function

Planning.Bezier.septicControlPoints

Construct a degree-seven curve from endpoint derivatives through jerk

The eight endpoint constraints uniquely determine the eight control points. The resulting segment is suitable for position trajectories whose snap must also be evaluated.

Public declarations

Explicit source declarations; dimensions, modifications and defaults are shown as written, without evaluation.

Role	Name	Type	Dimensions / attributes / default	Description
input	`startDerivative`	`Real`	`[:, 4]`	Columns are position, velocity, acceleration, and jerk at t=0
input	`endDerivative`	`Real`	`[size(startDerivative, 1), 4]`	Columns are position, velocity, acceleration, and jerk at t=duration
input	`duration`	`Real`	`(unit = "s")`	Curve duration
output	`controlPoint`	`Real`	`[size(startDerivative, 1), 8]`	Degree-seven Bezier control points

Modelica declarations and implementation

Show parameters, interfaces and source

Parameters, inputs, outputs, defaults and equations from the source file.

function septicControlPoints
    "Construct a degree-seven curve from endpoint derivatives through jerk"
    input Real startDerivative[:, 4]
      "Columns are position, velocity, acceleration, and jerk at t=0";
    input Real endDerivative[size(startDerivative, 1), 4]
      "Columns are position, velocity, acceleration, and jerk at t=duration";
    input Real duration(unit = "s") "Curve duration";
    output Real controlPoint[size(startDerivative, 1), 8]
      "Degree-seven Bezier control points";
  algorithm
    assert(duration > 0.0, "Bezier duration must be positive");
    controlPoint[:, 1] := startDerivative[:, 1];
    controlPoint[:, 2] := controlPoint[:, 1]
      + duration * startDerivative[:, 2] / 7.0;
    controlPoint[:, 3] := duration^2 * startDerivative[:, 3] / 42.0
      + 2.0 * controlPoint[:, 2] - controlPoint[:, 1];
    controlPoint[:, 4] := duration^3 * startDerivative[:, 4] / 210.0
      + 3.0 * controlPoint[:, 3] - 3.0 * controlPoint[:, 2]
      + controlPoint[:, 1];
    controlPoint[:, 8] := endDerivative[:, 1];
    controlPoint[:, 7] := controlPoint[:, 8]
      - duration * endDerivative[:, 2] / 7.0;
    controlPoint[:, 6] := duration^2 * endDerivative[:, 3] / 42.0
      + 2.0 * controlPoint[:, 7] - controlPoint[:, 8];
    controlPoint[:, 5] := controlPoint[:, 8] - 3.0 * controlPoint[:, 7]
      + 3.0 * controlPoint[:, 6]
      - duration^3 * endDerivative[:, 4] / 210.0;
    annotation(Documentation(info="<html>
      <p>The eight endpoint constraints uniquely determine the eight control
      points. The resulting segment is suitable for position trajectories
      whose snap must also be evaluated.</p>
    </html>"));
  end septicControlPoints;