249 lines
13 KiB
C#
249 lines
13 KiB
C#
using System;
|
|
using System.Collections.Generic;
|
|
using MultiWheelC.TrajectoryPlanning.CoarsePath;
|
|
|
|
namespace MultiWheelC.TrajectoryPlanning.EMPlanner;
|
|
|
|
/// <summary>Builds normalized squared-residual costs in OSQP's 0.5*x'P*x + q'x convention.</summary>
|
|
public sealed class LateralObjectiveBuilder
|
|
{
|
|
public void AddTerms(LateralPlanningInput input, LateralVariableLayout layout, LateralCandidate linearization,
|
|
SparseTripletBuilder hessian, IList<double> linearCost)
|
|
{
|
|
if (input == null)
|
|
throw new ArgumentNullException(nameof(input));
|
|
if (layout == null)
|
|
throw new ArgumentNullException(nameof(layout));
|
|
if (linearization == null)
|
|
throw new ArgumentNullException(nameof(linearization));
|
|
if (hessian == null)
|
|
throw new ArgumentNullException(nameof(hessian));
|
|
if (linearCost == null || linearCost.Count != layout.VariableCount)
|
|
throw new ArgumentException("Linear cost must match the lateral layout.", nameof(linearCost));
|
|
|
|
LateralConfiguration lateral = input.Configuration.Lateral ?? throw new ArgumentException("Missing lateral configuration.");
|
|
LateralWeights weights = lateral.Weights ?? throw new ArgumentException("Missing lateral weights.");
|
|
double lateralScale = RequirePositive(input.Configuration.Corridor.MaximumLateralOffsetMeters, "lateral scale");
|
|
double slopeScale = RequirePositive(lateral.MaximumLateralSlope, "slope scale");
|
|
double secondDerivativeScale = RequirePositive(lateral.MaximumLateralSecondDerivativePerMeter, "second-derivative scale");
|
|
double thirdDerivativeScale = RequirePositive(lateral.MaximumLateralThirdDerivativePerSquareMeter, "third-derivative scale");
|
|
double curvatureScale = RequirePositive(GetMaximumVehicleCurvature(input.Vehicle), "curvature scale");
|
|
double curvatureVariationScale = GetCurvatureVariationScale(input);
|
|
|
|
for (int station = 0; station < layout.StationCount; station++)
|
|
{
|
|
AddSquaredResidual(hessian, linearCost, new[] { layout.L(station) }, new[] { 1d }, 0d,
|
|
weights.ReferenceOffset, lateralScale);
|
|
AddSquaredResidual(hessian, linearCost, new[] { layout.DL(station) }, new[] { 1d }, 0d,
|
|
weights.HeadingDeviation, slopeScale);
|
|
AddSquaredResidual(hessian, linearCost, new[] { layout.DDL(station) }, new[] { 1d }, 0d,
|
|
weights.SecondDerivative, secondDerivativeScale);
|
|
}
|
|
for (int interval = 0; interval < layout.StationCount - 1; interval++)
|
|
{
|
|
AddSquaredResidual(hessian, linearCost, new[] { layout.DDDL(interval) }, new[] { 1d }, 0d,
|
|
weights.ThirdDerivative, thirdDerivativeScale);
|
|
}
|
|
|
|
AddPreviousTrajectoryTerms(input, layout, hessian, linearCost, weights.PreviousTrajectory, lateralScale);
|
|
CurvatureAffine[] curvature = CreateCurvatureAffines(input, layout, linearization);
|
|
for (int station = 0; station < curvature.Length; station++)
|
|
{
|
|
AddSquaredResidual(hessian, linearCost, curvature[station].Indices, curvature[station].Gradient,
|
|
curvature[station].Constant, weights.Curvature, curvatureScale);
|
|
}
|
|
AddCurvatureVariationTerms(input.ReferenceStations, curvature, hessian, linearCost, weights.CurvatureVariation,
|
|
curvatureVariationScale);
|
|
if (input.TerminalType == EmTerminalType.RollingSafetyStop)
|
|
{
|
|
AddSquaredResidual(hessian, linearCost, new[] { layout.L(layout.StationCount - 1) }, new[] { 1d }, 0d,
|
|
weights.RollingTerminal, lateralScale);
|
|
}
|
|
}
|
|
|
|
private static void AddPreviousTrajectoryTerms(LateralPlanningInput input, LateralVariableLayout layout,
|
|
SparseTripletBuilder hessian, IList<double> linearCost, double weight, double lateralScale)
|
|
{
|
|
if (input.PreviousTrajectorySeed.Count == 0)
|
|
return;
|
|
|
|
for (int station = 0; station < layout.StationCount; station++)
|
|
{
|
|
double previousL = InterpolatePreviousL(input.PreviousTrajectorySeed, input.ReferenceStations[station]);
|
|
AddSquaredResidual(hessian, linearCost, new[] { layout.L(station) }, new[] { 1d }, -previousL,
|
|
weight, lateralScale);
|
|
}
|
|
}
|
|
|
|
private static CurvatureAffine[] CreateCurvatureAffines(LateralPlanningInput input, LateralVariableLayout layout,
|
|
LateralCandidate linearization)
|
|
{
|
|
var affines = new CurvatureAffine[layout.StationCount];
|
|
double directionSign = input.ReferenceSegment.Direction == TravelDirection.Forward ? 1d : -1d;
|
|
for (int station = 0; station < layout.StationCount; station++)
|
|
{
|
|
FrenetReferencePoint reference = ReferencePathInterpolator.Interpolate(input.ReferenceSegment,
|
|
input.ReferenceStations[station]);
|
|
double l = linearization.L[station];
|
|
double dl = linearization.DL[station];
|
|
double ddl = linearization.DDL[station];
|
|
double referenceCurvature = reference.GeometricCurvature;
|
|
double referenceCurvatureDerivative = directionSign * reference.VehicleCurvatureDerivative;
|
|
double a = 1d - referenceCurvature * l;
|
|
double denominatorSquared = a * a + dl * dl;
|
|
if (!IsFinite(denominatorSquared) || denominatorSquared <= 0d)
|
|
throw new ArgumentException("Curvature linearization denominator is invalid.", nameof(linearization));
|
|
|
|
double denominatorPow3Over2 = denominatorSquared * Math.Sqrt(denominatorSquared);
|
|
double denominatorPow5Over2 = denominatorPow3Over2 * denominatorSquared;
|
|
double numerator = a * a * referenceCurvature + a * ddl +
|
|
referenceCurvatureDerivative * l * dl + 2d * referenceCurvature * dl * dl;
|
|
double geometricCurvature = numerator / denominatorPow3Over2;
|
|
double dNumeratorDLateral = -2d * a * referenceCurvature * referenceCurvature -
|
|
referenceCurvature * ddl + referenceCurvatureDerivative * dl;
|
|
double dNumeratorDSlope = referenceCurvatureDerivative * l + 4d * referenceCurvature * dl;
|
|
double dDenominatorSquaredDLateral = -2d * a * referenceCurvature;
|
|
double dDenominatorSquaredDSlope = 2d * dl;
|
|
double dGeometricDLateral = dNumeratorDLateral / denominatorPow3Over2 -
|
|
1.5d * numerator * dDenominatorSquaredDLateral / denominatorPow5Over2;
|
|
double dGeometricDSlope = dNumeratorDSlope / denominatorPow3Over2 -
|
|
1.5d * numerator * dDenominatorSquaredDSlope / denominatorPow5Over2;
|
|
double dGeometricDSecondDerivative = a / denominatorPow3Over2;
|
|
double vehicleCurvature = directionSign * geometricCurvature;
|
|
double[] gradient =
|
|
{
|
|
directionSign * dGeometricDLateral,
|
|
directionSign * dGeometricDSlope,
|
|
directionSign * dGeometricDSecondDerivative,
|
|
};
|
|
double constant = vehicleCurvature - gradient[0] * l - gradient[1] * dl - gradient[2] * ddl;
|
|
if (!IsFinite(vehicleCurvature) || !IsFinite(constant) || !IsFinite(gradient[0]) ||
|
|
!IsFinite(gradient[1]) || !IsFinite(gradient[2]))
|
|
{
|
|
throw new ArgumentException("Curvature linearization is non-finite.", nameof(linearization));
|
|
}
|
|
affines[station] = new CurvatureAffine(new[] { layout.L(station), layout.DL(station), layout.DDL(station) },
|
|
gradient, constant);
|
|
}
|
|
return affines;
|
|
}
|
|
|
|
private static void AddCurvatureVariationTerms(IReadOnlyList<double> stations, CurvatureAffine[] curvature,
|
|
SparseTripletBuilder hessian, IList<double> linearCost, double weight, double scale)
|
|
{
|
|
for (int station = 0; station < curvature.Length; station++)
|
|
{
|
|
int lower = station == 0 ? 0 : station - 1;
|
|
int upper = station == curvature.Length - 1 ? curvature.Length - 1 : station + 1;
|
|
double ds = stations[upper] - stations[lower];
|
|
if (!IsFinite(ds) || ds <= 0d)
|
|
throw new ArgumentException("Curvature variation requires strictly increasing stations.", nameof(stations));
|
|
CurvatureAffine left = curvature[lower];
|
|
CurvatureAffine right = curvature[upper];
|
|
var indices = new int[left.Indices.Length + right.Indices.Length];
|
|
var gradient = new double[indices.Length];
|
|
for (int index = 0; index < left.Indices.Length; index++)
|
|
{
|
|
indices[index] = left.Indices[index];
|
|
gradient[index] = -left.Gradient[index] / ds;
|
|
indices[left.Indices.Length + index] = right.Indices[index];
|
|
gradient[left.Indices.Length + index] = right.Gradient[index] / ds;
|
|
}
|
|
AddSquaredResidual(hessian, linearCost, indices, gradient, (right.Constant - left.Constant) / ds, weight, scale);
|
|
}
|
|
}
|
|
|
|
private static void AddSquaredResidual(SparseTripletBuilder hessian, IList<double> linearCost,
|
|
IReadOnlyList<int> indices, IReadOnlyList<double> gradient, double constant, double weight, double scale)
|
|
{
|
|
if (indices.Count != gradient.Count || indices.Count == 0 || !IsFinite(constant))
|
|
throw new ArgumentException("Affine residual is invalid.");
|
|
if (!IsFinite(weight) || weight < 0d)
|
|
throw new ArgumentOutOfRangeException(nameof(weight));
|
|
double coefficient = 2d * weight / (scale * scale);
|
|
for (int left = 0; left < indices.Count; left++)
|
|
{
|
|
if (!IsFinite(gradient[left]) || indices[left] < 0 || indices[left] >= linearCost.Count)
|
|
throw new ArgumentOutOfRangeException(nameof(gradient));
|
|
linearCost[indices[left]] += coefficient * constant * gradient[left];
|
|
for (int right = left; right < indices.Count; right++)
|
|
{
|
|
if (!IsFinite(gradient[right]) || indices[right] < 0 || indices[right] >= linearCost.Count)
|
|
throw new ArgumentOutOfRangeException(nameof(gradient));
|
|
int row = Math.Min(indices[left], indices[right]);
|
|
int column = Math.Max(indices[left], indices[right]);
|
|
hessian.Add(row, column, coefficient * gradient[left] * gradient[right]);
|
|
}
|
|
}
|
|
}
|
|
|
|
private static double InterpolatePreviousL(IReadOnlyList<FrenetProjection> seed, double referenceS)
|
|
{
|
|
if (referenceS <= seed[0].ReferenceS)
|
|
return seed[0].LateralOffset;
|
|
for (int index = 1; index < seed.Count; index++)
|
|
{
|
|
if (referenceS <= seed[index].ReferenceS)
|
|
{
|
|
FrenetProjection lower = seed[index - 1];
|
|
FrenetProjection upper = seed[index];
|
|
double span = upper.ReferenceS - lower.ReferenceS;
|
|
if (span <= 0d)
|
|
return upper.LateralOffset;
|
|
return lower.LateralOffset + (upper.LateralOffset - lower.LateralOffset) *
|
|
(referenceS - lower.ReferenceS) / span;
|
|
}
|
|
}
|
|
return seed[seed.Count - 1].LateralOffset;
|
|
}
|
|
|
|
private static double GetCurvatureVariationScale(LateralPlanningInput input)
|
|
{
|
|
double maximum = 0d;
|
|
for (int station = 0; station < input.ReferenceStations.Count; station++)
|
|
{
|
|
FrenetReferencePoint reference = ReferencePathInterpolator.Interpolate(input.ReferenceSegment,
|
|
input.ReferenceStations[station]);
|
|
maximum = Math.Max(maximum, Math.Abs(reference.VehicleCurvatureDerivative));
|
|
}
|
|
return Math.Max(1d, maximum);
|
|
}
|
|
|
|
private static double GetMaximumVehicleCurvature(VehicleParameters vehicle)
|
|
{
|
|
if (vehicle == null)
|
|
throw new ArgumentNullException(nameof(vehicle));
|
|
if (vehicle.MaximumCurvaturePerMeter.HasValue)
|
|
return vehicle.MaximumCurvaturePerMeter.Value;
|
|
if (vehicle.MinimumTurningRadiusMeters.HasValue && vehicle.MinimumTurningRadiusMeters.Value > 0d)
|
|
return 1d / vehicle.MinimumTurningRadiusMeters.Value;
|
|
throw new ArgumentException("Vehicle maximum curvature is required.", nameof(vehicle));
|
|
}
|
|
|
|
private static double RequirePositive(double value, string name)
|
|
{
|
|
if (!IsFinite(value) || value <= 0d)
|
|
throw new ArgumentOutOfRangeException(name);
|
|
return value;
|
|
}
|
|
|
|
private static bool IsFinite(double value)
|
|
{
|
|
return !double.IsNaN(value) && !double.IsInfinity(value);
|
|
}
|
|
|
|
private sealed class CurvatureAffine
|
|
{
|
|
public CurvatureAffine(int[] indices, double[] gradient, double constant)
|
|
{
|
|
Indices = indices;
|
|
Gradient = gradient;
|
|
Constant = constant;
|
|
}
|
|
|
|
public int[] Indices { get; }
|
|
public double[] Gradient { get; }
|
|
public double Constant { get; }
|
|
}
|
|
}
|