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Interpolate reference path at provided arc lengths

Since R2020b



pathPoints = interpolate(refPath,arclengths) interpolates the reference path at the provided arc lengths and returns the interpolated points on the path in global coordinates.


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Generate a reference path from a set of waypoints.

waypoints = [0 0; 50 20; 100 0; 150 10];
refPath = referencePathFrenet(waypoints);

Create a trajectoryGeneratorFrenet object from the reference path.

connector = trajectoryGeneratorFrenet(refPath);

Generate a five-second trajectory between the path origin and a point 30 meters down the path as Frenet states.

initCartState = refPath.SegmentParameters(1,:);
initFrenetState = global2frenet(refPath,initCartState);
termFrenetState = initFrenetState + [30 zeros(1,5)];
frenetTraj = connect(connector,initFrenetState,termFrenetState,5);

Convert the trajectory to the global states.

globalTraj = frenet2global(refPath,frenetTraj.Trajectory);

Display the reference path and the trajectory.

axis equal
hold on

Specify global points and find the closest points on reference path.

globalPoints = waypoints(2:end,:) + [20 -50];
nearestPathPoint = closestPoint(refPath,globalPoints);

Display the global points and the closest points on reference path.


Interpolate between the arc lengths of the first two closest points along the reference path.

arclengths = linspace(nearestPathPoint(1,6),nearestPathPoint(2,6),10);
pathStates = interpolate(refPath,arclengths);

Display the interpolated path points.

legend(["Waypoints","Reference Path","Trajectory to 30m",...
        "Global Points","Closest Points","Interpolated Path Points"])

Input Arguments

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Reference path, specified as a referencePathFrenet object.

Distances along the reference path, specified as an N-element vector. N is the number of arc lengths at which to sample points. Each distance is in meters.

Output Arguments

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Points on the reference path , returned as an N-by-6 numeric matrix with rows of form [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 m-1

  • dkappa — Derivative of curvature with respect to arc length in m-2

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

N is the number of points sampled along the reference path.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced in R2020b