Main Content

Smooth reference path fit to waypoints

The `referencePathFrenet`

object fits a smooth, piecewise,
continuous curve to a set of waypoints given as `[x y]`

or ```
[x y
theta]
```

. After fitting, points along the curve, the path points are expressed as
`[x y theta kappa dkappa s]`

, where:

`x`

`y`

and`theta`

— SE(2) state expressed in global coordinates, with`x`

and`y`

in meters and`theta`

in radians`kappa`

— Curvature, or inverse of the radius, in meters`dkappa`

— Derivative of curvature expressed as an arc length in meters`s`

— Arc length, or distance along path from path origin, in meters

Using this object, convert trajectories between global and Frenet coordinate systems, interpolate states along the path based on arc length, and query the closest point on a path from a global state.

The object expresses Frenet states as a vector of form ```
[S dS ddS L dL
ddL]
```

, where `S`

is the arc length and `L`

is the
perpendicular deviation from the direction of the reference path. Derivatives of
`S`

are relative to time. Derivatives of `L`

are relative
to the arc length, `S`

.

`refPathObj = referencePathFrenet(`

fits a piecewise, continuous set of curves to the specified waypoints. The
`waypoints`

)`waypoints`

argument sets the `Waypoints`

property.

`refPathObj = referencePathFrenet(`

fits a piecewise, continuous set of curves to waypoints using the specified distance
between interpolated path points. The `waypoints`

,'DiscretizationDistance',discretionDist)`discretionDist`

argument sets
the `DiscretizationDistance`

property.

`closestPoint` | Find closest point on reference path to global point |

`frenet2global` | Convert Frenet states to global states |

`global2frenet` | Convert global states to Frenet states |

`interpolate` | Interpolate reference path at provided arc lengths |

`show` | Display reference path in figure |