of the cones. The worst-case overshoot was 0.1766 m or 1.766 cm, and is indicated as
a point in Fig. 10 and a red-highlighted path in Fig. 11. A comparison between the lateral error and the
actual position of the car is shown in Fig. 12. In this case, the steering servo itself responded much slower
to commands to turn than in previous runs, which caused our car to ”sway” more and required a higher kd
in order to compensate.
Figure 10: Time Plots of the Lateral Error and Steering Angle
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Figure 11: Actual x vs. y Position of Car
Figure 12: Lateral Error and Actual Position Plots for Comparison
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4 PC Control, Steering Servo Limit, & Speed Control
With PD control, a more reasonable steering servo and a simple if statement shown below for speed control
(where, if the lateral error was greater than 0.15 the car would slow down to V = 2.5, otherwise it would
maintain a decent speed of V = 3.0), a kp = 500.0, and a kd = 100.0, the car to successfully complete the
track without hitting any of the cones. The worst-case overshoot was 0.31 m or 3.1 cm, and is indicated as
a point in Fig. 13 and a red-highlighted path in Fig. 14. A comparison between the lateral error and the
actual position of the car is shown in Fig. 15.
It’s not as clean as we’d like it to be (the easiest way to achieve that would be to tune a bit more carefully,
or just slow down the car), but it did avoid the cones. The velocity controller helped a bit with the swaying
and some of the larger turns, but the car still struggles to make tight turns without a lot of overshoot. The
laptime was 31.42 seconds, which was pretty similar to when we had just a fixed car speed. Most likely, we
need to implement a more advanced controller (probably PID or just PD control) for speed as well.
# Constant speed for now. You can tune this and/or implement advanced
# controllers.
#car.set_speed(ve)
if (np.absolute(lat_err) 0.15):
car.set_speed(2.5) #slow down
else:
car.set_speed(3.0) #setpoint
Figure 13: Time Plots of the Lateral Error and Steering Angle
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Figure 14: Actual x vs. y Position of Car
Figure 15: Lateral Error and Actual Position Plots for Comparison
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