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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"])

Figure contains an axes object. The axes object contains 6 objects of type line. One or more of the lines displays its values using only markers These objects represent 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