PID Controller

General Info

In this approach, I manually tune Kp, Ki, and Kd. It was tough to obtain a sturdy figure owing to the different contours of the road, but I ultimately got excellent values that allow the car to travel a full loop without colliding.

Output

Manual Tuning

I began by utilizing the P controller with Kp = 0.15 because I had used this value in my last project, which was behavioral cloning. Based on what I learned in class, I understand the distinction between P, PD, and PID controllers, as depicted in the graphic below.

Using the P controller, the automobile began to occilate. As a result, I inserted an arbitrary integer for Kd in order to create a PD controller. Kd = 2.0 is the value I chose. This constant is enough for handling an automobile traveling at a peak speed of 30 mph. It can manage a quick curve while still allowing the automobile to complete the course. However, because steering shift may occur in the actual world, a PID controller is a popular approach. Based on this, I chose an extremely tiny number for Ki, 5.0e-4. This arrangement produces a nice outcome, which I believe is adequate for passing the project.

Twiddle

Another method for determining the best settings is to twiddle. The course’s pseudo code for twiddle and its Python implementation are shown below.

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def twiddle(tol=1e-10): 
    p = [0, 0, 0]
    dp = [1, 1, 1]
    robot = make_robot()
    x_trajectory, y_trajectory, best_err = run(robot, p)
    while best_err > tol:
        for i in range(3):
            p[i] += dp[i]
            robot = make_robot()
            x_trajectory, y_trajectory, err = run(robot, p)
            if err < best_err:
                best_err = err
                dp[i] *= 1.1
            else:
                p[i] -= 2*dp[i]
                robot = make_robot()
                x_trajectory, y_trajectory, err = run(robot, p)
                if err < best_err:
                    best_err = err
                    dp[i] *= 1.1
                else:
                    p[i] += dp[i]
                    dp[i] *= 0.9
    return p, best_err
 

The car is able to go explore full track without any collision. The result can be found on YouTube video here.