feat: assemble lateral LS quadratic programs
This commit is contained in:
梁薄云
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using System;
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using System.Collections.Generic;
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namespace MultiWheelC.TrajectoryPlanning.EMPlanner;
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/// <summary>Assembles one lateral SQP QP with exact dynamics and finite hard bounds.</summary>
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public sealed class LateralConstraintBuilder
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{
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private const double Epsilon = 1e-12d;
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private readonly LateralObjectiveBuilder _objectiveBuilder;
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public LateralConstraintBuilder(LateralObjectiveBuilder objectiveBuilder)
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{
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_objectiveBuilder = objectiveBuilder ?? throw new ArgumentNullException(nameof(objectiveBuilder));
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}
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public bool TryBuild(LateralPlanningInput input, LateralCandidate linearization, out QuadraticProgram problem,
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out string failureReason)
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{
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problem = null;
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failureReason = string.Empty;
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if (input == null || linearization == null)
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{
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failureReason = "Lateral input and linearization are required.";
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return false;
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}
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if (!TryValidateCandidateStations(input, linearization, out failureReason))
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return false;
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try
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{
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var layout = new LateralVariableLayout(input.ReferenceStations.Count);
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var hessian = new SparseTripletBuilder(layout.VariableCount, layout.VariableCount, true);
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var linearCost = new double[layout.VariableCount];
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_objectiveBuilder.AddTerms(input, layout, linearization, hessian, linearCost);
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int terminalRows = input.TerminalType == EmTerminalType.RollingSafetyStop ? 0 : 2;
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var constraints = new SparseTripletBuilder(7 * layout.StationCount - 2 + terminalRows, layout.VariableCount);
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var lower = new List<double>();
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var upper = new List<double>();
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int row = 0;
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if (!TryAddLateralBounds(input, layout, linearization, constraints, lower, upper, ref row, out failureReason))
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return false;
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AddDerivativeBounds(input, layout, constraints, lower, upper, ref row);
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AddStartConstraints(input, layout, constraints, lower, upper, ref row);
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AddExactDynamics(input.ReferenceStations, layout, constraints, lower, upper, ref row);
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if (input.TerminalType != EmTerminalType.RollingSafetyStop)
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AddTerminalConstraints(layout, constraints, lower, upper, ref row);
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if (row != 7 * layout.StationCount - 2 + terminalRows)
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throw new InvalidOperationException("Lateral constraint row accounting is inconsistent.");
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problem = new QuadraticProgram(hessian.Build(), linearCost, constraints.Build(), lower, upper);
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return true;
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}
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catch (ArgumentException exception)
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{
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failureReason = exception.Message;
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return false;
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}
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}
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private static bool TryValidateCandidateStations(LateralPlanningInput input, LateralCandidate candidate,
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out string failureReason)
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{
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failureReason = string.Empty;
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if (candidate.ReferenceStations.Count != input.ReferenceStations.Count)
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{
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failureReason = "Linearization station count does not match the lateral input.";
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return false;
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}
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for (int index = 0; index < input.ReferenceStations.Count; index++)
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{
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if (Math.Abs(candidate.ReferenceStations[index] - input.ReferenceStations[index]) > Epsilon)
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{
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failureReason = "Linearization stations do not match the lateral input.";
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return false;
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}
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}
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return true;
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}
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private static bool TryAddLateralBounds(LateralPlanningInput input, LateralVariableLayout layout,
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LateralCandidate linearization, SparseTripletBuilder constraints, IList<double> lower, IList<double> upper,
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ref int row, out string failureReason)
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{
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failureReason = string.Empty;
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double maximumOffset = RequireNonnegative(input.Configuration.Corridor.MaximumLateralOffsetMeters,
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"maximum lateral offset");
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double trustRegion = RequirePositive(input.Configuration.Lateral.MaximumLateralStepPerIterationMeters,
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"lateral trust region");
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double minimumDenominator = RequirePositive(input.Configuration.Frenet.MinimumFrenetDenominator,
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"minimum Frenet denominator");
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for (int station = 0; station < layout.StationCount; station++)
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{
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LateralInterval corridor = input.Corridor.Stations[station];
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double minimum = Math.Max(corridor.MinimumL, Math.Max(-maximumOffset, linearization.L[station] - trustRegion));
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double maximum = Math.Min(corridor.MaximumL, Math.Min(maximumOffset, linearization.L[station] + trustRegion));
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double referenceCurvature = ReferencePathInterpolator.Interpolate(input.ReferenceSegment,
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input.ReferenceStations[station]).GeometricCurvature;
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if (referenceCurvature > 0d)
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maximum = Math.Min(maximum, (1d - minimumDenominator) / referenceCurvature);
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else if (referenceCurvature < 0d)
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minimum = Math.Max(minimum, (1d - minimumDenominator) / referenceCurvature);
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if (!IsFinite(minimum) || !IsFinite(maximum) || minimum > maximum + Epsilon)
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{
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failureReason = "The lateral corridor, offset, trust-region, and Frenet denominator bounds do not intersect at station " + station + ".";
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return false;
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}
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AddSingleVariableRow(constraints, lower, upper, ref row, layout.L(station), minimum, maximum);
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}
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return true;
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}
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private static void AddDerivativeBounds(LateralPlanningInput input, LateralVariableLayout layout,
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SparseTripletBuilder constraints, IList<double> lower, IList<double> upper, ref int row)
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{
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double slope = RequirePositive(input.Configuration.Lateral.MaximumLateralSlope, "maximum lateral slope");
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double second = RequirePositive(input.Configuration.Lateral.MaximumLateralSecondDerivativePerMeter,
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"maximum lateral second derivative");
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double third = RequirePositive(input.Configuration.Lateral.MaximumLateralThirdDerivativePerSquareMeter,
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"maximum lateral third derivative");
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for (int station = 0; station < layout.StationCount; station++)
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{
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AddSingleVariableRow(constraints, lower, upper, ref row, layout.DL(station), -slope, slope);
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AddSingleVariableRow(constraints, lower, upper, ref row, layout.DDL(station), -second, second);
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}
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for (int interval = 0; interval < layout.StationCount - 1; interval++)
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AddSingleVariableRow(constraints, lower, upper, ref row, layout.DDDL(interval), -third, third);
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}
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private static void AddStartConstraints(LateralPlanningInput input, LateralVariableLayout layout,
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SparseTripletBuilder constraints, IList<double> lower, IList<double> upper, ref int row)
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{
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double denominator = 1d - input.StartProjection.ReferencePoint.GeometricCurvature *
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input.StartProjection.LateralOffset;
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double startSlope = denominator * Math.Tan(input.StartProjection.HeadingError);
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if (!IsFinite(startSlope))
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throw new ArgumentException("The start lateral slope is non-finite.", nameof(input));
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AddSingleVariableRow(constraints, lower, upper, ref row, layout.L(0), input.StartProjection.LateralOffset,
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input.StartProjection.LateralOffset);
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AddSingleVariableRow(constraints, lower, upper, ref row, layout.DL(0), startSlope, startSlope);
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}
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private static void AddExactDynamics(IReadOnlyList<double> stations, LateralVariableLayout layout,
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SparseTripletBuilder constraints, IList<double> lower, IList<double> upper, ref int row)
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{
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for (int interval = 0; interval < layout.StationCount - 1; interval++)
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{
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double ds = stations[interval + 1] - stations[interval];
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AddRow(constraints, lower, upper, ref row, 0d, 0d,
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new[] { layout.DDL(interval), layout.DDL(interval + 1), layout.DDDL(interval) },
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new[] { -1d, 1d, -ds });
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AddRow(constraints, lower, upper, ref row, 0d, 0d,
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new[] { layout.DL(interval), layout.DL(interval + 1), layout.DDL(interval), layout.DDDL(interval) },
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new[] { -1d, 1d, -ds, -0.5d * ds * ds });
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AddRow(constraints, lower, upper, ref row, 0d, 0d,
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new[] { layout.L(interval), layout.L(interval + 1), layout.DL(interval), layout.DDL(interval), layout.DDDL(interval) },
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new[] { -1d, 1d, -ds, -0.5d * ds * ds, -ds * ds * ds / 6d });
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}
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}
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private static void AddTerminalConstraints(LateralVariableLayout layout, SparseTripletBuilder constraints,
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IList<double> lower, IList<double> upper, ref int row)
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{
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AddSingleVariableRow(constraints, lower, upper, ref row, layout.L(layout.StationCount - 1), 0d, 0d);
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AddSingleVariableRow(constraints, lower, upper, ref row, layout.DL(layout.StationCount - 1), 0d, 0d);
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}
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private static void AddSingleVariableRow(SparseTripletBuilder constraints, IList<double> lower, IList<double> upper,
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ref int row, int variable, double minimum, double maximum)
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{
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AddRow(constraints, lower, upper, ref row, minimum, maximum, new[] { variable }, new[] { 1d });
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}
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private static void AddRow(SparseTripletBuilder constraints, IList<double> lower, IList<double> upper, ref int row,
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double minimum, double maximum, IReadOnlyList<int> variables, IReadOnlyList<double> coefficients)
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{
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if (!IsFinite(minimum) || !IsFinite(maximum) || minimum > maximum || variables.Count != coefficients.Count)
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throw new ArgumentException("Lateral constraint bounds are invalid.");
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for (int index = 0; index < variables.Count; index++)
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constraints.Add(row, variables[index], coefficients[index]);
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lower.Add(minimum);
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upper.Add(maximum);
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row++;
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}
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private static double RequirePositive(double value, string name)
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{
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if (!IsFinite(value) || value <= 0d)
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throw new ArgumentOutOfRangeException(name);
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return value;
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}
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private static double RequireNonnegative(double value, string name)
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{
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if (!IsFinite(value) || value < 0d)
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throw new ArgumentOutOfRangeException(name);
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return value;
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}
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private static bool IsFinite(double value)
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{
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return !double.IsNaN(value) && !double.IsInfinity(value);
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}
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}
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@@ -0,0 +1,248 @@
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using System;
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using System.Collections.Generic;
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using MultiWheelC.TrajectoryPlanning.CoarsePath;
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namespace MultiWheelC.TrajectoryPlanning.EMPlanner;
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/// <summary>Builds normalized squared-residual costs in OSQP's 0.5*x'P*x + q'x convention.</summary>
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public sealed class LateralObjectiveBuilder
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{
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public void AddTerms(LateralPlanningInput input, LateralVariableLayout layout, LateralCandidate linearization,
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SparseTripletBuilder hessian, IList<double> linearCost)
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{
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if (input == null)
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throw new ArgumentNullException(nameof(input));
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if (layout == null)
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throw new ArgumentNullException(nameof(layout));
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if (linearization == null)
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throw new ArgumentNullException(nameof(linearization));
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if (hessian == null)
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throw new ArgumentNullException(nameof(hessian));
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if (linearCost == null || linearCost.Count != layout.VariableCount)
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throw new ArgumentException("Linear cost must match the lateral layout.", nameof(linearCost));
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LateralConfiguration lateral = input.Configuration.Lateral ?? throw new ArgumentException("Missing lateral configuration.");
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LateralWeights weights = lateral.Weights ?? throw new ArgumentException("Missing lateral weights.");
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double lateralScale = RequirePositive(input.Configuration.Corridor.MaximumLateralOffsetMeters, "lateral scale");
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double slopeScale = RequirePositive(lateral.MaximumLateralSlope, "slope scale");
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double secondDerivativeScale = RequirePositive(lateral.MaximumLateralSecondDerivativePerMeter, "second-derivative scale");
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double thirdDerivativeScale = RequirePositive(lateral.MaximumLateralThirdDerivativePerSquareMeter, "third-derivative scale");
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double curvatureScale = RequirePositive(GetMaximumVehicleCurvature(input.Vehicle), "curvature scale");
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double curvatureVariationScale = GetCurvatureVariationScale(input);
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for (int station = 0; station < layout.StationCount; station++)
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{
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AddSquaredResidual(hessian, linearCost, new[] { layout.L(station) }, new[] { 1d }, 0d,
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weights.ReferenceOffset, lateralScale);
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AddSquaredResidual(hessian, linearCost, new[] { layout.DL(station) }, new[] { 1d }, 0d,
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weights.HeadingDeviation, slopeScale);
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AddSquaredResidual(hessian, linearCost, new[] { layout.DDL(station) }, new[] { 1d }, 0d,
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weights.SecondDerivative, secondDerivativeScale);
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}
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for (int interval = 0; interval < layout.StationCount - 1; interval++)
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{
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AddSquaredResidual(hessian, linearCost, new[] { layout.DDDL(interval) }, new[] { 1d }, 0d,
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weights.ThirdDerivative, thirdDerivativeScale);
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}
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AddPreviousTrajectoryTerms(input, layout, hessian, linearCost, weights.PreviousTrajectory, lateralScale);
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CurvatureAffine[] curvature = CreateCurvatureAffines(input, layout, linearization);
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for (int station = 0; station < curvature.Length; station++)
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{
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AddSquaredResidual(hessian, linearCost, curvature[station].Indices, curvature[station].Gradient,
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curvature[station].Constant, weights.Curvature, curvatureScale);
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}
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AddCurvatureVariationTerms(input.ReferenceStations, curvature, hessian, linearCost, weights.CurvatureVariation,
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curvatureVariationScale);
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if (input.TerminalType == EmTerminalType.RollingSafetyStop)
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{
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AddSquaredResidual(hessian, linearCost, new[] { layout.L(layout.StationCount - 1) }, new[] { 1d }, 0d,
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weights.RollingTerminal, lateralScale);
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}
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}
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private static void AddPreviousTrajectoryTerms(LateralPlanningInput input, LateralVariableLayout layout,
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SparseTripletBuilder hessian, IList<double> linearCost, double weight, double lateralScale)
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{
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if (input.PreviousTrajectorySeed.Count == 0)
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return;
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for (int station = 0; station < layout.StationCount; station++)
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{
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double previousL = InterpolatePreviousL(input.PreviousTrajectorySeed, input.ReferenceStations[station]);
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AddSquaredResidual(hessian, linearCost, new[] { layout.L(station) }, new[] { 1d }, -previousL,
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weight, lateralScale);
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}
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}
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private static CurvatureAffine[] CreateCurvatureAffines(LateralPlanningInput input, LateralVariableLayout layout,
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LateralCandidate linearization)
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{
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var affines = new CurvatureAffine[layout.StationCount];
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double directionSign = input.ReferenceSegment.Direction == TravelDirection.Forward ? 1d : -1d;
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for (int station = 0; station < layout.StationCount; station++)
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{
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FrenetReferencePoint reference = ReferencePathInterpolator.Interpolate(input.ReferenceSegment,
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input.ReferenceStations[station]);
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double l = linearization.L[station];
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double dl = linearization.DL[station];
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double ddl = linearization.DDL[station];
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double referenceCurvature = reference.GeometricCurvature;
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double referenceCurvatureDerivative = directionSign * reference.VehicleCurvatureDerivative;
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double a = 1d - referenceCurvature * l;
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double denominatorSquared = a * a + dl * dl;
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if (!IsFinite(denominatorSquared) || denominatorSquared <= 0d)
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throw new ArgumentException("Curvature linearization denominator is invalid.", nameof(linearization));
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double denominatorPow3Over2 = denominatorSquared * Math.Sqrt(denominatorSquared);
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double denominatorPow5Over2 = denominatorPow3Over2 * denominatorSquared;
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double numerator = a * a * referenceCurvature + a * ddl +
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referenceCurvatureDerivative * l * dl + 2d * referenceCurvature * dl * dl;
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double geometricCurvature = numerator / denominatorPow3Over2;
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double dNumeratorDLateral = -2d * a * referenceCurvature * referenceCurvature -
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referenceCurvature * ddl + referenceCurvatureDerivative * dl;
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double dNumeratorDSlope = referenceCurvatureDerivative * l + 4d * referenceCurvature * dl;
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double dDenominatorSquaredDLateral = -2d * a * referenceCurvature;
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double dDenominatorSquaredDSlope = 2d * dl;
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double dGeometricDLateral = dNumeratorDLateral / denominatorPow3Over2 -
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1.5d * numerator * dDenominatorSquaredDLateral / denominatorPow5Over2;
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double dGeometricDSlope = dNumeratorDSlope / denominatorPow3Over2 -
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1.5d * numerator * dDenominatorSquaredDSlope / denominatorPow5Over2;
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double dGeometricDSecondDerivative = a / denominatorPow3Over2;
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double vehicleCurvature = directionSign * geometricCurvature;
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double[] gradient =
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{
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directionSign * dGeometricDLateral,
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directionSign * dGeometricDSlope,
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directionSign * dGeometricDSecondDerivative,
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};
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double constant = vehicleCurvature - gradient[0] * l - gradient[1] * dl - gradient[2] * ddl;
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if (!IsFinite(vehicleCurvature) || !IsFinite(constant) || !IsFinite(gradient[0]) ||
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!IsFinite(gradient[1]) || !IsFinite(gradient[2]))
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{
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throw new ArgumentException("Curvature linearization is non-finite.", nameof(linearization));
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}
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affines[station] = new CurvatureAffine(new[] { layout.L(station), layout.DL(station), layout.DDL(station) },
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gradient, constant);
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}
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return affines;
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}
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private static void AddCurvatureVariationTerms(IReadOnlyList<double> stations, CurvatureAffine[] curvature,
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SparseTripletBuilder hessian, IList<double> linearCost, double weight, double scale)
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{
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for (int station = 0; station < curvature.Length; station++)
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{
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int lower = station == 0 ? 0 : station - 1;
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int upper = station == curvature.Length - 1 ? curvature.Length - 1 : station + 1;
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double ds = stations[upper] - stations[lower];
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if (!IsFinite(ds) || ds <= 0d)
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throw new ArgumentException("Curvature variation requires strictly increasing stations.", nameof(stations));
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CurvatureAffine left = curvature[lower];
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CurvatureAffine right = curvature[upper];
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var indices = new int[left.Indices.Length + right.Indices.Length];
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var gradient = new double[indices.Length];
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for (int index = 0; index < left.Indices.Length; index++)
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{
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indices[index] = left.Indices[index];
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gradient[index] = -left.Gradient[index] / ds;
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indices[left.Indices.Length + index] = right.Indices[index];
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gradient[left.Indices.Length + index] = right.Gradient[index] / ds;
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}
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AddSquaredResidual(hessian, linearCost, indices, gradient, (right.Constant - left.Constant) / ds, weight, scale);
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}
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}
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private static void AddSquaredResidual(SparseTripletBuilder hessian, IList<double> linearCost,
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IReadOnlyList<int> indices, IReadOnlyList<double> gradient, double constant, double weight, double scale)
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{
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if (indices.Count != gradient.Count || indices.Count == 0 || !IsFinite(constant))
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throw new ArgumentException("Affine residual is invalid.");
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if (!IsFinite(weight) || weight < 0d)
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throw new ArgumentOutOfRangeException(nameof(weight));
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double coefficient = 2d * weight / (scale * scale);
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for (int left = 0; left < indices.Count; left++)
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{
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if (!IsFinite(gradient[left]) || indices[left] < 0 || indices[left] >= linearCost.Count)
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throw new ArgumentOutOfRangeException(nameof(gradient));
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linearCost[indices[left]] += coefficient * constant * gradient[left];
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for (int right = left; right < indices.Count; right++)
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{
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if (!IsFinite(gradient[right]) || indices[right] < 0 || indices[right] >= linearCost.Count)
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throw new ArgumentOutOfRangeException(nameof(gradient));
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int row = Math.Min(indices[left], indices[right]);
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int column = Math.Max(indices[left], indices[right]);
|
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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; }
|
||||
}
|
||||
}
|
||||
Reference in New Issue
Block a user