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Model Documentation

This file contains the documentation for the Udacity Path-Planning Project.

Task Description

The goal in this project is to build a path planner that is able to create smooth, safe trajectories for the car to follow. The highway track has other vehicles, all going different speeds, but approximately obeying the 50 MPH speed limit.

The car transmits its location, along with its sensor fusion data, which estimates the location of all the vehicles on the same side of the road.

What is the Path

A trajectory is constituted by as set of (x, y) points. Every 20 ms the car moves to the next point on the list. In this framework, the car moves from point to point perfectly.

Since the car always moves to the next waypoint after 20ms, the velocity of the vehicle is given by how much future waypoints are spaced. In other words, the larger the space between waypoints, the faster the car will be.

Rubric

Here's a bullet list of rubric points along with an explanation of how constraints are satisfied.

  • The car drives according to the speed limit

    A reference velocity variable is used to keep track of current speed of the vehicle. Also, another constant variable is used to make sure the car never exeed the maximum speed of 50 mph.

  • Max acceleration and jerk are not exceeded.

    The rubric sets as hard constraint the fact that car does not exceed a total acceleration of 10 m/s^2 and a jerk of 10 m/s^3. This is obtained by setting the initial speed of vehicle to zero, and gradually accelerating until the vehicle has reached the maximum speed allowed (either by the speed limit or by the current road situation).

  • Car does not have collisions.

    Under the reasonable assumption that other cars drive reasonably well, the main risk to hit another car is rear-ending. This is avoided using sensor fusion data to make sure that no other car is dangerously close in our same lane. If this is the case, the car gracefully decelerates until the situation gets safer.

    Another possibly dangerous situation is the one of lane changing. This will be examined in the next point.

  • The car stays in its lane, except for the time between changing lanes.

    One of the first things that we would demand from a self-driving car is being able to drive inside a certain lane. In our framework, we know that each lane is 4m width, and that there are three lanes for each direction of travel.

    For the task of lane keeping we'll rely on Frenet coordinates, which measure longitudinal (s) and lateral (d) motion along the road and are much easier to deal with w.r.t. euclidean ones. By the way, the code for converting between Eunclidean and Frenet coordinates is in coords_transform.h.

    In order for the car to keep the lane, three future waypoints are generated equally spaced 30m, 60m and 90m before the car respectively. These are quite far apart one from the other, so in order to obtain a smooth trajectory a spline is used to interpolate intermediate locations.

    Notice that these waypoints are created using the lane variable to make sure that the d coordinate is just in the middle of the lane the car is currently on. In case a lane change is needed, the lane variable will already contain the coordinate of the future lane (see below).

  • The car is able to change lanes