mirror of
https://github.com/wpilibsuite/allwpilib
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195 lines
7.1 KiB
C++
195 lines
7.1 KiB
C++
/*----------------------------------------------------------------------------*/
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/* Copyright (c) 2019 FIRST. All Rights Reserved. */
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/* Open Source Software - may be modified and shared by FRC teams. The code */
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/* must be accompanied by the FIRST BSD license file in the root directory of */
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/* the project. */
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/*----------------------------------------------------------------------------*/
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#include "frc/spline/SplineHelper.h"
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#include <cstddef>
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using namespace frc;
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std::vector<CubicHermiteSpline> SplineHelper::CubicSplinesFromControlVectors(
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const Spline<3>::ControlVector& start, std::vector<Translation2d> waypoints,
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const Spline<3>::ControlVector& end) {
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std::vector<CubicHermiteSpline> splines;
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std::array<double, 2> xInitial = start.x;
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std::array<double, 2> yInitial = start.y;
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std::array<double, 2> xFinal = end.x;
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std::array<double, 2> yFinal = end.y;
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if (waypoints.size() > 1) {
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waypoints.emplace(waypoints.begin(),
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Translation2d{units::meter_t(xInitial[0]),
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units::meter_t(yInitial[0])});
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waypoints.emplace_back(
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Translation2d{units::meter_t(xFinal[0]), units::meter_t(yFinal[0])});
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std::vector<double> a;
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std::vector<double> b(waypoints.size() - 2, 4.0);
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std::vector<double> c;
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std::vector<double> dx, dy;
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std::vector<double> fx(waypoints.size() - 2, 0.0),
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fy(waypoints.size() - 2, 0.0);
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a.emplace_back(0);
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for (size_t i = 0; i < waypoints.size() - 3; ++i) {
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a.emplace_back(1);
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c.emplace_back(1);
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}
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c.emplace_back(0);
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dx.emplace_back(
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3 * (waypoints[2].X().to<double>() - waypoints[0].X().to<double>()) -
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xInitial[1]);
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dy.emplace_back(
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3 * (waypoints[2].Y().to<double>() - waypoints[0].Y().to<double>()) -
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yInitial[1]);
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if (waypoints.size() > 4) {
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for (size_t i = 1; i <= waypoints.size() - 4; ++i) {
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dx.emplace_back(3 * (waypoints[i + 1].X().to<double>() -
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waypoints[i - 1].X().to<double>()));
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dy.emplace_back(3 * (waypoints[i + 1].Y().to<double>() -
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waypoints[i - 1].Y().to<double>()));
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}
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}
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dx.emplace_back(3 * (waypoints[waypoints.size() - 1].X().to<double>() -
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waypoints[waypoints.size() - 3].X().to<double>()) -
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xFinal[1]);
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dy.emplace_back(3 * (waypoints[waypoints.size() - 1].Y().to<double>() -
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waypoints[waypoints.size() - 3].Y().to<double>()) -
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yFinal[1]);
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ThomasAlgorithm(a, b, c, dx, &fx);
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ThomasAlgorithm(a, b, c, dy, &fy);
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fx.emplace(fx.begin(), xInitial[1]);
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fx.emplace_back(xFinal[1]);
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fy.emplace(fy.begin(), yInitial[1]);
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fy.emplace_back(yFinal[1]);
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for (size_t i = 0; i < fx.size() - 1; ++i) {
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// Create the spline.
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const CubicHermiteSpline spline{
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{waypoints[i].X().to<double>(), fx[i]},
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{waypoints[i + 1].X().to<double>(), fx[i + 1]},
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{waypoints[i].Y().to<double>(), fy[i]},
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{waypoints[i + 1].Y().to<double>(), fy[i + 1]}};
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splines.push_back(spline);
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}
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} else if (waypoints.size() == 1) {
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const double xDeriv =
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(3 * (xFinal[0] - xInitial[0]) - xFinal[1] - xInitial[1]) / 4.0;
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const double yDeriv =
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(3 * (yFinal[0] - yInitial[0]) - yFinal[1] - yInitial[1]) / 4.0;
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std::array<double, 2> midXControlVector{waypoints[0].X().to<double>(),
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xDeriv};
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std::array<double, 2> midYControlVector{waypoints[0].Y().to<double>(),
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yDeriv};
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splines.emplace_back(xInitial, midXControlVector, yInitial,
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midYControlVector);
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splines.emplace_back(midXControlVector, xFinal, midYControlVector, yFinal);
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} else {
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// Create the spline.
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const CubicHermiteSpline spline{xInitial, xFinal, yInitial, yFinal};
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splines.push_back(spline);
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}
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return splines;
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}
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std::vector<QuinticHermiteSpline>
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SplineHelper::QuinticSplinesFromControlVectors(
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const std::vector<Spline<5>::ControlVector>& controlVectors) {
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std::vector<QuinticHermiteSpline> splines;
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for (size_t i = 0; i < controlVectors.size() - 1; ++i) {
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auto& xInitial = controlVectors[i].x;
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auto& yInitial = controlVectors[i].y;
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auto& xFinal = controlVectors[i + 1].x;
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auto& yFinal = controlVectors[i + 1].y;
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splines.emplace_back(xInitial, xFinal, yInitial, yFinal);
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}
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return splines;
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}
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std::array<Spline<3>::ControlVector, 2>
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SplineHelper::CubicControlVectorsFromWaypoints(
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const Pose2d& start, const std::vector<Translation2d>& interiorWaypoints,
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const Pose2d& end) {
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double scalar;
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if (interiorWaypoints.empty()) {
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scalar = 1.2 * start.Translation().Distance(end.Translation()).to<double>();
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} else {
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scalar =
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1.2 *
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start.Translation().Distance(interiorWaypoints.front()).to<double>();
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}
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const auto initialCV = CubicControlVector(scalar, start);
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if (!interiorWaypoints.empty()) {
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scalar =
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1.2 * end.Translation().Distance(interiorWaypoints.back()).to<double>();
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}
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const auto finalCV = CubicControlVector(scalar, end);
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return {initialCV, finalCV};
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}
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std::vector<Spline<5>::ControlVector>
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SplineHelper::QuinticControlVectorsFromWaypoints(
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const std::vector<Pose2d>& waypoints) {
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std::vector<Spline<5>::ControlVector> vectors;
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for (size_t i = 0; i < waypoints.size() - 1; ++i) {
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auto& p0 = waypoints[i];
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auto& p1 = waypoints[i + 1];
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// This just makes the splines look better.
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const auto scalar =
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1.2 * p0.Translation().Distance(p1.Translation()).to<double>();
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vectors.push_back(QuinticControlVector(scalar, p0));
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vectors.push_back(QuinticControlVector(scalar, p1));
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}
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return vectors;
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}
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void SplineHelper::ThomasAlgorithm(const std::vector<double>& a,
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const std::vector<double>& b,
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const std::vector<double>& c,
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const std::vector<double>& d,
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std::vector<double>* solutionVector) {
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auto& f = *solutionVector;
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size_t N = d.size();
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// Create the temporary vectors
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// Note that this is inefficient as it is possible to call
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// this function many times. A better implementation would
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// pass these temporary matrices by non-const reference to
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// save excess allocation and deallocation
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std::vector<double> c_star(N, 0.0);
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std::vector<double> d_star(N, 0.0);
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// This updates the coefficients in the first row
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// Note that we should be checking for division by zero here
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c_star[0] = c[0] / b[0];
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d_star[0] = d[0] / b[0];
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// Create the c_star and d_star coefficients in the forward sweep
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for (size_t i = 1; i < N; ++i) {
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double m = 1.0 / (b[i] - a[i] * c_star[i - 1]);
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c_star[i] = c[i] * m;
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d_star[i] = (d[i] - a[i] * d_star[i - 1]) * m;
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}
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f[N - 1] = d_star[N - 1];
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// This is the reverse sweep, used to update the solution vector f
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for (int i = N - 2; i >= 0; i--) {
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f[i] = d_star[i] - c_star[i] * f[i + 1];
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}
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}
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