Trajectory Class

Overview

Trajectory Definition

Racing line defined by control points

Trajectory formed by interpolating between control points using SciPy make_interp_spline (https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.make_interp_spline.html#scipy.interpolate.make_interp_spline)

(2D) curvature calculated as Menger curvature (https://en.wikipedia.org/wiki/Menger_curvature), made signed by determining if the points curve left (negative) or right (positive)

Track Limits

From the track left/right edge coordinates, “gates” are drawn perpendicular to the track centreline

Each gate is represented with a Shapely LineString (https://shapely.readthedocs.io/en/stable/reference/shapely.LineString.html#shapely.LineString**)**

Checks the number of track limits gates skipped by making a Shapely LineString from the discretized trajectory coordinates, iterating through all gates and using the intersects function

However the current approach causes problems with gradient descent since the “track limits punishment” function is stepped so gradient descent is bad with it

Attributes

init()

Track limits

• if exceeded limits then do a “limits solve recovery” type thing - idk how necessary this is though since track limits need to be exceeded by quite a lot to completely miss a very wide gate

Inputs

A * indicates the input is optional

To Do

• Improve handling of start line crossing if the trajectory doesn’t cross the start gate
  • Maybe find the closest spline sample point to the start gate (Shapely distance function) with a dot product between their 2D xy directions > threshold
• Add sDelta
• ALTERNATIVELY for track limits:
  • Start with startGate’s gateWide LineString
  • Iterate over trajectory points
    • Make a Shapely LineString from that point to the next point
    • Check if it intersects the next gateWide LineString
    • If it intersects, then check whether the intersection point is within track limits or not based on the carWidth and coordinates of the corresponding gate and gateExtend
    • Also calculate the amount the intersection point exceeds track limits (negative to show the extent that it’s legal)
    • Then increment the gate index
  • If the trajectory type means it has a run-up before the startGate, then iterate over the trajectory points from the start line backwards
  • Sum of the distances exceeded is the penalty
• Elevation and everything related to that (slope, camber, warp, changes to curvature calc to be purely lateral curvature)
  • Use linear interpolation to get elevation (https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.LinearNDInterpolator.html#scipy.interpolate.LinearNDInterpolator) and if that returns NaN for out of bounds then use nearest neighbour (https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.NearestNDInterpolator.html#scipy.interpolate.NearestNDInterpolator)
  • Requires at least track limits left/right edges to have elevation data to feed into the interpolators, but the more points there are the better with this method
  • May need to do a low pass filter on input elevation points though
  • Pass the 2 interpolation objects into the generateTrajectory function as arguments
• Rework gate generation logic so it can use any arbitrary left/right edge coordinate list while still remaining perpendicular across the track and still being at regular intervals
• Support for all trajectory types:
  • Closed circuit (currently assumed)
  • Point to point like a hillclimb - variations of fixed start point or run-up allowed
  • Qualifying/single-lap

Ideas

• Calculate arrays of unit vectors representing trajectory direction and another array of unit vectors representing track normal? Probably makes it easier to get camber/slope info when I get to doing 3D
• Experiment with using different spline degrees (higher for more smooth spline)
• Allow a Trajectory object to be initialised from a dictionary definition (potentially with a reduced set of attributes)
• Is it possible to make an interactive matplotlib window to make creating the first spline definition faster?
  • Left-click to add control point, right click remove control point + click in a box to say next corner/prev corner?
  • Control point placement just goes to midpoint of the nearest track limits gate to the cursor
  • Candidate new control point plotted in blue, existing control points plotted in green, if the cursor is hovering over an existing control point the plot that one in red