Self-Driving Car Engineer Nanodegree Program

This project is to use the Proportional-Integral-Derivative controller to fine tune the car so that it will autonomously drive on the given track in simultor.

PID controller has the member method to update the Error for each PID component:

void PID::UpdateError(double cte) {

d_error = cte - p_error;

p_error = cte;

i_error = i_error + cte;

}

where the input cte is from the simulator calcuate the cross track error, i.e. offset from center of lane. The differential error d_error equals to current cte - p_error, this is the delta between current CTE and previous timestamp CTE. The proportional error p_error equals to the input cte, i.e. p_error = cte; The integral error equals to all cte error cumulated so far, i.e. i_error = i_error + cte;

the overall error is calculated in following formula in TotalError method: -(Kp * p_error + Ki * i_error + Kd * d_error)

if the PID just has the P component, the data shows that the car will have error, i.e. overshoot and then oscilate along center of lane. one the error keeps becoming bigger, the car veers off track and loses control completely. Following short video shows the [Kp, Ki, Kd] = [0.17 0.0 0.0]. the car can not even reach first turn of road. This is expected that Kp only control system is not good enough to avoid the oscilation.

kp_only

Now, in order to avoid the overshoot and marginal stability of P component only, the derivative component is added, which is temporal error measurement against rate of change error. The effect of derivative error is to counter the steering so overshoot is reduced. when the derivative becomes smaller, the steering angle depends on proportional error again so it keeps close to the center lane. Following videos shows the two components are used, Kp and Kd, i.e. [0.17 0.0 1.5]. At least now the car can remains on the track and alsmot finish one lap. Adding the Kd is expected to avoid the oscilation.

kp_kd_only

Every system has the system bias where not all paramters are perfect against design definition. The tiny bias is needed to be modeled in the system since this small error can accumulate and become large error in the model behavior over long period time. Here the integral component is used to emulated the tiny angle offset of steering given perfect product. Since this is very tiny error offset, the efficient is not expected to be very big compared to other two Kp and Kd, it is more 100x smaller than other two. The following video shows the additional Ki is added to control system, i.e. [Kp Ki Kd] = [0.17 0.0016 1.9]

Kp_Ki_Kd

I start with PID [0.5 0 0.5] and sooner realized that car veers off the road before the first turn. Then decrease the Kp to 0.2 range and car is able to stay most of track. However car is oscillating a lot. In order to avoid the oscillation, increate the Kd to 1.6 range. The car can stays on the road most of time. Meanwhile, increase the Ki by small number so that car drives to bit close to the center of road.

After handful of iteration, the final parameters is setllted at: [0.17 0.0016 2.1]

A seperate PID is used to throttle the speed at 35MPH.

The portion of video is here:

pid_drive video

1. Clone this repo.
2. Make a build directory: mkdir build && cd build
3. Compile: cmake .. && make
4. Run it: ./pid.