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ThrustAllocator: one bounded least-squares solve, yaw first, translation error paid linearly

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Rules TA-R1 to TA-R4 of cut-thrust-allocator-core.r2, tests on synthetic columns
(Duel, damaged Duel, symmetric hull). First draft; not yet run.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
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Meta Vens 2026-10-10 00:29:05 +02:00
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/* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
* file, You can obtain one at https://mozilla.org/MPL/2.0/. */
using System;
using CultMath;
/// <summary>
/// Turns intent (which way to go, which way to turn) into every thruster's throttle, whatever the thrusters' actual
/// strength and position. One per ship. A column is one thruster's effect per unit throttle: x starboard acceleration,
/// y forward acceleration, z clockwise yaw rate in rad/s. Throttles are bounded to [0,1].
///
/// One <see cref="BoundedLeastSquares"/> solve per call over the n throttles and four error variables (the unwanted or
/// missing translation on each half-axis, paid for linearly). Yaw is a heavily weighted row, so a hold is exact and a
/// turn is served first; the linear translation cost means the actuator with the least translation per unit of turn
/// serves first and the next joins only as it saturates. Nothing classifies a column as attitude or drive: the onset
/// at which a second actuator joins a turn falls out of the columns.
/// </summary>
public sealed class ThrustAllocator
{
const float TranslationWeight = 100f;
const float YawWeight = 1000f;
const float ErrorCostWeight = .3f;
const float ErrorCostOffset = 10f;
const float Ridge = .1f;
const float ErrorMax = 2f;
const double KktRelativeTolerance = 1e-12;
const int ErrorVariables = 4;
const int FixedRows = 3 + ErrorVariables;
int _columns = -1;
float[] _a, _b, _lo, _hi, _x, _workspace;
public void Allocate(ReadOnlySpan<float3> columns, float2 move, float turn, Span<float> throttle)
{
var n = columns.Length;
if (n != _columns) Resize(n);
for (var i = 0; i < n; i++) throttle[i] = 0;
var vars = n + ErrorVariables;
var rows = FixedRows + n;
Array.Clear(_a, 0, rows * vars);
Array.Clear(_b, 0, rows);
// Rows 0 and 1 are the translation axes (starboard, forward), row 2 the yaw.
for (var axis = 0; axis < 3; axis++)
{
float plus = 0, minus = 0;
for (var i = 0; i < n; i++)
{
var c = Component(columns[i], axis);
if (c > 0) plus += c;
else if (c < 0) minus -= c;
}
var extreme = Math.Max(plus, minus);
var intent = Math.Min(Math.Max(axis == 0 ? move.x : axis == 1 ? move.y : turn, -1f), 1f);
var weight = axis == 2 ? YawWeight : TranslationWeight;
// Intent is a fraction of the half-axis extreme it points into.
var demand = intent >= 0 ? intent * plus : intent * minus;
var scale = extreme > 0 ? weight / extreme : 0f;
var row = axis * vars;
for (var i = 0; i < n; i++) _a[row + i] = Component(columns[i], axis) * scale;
_b[axis] = demand * scale;
if (axis < 2 && extreme > 0)
{
_a[row + n + 2 * axis] = -weight;
_a[row + n + 2 * axis + 1] = weight;
}
}
// A linear cost on each error variable, as w*e = -w*kappa, and a ridge on each throttle.
for (var k = 0; k < ErrorVariables; k++)
{
_a[(3 + k) * vars + n + k] = ErrorCostWeight;
_b[3 + k] = -ErrorCostWeight * ErrorCostOffset;
}
for (var i = 0; i < n; i++) _a[(FixedRows + i) * vars + i] = Ridge;
var status = BoundedLeastSquares.Solve(rows, vars, _a, _b, _lo, _hi, _x, _workspace, out _, KktRelativeTolerance);
if (status == BoundedLeastSquaresStatus.InvalidInput) return;
for (var i = 0; i < n; i++) throttle[i] = _x[i];
}
static float Component(float3 c, int axis) => axis == 0 ? c.x : axis == 1 ? c.y : c.z;
void Resize(int n)
{
_columns = n;
var vars = n + ErrorVariables;
var rows = FixedRows + n;
_a = new float[rows * vars];
_b = new float[rows];
_lo = new float[vars];
_hi = new float[vars];
_x = new float[vars];
_workspace = new float[BoundedLeastSquares.WorkspaceLength(vars)];
for (var i = 0; i < vars; i++) _hi[i] = i < n ? 1f : ErrorMax;
}
}

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using System;
using System.Collections.Generic;
using CultMath;
using Xunit;
namespace Aetheria.Shared.Tests;
// ThrustAllocator on synthetic columns. A column is (starboard m/s^2, forward m/s^2, clockwise yaw rad/s) per unit
// throttle; the fixtures are written in deg/s the way the probes measured them (map TA3, TA12).
public class ThrustAllocatorTests
{
const float Deg = MathF.PI / 180f;
static float3 Col(float starboard, float forward, float yawDeg) => new(starboard, forward, yawDeg * Deg);
// TA3, the Duel Longinus: two mismatched drives (0, 1) and two Talarias (2 clockwise, 3 counter-clockwise).
static float3[] Duel() => new[]
{
Col(0, 53.94f, 49.24f), Col(0, 61.19f, -55.86f), Col(29.08f, 0, 166.26f), Col(-21.80f, 0, -124.63f),
};
// The clockwise Talaria lost.
static float3[] DamagedDuel() => new[]
{
Col(0, 53.94f, 49.24f), Col(0, 61.19f, -55.86f), default, Col(-21.80f, 0, -124.63f),
};
// TA12's symmetric hull: mains, fore and aft laterals in torque-free pairs, a bow thruster.
static float3[] Symmetric() => new[]
{
Col(0, 50, 20), Col(0, 50, -20), Col(20, 0, 80), Col(-20, 0, -80), Col(20, 0, -60), Col(-20, 0, 60), Col(0, -30, 0),
};
// The hull's half-axis extremes, from the definition: the sum of a row's positive entries, or of the negated
// negative ones. Axis 0 starboard, 1 forward, 2 clockwise yaw.
static (float plus, float minus) Extremes(float3[] columns, int axis)
{
float plus = 0, minus = 0;
foreach (var c in columns)
{
var v = axis == 0 ? c.x : axis == 1 ? c.y : c.z;
if (v > 0) plus += v; else minus -= v;
}
return (plus, minus);
}
static float3 Net(float3[] columns, float[] throttle)
{
float3 net = default;
for (var i = 0; i < columns.Length; i++) net += columns[i] * throttle[i];
return net;
}
static float[] Solve(ThrustAllocator allocator, float3[] columns, float moveX, float moveY, float turn)
{
var throttle = new float[columns.Length];
allocator.Allocate(columns, new float2(moveX, moveY), turn, throttle);
return throttle;
}
static float[] Solve(float3[] columns, float moveX, float moveY, float turn) => Solve(new ThrustAllocator(), columns, moveX, moveY, turn);
static float YawDeg(float3[] columns, float[] throttle) => Net(columns, throttle).z / Deg;
[Fact]
public void AHoldIsExactWithMismatchedDrives()
{
var duel = Duel();
var throttle = Solve(duel, 0, 1, 0);
var clockwise = Extremes(duel, 2).plus;
var net = Net(duel, throttle);
Assert.True(MathF.Abs(net.z) <= 1e-5f * clockwise, $"yaw {net.z / Deg} deg/s");
Assert.True(net.y >= .99f * Extremes(duel, 1).plus, $"forward {net.y}");
}
[Theory]
[InlineData(0)]
[InlineData(1)]
public void ALostDriveIsBalancedByWhatIsLeft(int zeroed)
{
var columns = Duel();
var extreme = Extremes(columns, 2).plus;
columns[zeroed] = default;
var throttle = Solve(columns, 0, 1, 0);
var net = Net(columns, throttle);
Assert.True(MathF.Abs(net.z) <= 1e-5f * extreme, $"yaw {net.z / Deg} deg/s");
Assert.Equal(0f, throttle[zeroed]);
Assert.True(net.y > 0, $"forward {net.y}");
}
[Theory]
[InlineData(1f)]
[InlineData(.5f)]
[InlineData(-.5f)]
[InlineData(-1f)]
public void ATurnIsThatFractionOfTheBoxExtreme(float turn)
{
var duel = Duel();
var (plus, minus) = Extremes(duel, 2);
var expected = turn * (turn > 0 ? plus : minus);
var net = Net(duel, Solve(duel, 0, 0, turn));
Assert.True(MathF.Abs(net.z - expected) <= 1e-4f * MathF.Abs(expected), $"yaw {net.z / Deg} expected {expected / Deg}");
}
[Fact]
public void AttitudeServesFirstAndTheOnsetIsTheColumnsRatio()
{
var duel = Duel();
// The onset is the attitude thruster's yaw over the hull's extreme in that direction.
var clockwiseOnset = duel[2].z / Extremes(duel, 2).plus;
var counterOnset = -duel[3].z / Extremes(duel, 2).minus;
Assert.InRange(clockwiseOnset, .7714f, .7716f);
Assert.InRange(counterOnset, .6904f, .6906f);
var allocator = new ThrustAllocator();
for (var step = 0; step <= 1000; step++)
{
var turn = step * .001f;
var drive = Solve(allocator, duel, 0, 0, turn)[0];
if (turn <= clockwiseOnset - .005f) Assert.True(drive <= 1e-4f, $"clockwise turn {turn}: drive {drive}");
if (turn >= clockwiseOnset + .005f) Assert.True(drive > 1e-3f, $"clockwise turn {turn}: drive {drive}");
}
allocator = new ThrustAllocator();
for (var step = 0; step <= 1000; step++)
{
var turn = step * .001f;
var drive = Solve(allocator, duel, 0, 0, -turn)[1];
if (turn <= counterOnset - .005f) Assert.True(drive <= 1e-4f, $"counter-clockwise turn {turn}: drive {drive}");
if (turn >= counterOnset + .005f) Assert.True(drive > 1e-3f, $"counter-clockwise turn {turn}: drive {drive}");
}
}
[Fact]
public void TheOnsetMovesWithTheColumns()
{
// Clockwise Talaria lost: the drive serves a clockwise turn from the first touch.
var damaged = DamagedDuel();
var small = Solve(damaged, 0, 0, .01f);
Assert.True(small[0] > 0, $"drive {small[0]}");
Assert.True(MathF.Abs(YawDeg(damaged, small) - .01f * 49.24f) <= .01f * 49.24f * 1e-3f, $"yaw {YawDeg(damaged, small)}");
var full = Solve(damaged, 0, 0, 1f);
Assert.True(MathF.Abs(YawDeg(damaged, full) - 49.24f) <= 49.24f * 1e-3f, $"yaw {YawDeg(damaged, full)}");
// Clockwise Talaria halved: the onset is its new share of the clockwise extreme.
var halved = Duel();
halved[2] = halved[2] * .5f;
var onset = halved[2].z / Extremes(halved, 2).plus;
Assert.InRange(onset, .627f, .629f);
var allocator = new ThrustAllocator();
for (var step = 0; step <= 1000; step++)
{
var turn = step * .001f;
var drive = Solve(allocator, halved, 0, 0, turn)[0];
if (turn <= onset - .005f) Assert.True(drive <= 1e-4f, $"turn {turn}: drive {drive}");
if (turn >= onset + .005f) Assert.True(drive > 1e-3f, $"turn {turn}: drive {drive}");
}
}
[Fact]
public void EveryThrottleIsContinuousInTurn()
{
foreach (var columns in new[] { Duel(), DamagedDuel(), Symmetric() })
{
var allocator = new ThrustAllocator();
var previous = Solve(allocator, columns, 0, 0, -1f);
for (var step = -999; step <= 1000; step++)
{
var current = Solve(allocator, columns, 0, 0, step * .001f);
for (var i = 0; i < columns.Length; i++)
Assert.True(MathF.Abs(current[i] - previous[i]) <= .02f, $"turn {step * .001f}: throttle {i} {previous[i]} -> {current[i]}");
previous = current;
}
}
}
[Fact]
public void PureTorqueNeedsNoTranslation()
{
var hull = Symmetric();
var allocator = new ThrustAllocator();
var starboard = Extremes(hull, 0).plus;
var forward = Extremes(hull, 1).plus;
for (var step = -87; step <= 87; step++)
{
var net = Net(hull, Solve(allocator, hull, 0, 0, step * .01f));
Assert.True(MathF.Abs(net.x) <= 1e-3f * starboard, $"turn {step * .01f}: starboard {net.x}");
Assert.True(MathF.Abs(net.y) <= 1e-3f * forward, $"turn {step * .01f}: forward {net.y}");
}
var strafe = Net(hull, Solve(hull, 1, 0, 0));
Assert.True(strafe.x >= .9f * starboard, $"strafe {strafe.x} of {starboard}");
Assert.True(MathF.Abs(strafe.z) <= 1e-3f * Extremes(hull, 2).plus, $"yaw {strafe.z / Deg}");
}
[Fact]
public void TurnComesBeforeTranslation()
{
var duel = Duel();
var throttle = Solve(duel, 0, 1, 1f);
var net = Net(duel, throttle);
var extreme = Extremes(duel, 2).plus;
Assert.True(MathF.Abs(net.z - extreme) <= 1e-4f * extreme, $"yaw {net.z / Deg} of {extreme / Deg}");
Assert.True(throttle[1] < .01f, $"counter-turning drive {throttle[1]}");
}
[Fact]
public void MovementIsThatFractionOfTheHalfAxis()
{
// A torque-free strafe pair of unequal strength and a torque-free main.
var columns = new[] { Col(30, 0, 0), Col(-20, 0, 0), Col(0, 60, 0) };
const float yaw = 1e-4f;
var right = Net(columns, Solve(columns, .5f, 0, 0));
Assert.True(MathF.Abs(right.x - 15f) <= 15e-3f && MathF.Abs(right.z) <= yaw, $"right {right.x}");
var left = Net(columns, Solve(columns, -.5f, 0, 0));
Assert.True(MathF.Abs(left.x + 10f) <= 10e-3f && MathF.Abs(left.z) <= yaw, $"left {left.x}");
var ahead = Net(columns, Solve(columns, 0, .5f, 0));
Assert.True(MathF.Abs(ahead.y - 30f) <= 30e-3f && MathF.Abs(ahead.z) <= yaw, $"ahead {ahead.y}");
}
[Fact]
public void IntentBeyondOneIsClamped()
{
var duel = Duel();
Assert.Equal(Solve(duel, 0, 0, 1f), Solve(duel, 0, 0, 3f));
Assert.Equal(Solve(duel, 1, -1, 0), Solve(duel, 3, -3, 0));
Assert.Equal(Solve(duel, 0, 0, -1f), Solve(duel, 0, 0, -3f));
}
[Fact]
public void NothingAskedNothingFired()
{
Assert.All(Solve(Duel(), 0, 0, 0), t => Assert.Equal(0f, t));
Assert.All(Solve(new float3[4], 1, 1, 1), t => Assert.Equal(0f, t));
new ThrustAllocator().Allocate(ReadOnlySpan<float3>.Empty, new float2(1, 1), 1, Span<float>.Empty);
var withNaN = Duel();
withNaN[2] = new float3(float.NaN, 0, 0);
Assert.All(Solve(withNaN, 0, 1, 1), t => Assert.Equal(0f, t));
var nanYaw = Duel();
nanYaw[0] = new float3(0, 1, float.NaN);
Assert.All(Solve(nanYaw, 0, 1, 0), t => Assert.Equal(0f, t));
}
[Fact]
public void TheStartDoesNotChangeTheAnswer()
{
var duel = Duel();
var cold = Solve(duel, .3f, .8f, .6f);
foreach (var previous in new[] { (1f, 1f, 1f), (-1f, -.5f, -1f), (0f, 0f, 0f) })
{
var allocator = new ThrustAllocator();
Solve(allocator, duel, previous.Item1, previous.Item2, previous.Item3);
var warm = Solve(allocator, duel, .3f, .8f, .6f);
for (var i = 0; i < duel.Length; i++) Assert.True(MathF.Abs(warm[i] - cold[i]) <= 1e-5f, $"previous {previous}: throttle {i} {cold[i]} vs {warm[i]}");
}
}
[Fact]
public void EqualThrustersShareTheDemand()
{
var columns = new[] { Col(0, 50, 0), Col(0, 50, 0) };
var throttle = Solve(columns, 0, .5f, 0);
Assert.True(MathF.Abs(throttle[0] - throttle[1]) <= 1e-4f, $"{throttle[0]} vs {throttle[1]}");
Assert.True(throttle[0] > .1f);
}
[Fact]
public void AColumnCountChangeResets()
{
var four = Duel();
var three = new[] { four[0], four[2], four[3] };
var allocator = new ThrustAllocator();
var steps = new List<(float3[] columns, float x, float y, float turn)>
{
(four, .2f, .9f, -.7f), (three, -.4f, 1f, .9f), (four, .2f, .9f, -.7f),
};
foreach (var (columns, x, y, turn) in steps)
{
var warm = Solve(allocator, columns, x, y, turn);
var fresh = Solve(columns, x, y, turn);
for (var i = 0; i < columns.Length; i++) Assert.True(MathF.Abs(warm[i] - fresh[i]) <= 1e-5f, $"{columns.Length} columns: throttle {i}");
}
}
}