mirror of
https://github.com/wpilibsuite/allwpilib
synced 2026-06-20 00:51:42 +00:00
282 lines
10 KiB
C++
282 lines
10 KiB
C++
// Copyright (c) FIRST and other WPILib contributors.
|
|
// Open Source Software; you can modify and/or share it under the terms of
|
|
// the WPILib BSD license file in the root directory of this project.
|
|
|
|
#include "frc/spline/SplineHelper.h"
|
|
|
|
#include <cstddef>
|
|
#include <vector>
|
|
|
|
using namespace frc;
|
|
|
|
std::vector<CubicHermiteSpline> SplineHelper::CubicSplinesFromControlVectors(
|
|
const Spline<3>::ControlVector& start, std::vector<Translation2d> waypoints,
|
|
const Spline<3>::ControlVector& end) {
|
|
std::vector<CubicHermiteSpline> splines;
|
|
|
|
wpi::array<double, 2> xInitial = start.x;
|
|
wpi::array<double, 2> yInitial = start.y;
|
|
wpi::array<double, 2> xFinal = end.x;
|
|
wpi::array<double, 2> yFinal = end.y;
|
|
|
|
if (waypoints.size() > 1) {
|
|
waypoints.emplace(waypoints.begin(),
|
|
Translation2d{units::meter_t{xInitial[0]},
|
|
units::meter_t{yInitial[0]}});
|
|
waypoints.emplace_back(
|
|
Translation2d{units::meter_t{xFinal[0]}, units::meter_t{yFinal[0]}});
|
|
|
|
// Populate tridiagonal system for clamped cubic
|
|
/* See:
|
|
https://www.uio.no/studier/emner/matnat/ifi/nedlagte-emner/INF-MAT4350/h08
|
|
/undervisningsmateriale/chap7alecture.pdf
|
|
*/
|
|
|
|
// Above-diagonal of tridiagonal matrix, zero-padded
|
|
std::vector<double> a;
|
|
// Diagonal of tridiagonal matrix
|
|
std::vector<double> b(waypoints.size() - 2, 4.0);
|
|
// Below-diagonal of tridiagonal matrix, zero-padded
|
|
std::vector<double> c;
|
|
// rhs vectors
|
|
std::vector<double> dx, dy;
|
|
// solution vectors
|
|
std::vector<double> fx(waypoints.size() - 2, 0.0),
|
|
fy(waypoints.size() - 2, 0.0);
|
|
|
|
// populate above-diagonal and below-diagonal vectors
|
|
a.emplace_back(0);
|
|
for (size_t i = 0; i < waypoints.size() - 3; ++i) {
|
|
a.emplace_back(1);
|
|
c.emplace_back(1);
|
|
}
|
|
c.emplace_back(0);
|
|
|
|
// populate rhs vectors
|
|
dx.emplace_back(3 * (waypoints[2].X().value() - waypoints[0].X().value()) -
|
|
xInitial[1]);
|
|
dy.emplace_back(3 * (waypoints[2].Y().value() - waypoints[0].Y().value()) -
|
|
yInitial[1]);
|
|
if (waypoints.size() > 4) {
|
|
for (size_t i = 1; i <= waypoints.size() - 4; ++i) {
|
|
// dx and dy represent the derivatives of the internal waypoints. The
|
|
// derivative of the second internal waypoint should involve the third
|
|
// and first internal waypoint, which have indices of 1 and 3 in the
|
|
// waypoints list (which contains ALL waypoints).
|
|
dx.emplace_back(
|
|
3 * (waypoints[i + 2].X().value() - waypoints[i].X().value()));
|
|
dy.emplace_back(
|
|
3 * (waypoints[i + 2].Y().value() - waypoints[i].Y().value()));
|
|
}
|
|
}
|
|
dx.emplace_back(3 * (waypoints[waypoints.size() - 1].X().value() -
|
|
waypoints[waypoints.size() - 3].X().value()) -
|
|
xFinal[1]);
|
|
dy.emplace_back(3 * (waypoints[waypoints.size() - 1].Y().value() -
|
|
waypoints[waypoints.size() - 3].Y().value()) -
|
|
yFinal[1]);
|
|
|
|
// Compute solution to tridiagonal system
|
|
ThomasAlgorithm(a, b, c, dx, &fx);
|
|
ThomasAlgorithm(a, b, c, dy, &fy);
|
|
|
|
fx.emplace(fx.begin(), xInitial[1]);
|
|
fx.emplace_back(xFinal[1]);
|
|
fy.emplace(fy.begin(), yInitial[1]);
|
|
fy.emplace_back(yFinal[1]);
|
|
|
|
for (size_t i = 0; i < fx.size() - 1; ++i) {
|
|
// Create the spline.
|
|
const CubicHermiteSpline spline{
|
|
{waypoints[i].X().value(), fx[i]},
|
|
{waypoints[i + 1].X().value(), fx[i + 1]},
|
|
{waypoints[i].Y().value(), fy[i]},
|
|
{waypoints[i + 1].Y().value(), fy[i + 1]}};
|
|
|
|
splines.push_back(spline);
|
|
}
|
|
} else if (waypoints.size() == 1) {
|
|
const double xDeriv =
|
|
(3 * (xFinal[0] - xInitial[0]) - xFinal[1] - xInitial[1]) / 4.0;
|
|
const double yDeriv =
|
|
(3 * (yFinal[0] - yInitial[0]) - yFinal[1] - yInitial[1]) / 4.0;
|
|
|
|
wpi::array<double, 2> midXControlVector{waypoints[0].X().value(), xDeriv};
|
|
wpi::array<double, 2> midYControlVector{waypoints[0].Y().value(), yDeriv};
|
|
|
|
splines.emplace_back(xInitial, midXControlVector, yInitial,
|
|
midYControlVector);
|
|
splines.emplace_back(midXControlVector, xFinal, midYControlVector, yFinal);
|
|
|
|
} else {
|
|
// Create the spline.
|
|
const CubicHermiteSpline spline{xInitial, xFinal, yInitial, yFinal};
|
|
splines.push_back(spline);
|
|
}
|
|
|
|
return splines;
|
|
}
|
|
|
|
std::vector<QuinticHermiteSpline>
|
|
SplineHelper::QuinticSplinesFromControlVectors(
|
|
const std::vector<Spline<5>::ControlVector>& controlVectors) {
|
|
std::vector<QuinticHermiteSpline> splines;
|
|
for (size_t i = 0; i < controlVectors.size() - 1; ++i) {
|
|
auto& xInitial = controlVectors[i].x;
|
|
auto& yInitial = controlVectors[i].y;
|
|
auto& xFinal = controlVectors[i + 1].x;
|
|
auto& yFinal = controlVectors[i + 1].y;
|
|
splines.emplace_back(xInitial, xFinal, yInitial, yFinal);
|
|
}
|
|
return splines;
|
|
}
|
|
|
|
wpi::array<Spline<3>::ControlVector, 2>
|
|
SplineHelper::CubicControlVectorsFromWaypoints(
|
|
const Pose2d& start, const std::vector<Translation2d>& interiorWaypoints,
|
|
const Pose2d& end) {
|
|
double scalar;
|
|
if (interiorWaypoints.empty()) {
|
|
scalar = 1.2 * start.Translation().Distance(end.Translation()).value();
|
|
} else {
|
|
scalar =
|
|
1.2 * start.Translation().Distance(interiorWaypoints.front()).value();
|
|
}
|
|
const auto initialCV = CubicControlVector(scalar, start);
|
|
if (!interiorWaypoints.empty()) {
|
|
scalar = 1.2 * end.Translation().Distance(interiorWaypoints.back()).value();
|
|
}
|
|
const auto finalCV = CubicControlVector(scalar, end);
|
|
return {initialCV, finalCV};
|
|
}
|
|
|
|
std::vector<QuinticHermiteSpline> SplineHelper::QuinticSplinesFromWaypoints(
|
|
const std::vector<Pose2d>& waypoints) {
|
|
std::vector<QuinticHermiteSpline> splines;
|
|
splines.reserve(waypoints.size() - 1);
|
|
for (size_t i = 0; i < waypoints.size() - 1; ++i) {
|
|
auto& p0 = waypoints[i];
|
|
auto& p1 = waypoints[i + 1];
|
|
|
|
// This just makes the splines look better.
|
|
const auto scalar =
|
|
1.2 * p0.Translation().Distance(p1.Translation()).value();
|
|
|
|
auto controlVectorA = QuinticControlVector(scalar, p0);
|
|
auto controlVectorB = QuinticControlVector(scalar, p1);
|
|
splines.emplace_back(controlVectorA.x, controlVectorB.x, controlVectorA.y,
|
|
controlVectorB.y);
|
|
}
|
|
return splines;
|
|
}
|
|
|
|
std::vector<QuinticHermiteSpline> SplineHelper::OptimizeCurvature(
|
|
const std::vector<QuinticHermiteSpline>& splines) {
|
|
// If there's only one spline in the vector, we can't optimize anything so
|
|
// just return that.
|
|
if (splines.size() < 2) {
|
|
return splines;
|
|
}
|
|
|
|
// Implements Section 4.1.2 of
|
|
// http://www2.informatik.uni-freiburg.de/~lau/students/Sprunk2008.pdf.
|
|
|
|
// Cubic splines minimize the integral of the second derivative's absolute
|
|
// value. Therefore, we can create cubic splines with the same 0th and 1st
|
|
// derivatives and the provided quintic splines, find the second derivative of
|
|
// those cubic splines and then use a weighted average for the second
|
|
// derivatives of the quintic splines.
|
|
|
|
std::vector<QuinticHermiteSpline> optimizedSplines;
|
|
optimizedSplines.reserve(splines.size());
|
|
optimizedSplines.push_back(splines[0]);
|
|
|
|
for (size_t i = 0; i < splines.size() - 1; ++i) {
|
|
const auto& a = splines[i];
|
|
const auto& b = splines[i + 1];
|
|
|
|
// Get the control vectors that created the quintic splines above.
|
|
const auto& aInitial = a.GetInitialControlVector();
|
|
const auto& aFinal = a.GetFinalControlVector();
|
|
const auto& bInitial = b.GetInitialControlVector();
|
|
const auto& bFinal = b.GetFinalControlVector();
|
|
|
|
// Create cubic splines with the same control vectors.
|
|
auto Trim = [](const wpi::array<double, 3>& a) {
|
|
return wpi::array<double, 2>{a[0], a[1]};
|
|
};
|
|
CubicHermiteSpline ca{Trim(aInitial.x), Trim(aFinal.x), Trim(aInitial.y),
|
|
Trim(aFinal.y)};
|
|
CubicHermiteSpline cb{Trim(bInitial.x), Trim(bFinal.x), Trim(bInitial.y),
|
|
Trim(bFinal.y)};
|
|
|
|
// Calculate the second derivatives at the knot points.
|
|
frc::Vectord<4> bases{1.0, 1.0, 1.0, 1.0};
|
|
frc::Vectord<6> combinedA = ca.Coefficients() * bases;
|
|
|
|
double ddxA = combinedA(4);
|
|
double ddyA = combinedA(5);
|
|
double ddxB = cb.Coefficients()(4, 1);
|
|
double ddyB = cb.Coefficients()(5, 1);
|
|
|
|
// Calculate the parameters for weighted average.
|
|
double dAB =
|
|
std::hypot(aFinal.x[0] - aInitial.x[0], aFinal.y[0] - aInitial.y[0]);
|
|
double dBC =
|
|
std::hypot(bFinal.x[0] - bInitial.x[0], bFinal.y[0] - bInitial.y[0]);
|
|
double alpha = dBC / (dAB + dBC);
|
|
double beta = dAB / (dAB + dBC);
|
|
|
|
// Calculate the weighted average.
|
|
double ddx = alpha * ddxA + beta * ddxB;
|
|
double ddy = alpha * ddyA + beta * ddyB;
|
|
|
|
// Create new splines.
|
|
optimizedSplines[i] = {aInitial.x,
|
|
{aFinal.x[0], aFinal.x[1], ddx},
|
|
aInitial.y,
|
|
{aFinal.y[0], aFinal.y[1], ddy}};
|
|
optimizedSplines.push_back({{bInitial.x[0], bInitial.x[1], ddx},
|
|
bFinal.x,
|
|
{bInitial.y[0], bInitial.y[1], ddy},
|
|
bFinal.y});
|
|
}
|
|
|
|
return optimizedSplines;
|
|
}
|
|
|
|
void SplineHelper::ThomasAlgorithm(const std::vector<double>& a,
|
|
const std::vector<double>& b,
|
|
const std::vector<double>& c,
|
|
const std::vector<double>& d,
|
|
std::vector<double>* solutionVector) {
|
|
auto& f = *solutionVector;
|
|
size_t N = d.size();
|
|
|
|
// Create the temporary vectors
|
|
// Note that this is inefficient as it is possible to call
|
|
// this function many times. A better implementation would
|
|
// pass these temporary matrices by non-const reference to
|
|
// save excess allocation and deallocation
|
|
std::vector<double> c_star(N, 0.0);
|
|
std::vector<double> d_star(N, 0.0);
|
|
|
|
// This updates the coefficients in the first row
|
|
// Note that we should be checking for division by zero here
|
|
c_star[0] = c[0] / b[0];
|
|
d_star[0] = d[0] / b[0];
|
|
|
|
// Create the c_star and d_star coefficients in the forward sweep
|
|
for (size_t i = 1; i < N; ++i) {
|
|
double m = 1.0 / (b[i] - a[i] * c_star[i - 1]);
|
|
c_star[i] = c[i] * m;
|
|
d_star[i] = (d[i] - a[i] * d_star[i - 1]) * m;
|
|
}
|
|
|
|
f[N - 1] = d_star[N - 1];
|
|
// This is the reverse sweep, used to update the solution vector f
|
|
for (int i = N - 2; i >= 0; i--) {
|
|
f[i] = d_star[i] - c_star[i] * f[i + 1];
|
|
}
|
|
}
|