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Convert global states to Frenet states

Since R2020b



frenetState = global2frenet(refPath,globalState) converts global states to Frenet trajectory states.

[___,latTimeDerivatives] = global2frenet(refPath,globalState) returns latTimeDerivatives containing 1st and 2nd order derivatives of lateral deviation with respect to time and a flag indicating if the heading should flip when converting to global coordinates.

[___] = global2frenet(refPath,globalState,sFrame) accepts a vector of arclengths, sFrame at which the Frenet frame should be centered at.


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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.

States in the global coordinate frame, specified as a P-by-6 numeric matrix with rows of form [x y theta kappa speed accel], 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.

  • speed –– Speed in the theta direction in m/s.

  • accel –– Acceleration in the theta direction in m/s2.

P is the total number of Global states.

Arclength center locations for the Frenet frames, specified as an N-element vector in meters. For correct results, the vector between the frame and the xy location of the globalState must be orthogonal to the tangent angle.

Output Arguments

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States in the Frenet coordinate frame, returned as a P-by-6 numeric matrix with rows 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. P is the total number of Frenet states.

Lateral time derivatives, specified as an N-by-3 matrix where each row is of the form [dL/dt ddL/dt^2 invertHeading] and N is the total number of points in points. Each row contains the 1st and 2nd order time derivatives of lateral deviation and a flag, invertHeading, which indicates whether the heading should be flipped when converting to global coordinates (true) or not (false).


If defining latTimeDerivatives without the use of global2frenet, the following rules should be followed:

  1. The invertHeading flag should be true when:

    1. The vehicle is moving in reverse (speed is less than 0)

    2. The vehicle is stationary (speed is equal to 0), and the vehicle is facing away from the path's tangent vector. i.e. cos(|tangentAngle(obj,S)-thetaExpected|) < 0

  2. If 1b is true, then dL/dS must be negated.

Extended Capabilities

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

Version History

Introduced in R2020b