Team2890/allwpilib
4
0
Fork 0
mirror of https://github.com/wpilibsuite/allwpilib synced 2026-06-25 01:41:43 +00:00
Code Issues Packages Projects Releases Wiki Activity

[wpimath] Make controllers and some trajectory classes constexpr (#7343)

Browse Source
This commit is contained in:
Tyler Veness
2024-11-07 13:02:11 -08:00
committed by GitHub
parent 44a45d44e2
commit a66fa339dc
71 changed files with 1512 additions and 1900 deletions
Download Patch File Download Diff File Expand all files Collapse all files

45
wpimath/src/main/native/cpp/spline/CubicHermiteSpline.cpp
View File

@@ -1,45 +0,0 @@
// 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/CubicHermiteSpline.h"
using namespace frc;
CubicHermiteSpline::CubicHermiteSpline(
wpi::array<double, 2> xInitialControlVector,
wpi::array<double, 2> xFinalControlVector,
wpi::array<double, 2> yInitialControlVector,
wpi::array<double, 2> yFinalControlVector)
: m_initialControlVector{xInitialControlVector, yInitialControlVector},
m_finalControlVector{xFinalControlVector, yFinalControlVector} {
const auto hermite = MakeHermiteBasis();
const auto x =
ControlVectorFromArrays(xInitialControlVector, xFinalControlVector);
const auto y =
ControlVectorFromArrays(yInitialControlVector, yFinalControlVector);
// Populate first two rows with coefficients.
m_coefficients.template block<1, 4>(0, 0) = hermite * x;
m_coefficients.template block<1, 4>(1, 0) = hermite * y;
// Populate Row 2 and Row 3 with the derivatives of the equations above.
// Then populate row 4 and 5 with the second derivatives.
for (int i = 0; i < 4; i++) {
// Here, we are multiplying by (3 - i) to manually take the derivative. The
// power of the term in index 0 is 3, index 1 is 2 and so on. To find the
// coefficient of the derivative, we can use the power rule and multiply
// the existing coefficient by its power.
m_coefficients.template block<2, 1>(2, i) =
m_coefficients.template block<2, 1>(0, i) * (3 - i);
}
for (int i = 0; i < 3; i++) {
// Here, we are multiplying by (2 - i) to manually take the derivative. The
// power of the term in index 0 is 2, index 1 is 1 and so on. To find the
// coefficient of the derivative, we can use the power rule and multiply
// the existing coefficient by its power.
m_coefficients.template block<2, 1>(4, i) =
m_coefficients.template block<2, 1>(2, i) * (2 - i);
}
}

44
wpimath/src/main/native/cpp/spline/QuinticHermiteSpline.cpp
View File

@@ -1,44 +0,0 @@
// 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/QuinticHermiteSpline.h"
using namespace frc;
QuinticHermiteSpline::QuinticHermiteSpline(
wpi::array<double, 3> xInitialControlVector,
wpi::array<double, 3> xFinalControlVector,
wpi::array<double, 3> yInitialControlVector,
wpi::array<double, 3> yFinalControlVector)
: m_initialControlVector{xInitialControlVector, yInitialControlVector},
m_finalControlVector{xFinalControlVector, yFinalControlVector} {
const auto hermite = MakeHermiteBasis();
const auto x =
ControlVectorFromArrays(xInitialControlVector, xFinalControlVector);
const auto y =
ControlVectorFromArrays(yInitialControlVector, yFinalControlVector);
// Populate first two rows with coefficients.
m_coefficients.template block<1, 6>(0, 0) = (hermite * x).transpose();
m_coefficients.template block<1, 6>(1, 0) = (hermite * y).transpose();
// Populate Row 2 and Row 3 with the derivatives of the equations above.
// Then populate row 4 and 5 with the second derivatives.
for (int i = 0; i < 6; i++) {
// Here, we are multiplying by (5 - i) to manually take the derivative. The
// power of the term in index 0 is 5, index 1 is 4 and so on. To find the
// coefficient of the derivative, we can use the power rule and multiply
// the existing coefficient by its power.
m_coefficients.template block<2, 1>(2, i) =
m_coefficients.template block<2, 1>(0, i) * (5 - i);
}
for (int i = 0; i < 5; i++) {
// Here, we are multiplying by (4 - i) to manually take the derivative. The
// power of the term in index 0 is 4, index 1 is 3 and so on. To find the
// coefficient of the derivative, we can use the power rule and multiply
// the existing coefficient by its power.
m_coefficients.template block<2, 1>(4, i) =
m_coefficients.template block<2, 1>(2, i) * (4 - i);
}
}

281
wpimath/src/main/native/cpp/spline/SplineHelper.cpp
View File

@@ -1,281 +0,0 @@
// 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];
}
}