Dubins factory functions
This commit is contained in:
Erik Schouten
parent
3260c3d171
commit
8faa312424
@ -5,8 +5,16 @@
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package space.kscience.kmath.trajectory.dubins
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import space.kscience.kmath.geometry.Euclidean2DSpace.distanceTo
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import space.kscience.kmath.geometry.Vector2D
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import space.kscience.kmath.trajectory.segments.Arc
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import space.kscience.kmath.trajectory.segments.Segment
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import space.kscience.kmath.trajectory.segments.Straight
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import space.kscience.kmath.trajectory.segments.components.Circle
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import space.kscience.kmath.trajectory.segments.components.Pose2D
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import kotlin.math.acos
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import kotlin.math.cos
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import kotlin.math.sin
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public class DubinsPath(
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public val a: Arc,
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@ -27,4 +35,102 @@ public class DubinsPath(
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public enum class TYPE {
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RLR, LRL, RSR, LSL, RSL, LSR
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}
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public companion object {
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public fun all(start: Pose2D, end: Pose2D, turningRadius: Double): List<DubinsPath> =
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listOfNotNull(
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rlr(start, end, turningRadius),
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lrl(start, end, turningRadius),
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rsr(start, end, turningRadius),
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lsl(start, end, turningRadius),
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rsl(start, end, turningRadius),
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lsr(start, end, turningRadius)
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)
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public fun shortest(start: Pose2D, end: Pose2D, turningRadius: Double): DubinsPath =
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all(start, end, turningRadius).minByOrNull { it.length }!!
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public fun rlr(start: Pose2D, end: Pose2D, turningRadius: Double): DubinsPath? {
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val c1 = start.getRightCircle(turningRadius)
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val c2 = end.getRightCircle(turningRadius)
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val centers = Straight(c1.center, c2.center)
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if (centers.length > turningRadius * 4) return null
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var theta = theta(centers.theta - acos(centers.length / (turningRadius * 4)))
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var dX = turningRadius * sin(theta)
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var dY = turningRadius * cos(theta)
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val p = Vector2D(c1.center.x + dX * 2, c1.center.y + dY * 2)
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val e = Circle(p, turningRadius)
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val p1 = Vector2D(c1.center.x + dX, c1.center.y + dY)
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theta = theta(centers.theta + acos(centers.length / (turningRadius * 4)))
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dX = turningRadius * sin(theta)
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dY = turningRadius * cos(theta)
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val p2 = Vector2D(e.center.x + dX, e.center.y + dY)
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val a1 = Arc(c1.center, start, p1, Arc.Direction.RIGHT)
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val a2 = Arc(e.center, p1, p2, Arc.Direction.LEFT)
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val a3 = Arc(c2.center, p2, end, Arc.Direction.RIGHT)
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return DubinsPath(a1, a2, a3)
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}
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public fun lrl(start: Pose2D, end: Pose2D, turningRadius: Double): DubinsPath? {
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val c1 = start.getLeftCircle(turningRadius)
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val c2 = end.getLeftCircle(turningRadius)
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val centers = Straight(c1.center, c2.center)
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if (centers.length > turningRadius * 4) return null
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var theta = theta(centers.theta + acos(centers.length / (turningRadius * 4)))
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var dX = turningRadius * sin(theta)
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var dY = turningRadius * cos(theta)
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val p = Vector2D(c1.center.x + dX * 2, c1.center.y + dY * 2)
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val e = Circle(p, turningRadius)
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val p1 = Vector2D(c1.center.x + dX, c1.center.y + dY)
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theta = theta(centers.theta - acos(centers.length / (turningRadius * 4)))
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dX = turningRadius * sin(theta)
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dY = turningRadius * cos(theta)
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val p2 = Vector2D(e.center.x + dX, e.center.y + dY)
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val a1 = Arc(c1.center, start, p1, Arc.Direction.LEFT)
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val a2 = Arc(e.center, p1, p2, Arc.Direction.RIGHT)
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val a3 = Arc(c2.center, p2, end, Arc.Direction.LEFT)
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return DubinsPath(a1, a2, a3)
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}
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public fun rsr(start: Pose2D, end: Pose2D, turningRadius: Double): DubinsPath {
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val c1 = start.getRightCircle(turningRadius)
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val c2 = end.getRightCircle(turningRadius)
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val s = leftOuterTangent(c1, c2)
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val a1 = Arc(c1.center, start, s.start, Arc.Direction.RIGHT)
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val a3 = Arc(c2.center, s.end, end, Arc.Direction.RIGHT)
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return DubinsPath(a1, s, a3)
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}
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public fun lsl(start: Pose2D, end: Pose2D, turningRadius: Double): DubinsPath {
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val c1 = start.getLeftCircle(turningRadius)
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val c2 = end.getLeftCircle(turningRadius)
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val s = rightOuterTangent(c1, c2)
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val a1 = Arc(c1.center, start, s.start, Arc.Direction.LEFT)
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val a3 = Arc(c2.center, s.end, end, Arc.Direction.LEFT)
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return DubinsPath(a1, s, a3)
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}
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public fun rsl(start: Pose2D, end: Pose2D, turningRadius: Double): DubinsPath? {
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val c1 = start.getRightCircle(turningRadius)
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val c2 = end.getLeftCircle(turningRadius)
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val s = rightInnerTangent(c1, c2)
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if (c1.center.distanceTo(c2.center) < turningRadius * 2 || s == null) return null
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val a1 = Arc(c1.center, start, s.start, Arc.Direction.RIGHT)
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val a3 = Arc(c2.center, s.end, end, Arc.Direction.LEFT)
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return DubinsPath(a1, s, a3)
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}
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public fun lsr(start: Pose2D, end: Pose2D, turningRadius: Double): DubinsPath? {
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val c1 = start.getLeftCircle(turningRadius)
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val c2 = end.getRightCircle(turningRadius)
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val s = leftInnerTangent(c1, c2)
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if (c1.center.distanceTo(c2.center) < turningRadius * 2 || s == null) return null
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val a1 = Arc(c1.center, start, s.start, Arc.Direction.LEFT)
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val a3 = Arc(c2.center, s.end, end, Arc.Direction.RIGHT)
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return DubinsPath(a1, s, a3)
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}
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}
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}
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@ -1,169 +0,0 @@
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/*
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* Copyright 2018-2021 KMath contributors.
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* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
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*/
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package space.kscience.kmath.trajectory.dubins
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import space.kscience.kmath.geometry.Euclidean2DSpace.distanceTo
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import space.kscience.kmath.geometry.Vector2D
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import space.kscience.kmath.trajectory.segments.*
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import space.kscience.kmath.trajectory.segments.components.Circle
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import space.kscience.kmath.trajectory.segments.components.Pose2D
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import kotlin.math.PI
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import kotlin.math.acos
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import kotlin.math.cos
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import kotlin.math.sin
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public class DubinsPathFactory(
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private val start: Pose2D,
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private val end: Pose2D,
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private val turningRadius: Double
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) {
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public val all: List<DubinsPath> get() = listOfNotNull(rlr, lrl, rsr, lsl, rsl, lsr)
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public val shortest: DubinsPath get() = all.minByOrNull { it.length }!!
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public operator fun get(type: DubinsPath.TYPE): DubinsPath? = all.find { it.type == type }
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public val rlr: DubinsPath?
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get() {
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val c1 = start.getRightCircle(turningRadius)
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val c2 = end.getRightCircle(turningRadius)
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val centers = Straight(c1.center, c2.center)
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if (centers.length > turningRadius * 4) return null
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var theta = theta(centers.theta - acos(centers.length / (turningRadius * 4)))
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var dX = turningRadius * sin(theta)
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var dY = turningRadius * cos(theta)
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val p = Vector2D(c1.center.x + dX * 2, c1.center.y + dY * 2)
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val e = Circle(p, turningRadius)
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val p1 = Vector2D(c1.center.x + dX, c1.center.y + dY)
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theta = theta(centers.theta + acos(centers.length / (turningRadius * 4)))
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dX = turningRadius * sin(theta)
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dY = turningRadius * cos(theta)
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val p2 = Vector2D(e.center.x + dX, e.center.y + dY)
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val a1 = Arc(c1.center, start, p1, Arc.Direction.RIGHT)
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val a2 = Arc(e.center, p1, p2, Arc.Direction.LEFT)
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val a3 = Arc(c2.center, p2, end, Arc.Direction.RIGHT)
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return DubinsPath(a1, a2, a3)
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}
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private val lrl: DubinsPath?
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get() {
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val c1 = start.getLeftCircle(turningRadius)
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val c2 = end.getLeftCircle(turningRadius)
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val centers = Straight(c1.center, c2.center)
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if (centers.length > turningRadius * 4) return null
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var theta = theta(centers.theta + acos(centers.length / (turningRadius * 4)))
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var dX = turningRadius * sin(theta)
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var dY = turningRadius * cos(theta)
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val p = Vector2D(c1.center.x + dX * 2, c1.center.y + dY * 2)
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val e = Circle(p, turningRadius)
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val p1 = Vector2D(c1.center.x + dX, c1.center.y + dY)
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theta = theta(centers.theta - acos(centers.length / (turningRadius * 4)))
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dX = turningRadius * sin(theta)
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dY = turningRadius * cos(theta)
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val p2 = Vector2D(e.center.x + dX, e.center.y + dY)
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val a1 = Arc(c1.center, start, p1, Arc.Direction.LEFT)
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val a2 = Arc(e.center, p1, p2, Arc.Direction.RIGHT)
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val a3 = Arc(c2.center, p2, end, Arc.Direction.LEFT)
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return DubinsPath(a1, a2, a3)
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}
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public val rsr: DubinsPath
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get() {
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val c1 = start.getRightCircle(turningRadius)
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val c2 = end.getRightCircle(turningRadius)
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val s = leftOuterTangent(c1, c2)
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val a1 = Arc(c1.center, start, s.start, Arc.Direction.RIGHT)
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val a3 = Arc(c2.center, s.end, end, Arc.Direction.RIGHT)
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return DubinsPath(a1, s, a3)
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}
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public val lsl: DubinsPath
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get() {
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val c1 = start.getLeftCircle(turningRadius)
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val c2 = end.getLeftCircle(turningRadius)
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val s = rightOuterTangent(c1, c2)
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val a1 = Arc(c1.center, start, s.start, Arc.Direction.LEFT)
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val a3 = Arc(c2.center, s.end, end, Arc.Direction.LEFT)
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return DubinsPath(a1, s, a3)
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}
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public val rsl: DubinsPath?
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get() {
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val c1 = start.getRightCircle(turningRadius)
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val c2 = end.getLeftCircle(turningRadius)
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val s = rightInnerTangent(c1, c2)
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if (c1.center.distanceTo(c2.center) < turningRadius * 2 || s == null) return null
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val a1 = Arc(c1.center, start, s.start, Arc.Direction.RIGHT)
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val a3 = Arc(c2.center, s.end, end, Arc.Direction.LEFT)
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return DubinsPath(a1, s, a3)
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}
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public val lsr: DubinsPath?
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get() {
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val c1 = start.getLeftCircle(turningRadius)
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val c2 = end.getRightCircle(turningRadius)
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val s = leftInnerTangent(c1, c2)
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if (c1.center.distanceTo(c2.center) < turningRadius * 2 || s == null) return null
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val a1 = Arc(c1.center, start, s.start, Arc.Direction.LEFT)
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val a3 = Arc(c2.center, s.end, end, Arc.Direction.RIGHT)
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return DubinsPath(a1, s, a3)
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}
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}
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private enum class SIDE {
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LEFT, RIGHT
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}
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private fun Pose2D.getLeftCircle(radius: Double): Circle = getTangentCircles(radius).first
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private fun Pose2D.getRightCircle(radius: Double): Circle = getTangentCircles(radius).second
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private fun Pose2D.getTangentCircles(radius: Double): Pair<Circle, Circle> {
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val dX = radius * cos(theta)
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val dY = radius * sin(theta)
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return Circle(Vector2D(x - dX, y + dY), radius) to Circle(Vector2D(x + dX, y - dY), radius)
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}
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private fun leftOuterTangent(a: Circle, b: Circle) = outerTangent(a, b, SIDE.LEFT)
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private fun rightOuterTangent(a: Circle, b: Circle) = outerTangent(a, b, SIDE.RIGHT)
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private fun outerTangent(a: Circle, b: Circle, side: SIDE): Straight {
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val centers = Straight(a.center, b.center)
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val p1 = when (side) {
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SIDE.LEFT -> Vector2D(
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a.center.x - a.radius * cos(centers.theta),
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a.center.y + a.radius * sin(centers.theta)
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)
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SIDE.RIGHT -> Vector2D(
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a.center.x + a.radius * cos(centers.theta),
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a.center.y - a.radius * sin(centers.theta)
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)
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}
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return Straight(
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p1,
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Vector2D(p1.x + (centers.end.x - centers.start.x), p1.y + (centers.end.y - centers.start.y))
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)
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}
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private fun leftInnerTangent(base: Circle, direction: Circle) = innerTangent(base, direction, SIDE.LEFT)
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private fun rightInnerTangent(base: Circle, direction: Circle) = innerTangent(base, direction, SIDE.RIGHT)
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private fun innerTangent(base: Circle, direction: Circle, side: SIDE): Straight? {
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val centers = Straight(base.center, direction.center)
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if (centers.length < base.radius * 2) return null
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val angle = theta(
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when (side) {
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SIDE.LEFT -> centers.theta + acos(base.radius * 2 / centers.length)
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SIDE.RIGHT -> centers.theta - acos(base.radius * 2 / centers.length)
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}
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)
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val dX = base.radius * sin(angle)
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val dY = base.radius * cos(angle)
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val p1 = Vector2D(base.center.x + dX, base.center.y + dY)
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val p2 = Vector2D(direction.center.x - dX, direction.center.y - dY)
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return Straight(p1, p2)
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}
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internal fun theta(theta: Double) = (theta + (2 * PI)) % (2 * PI)
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@ -0,0 +1,67 @@
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/*
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* Copyright 2018-2021 KMath contributors.
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* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
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*/
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package space.kscience.kmath.trajectory.dubins
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import space.kscience.kmath.geometry.Vector2D
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import space.kscience.kmath.trajectory.segments.Straight
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import space.kscience.kmath.trajectory.segments.components.Circle
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import space.kscience.kmath.trajectory.segments.components.Pose2D
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import kotlin.math.PI
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import kotlin.math.acos
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import kotlin.math.cos
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import kotlin.math.sin
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private enum class SIDE {
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LEFT, RIGHT
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}
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internal fun Pose2D.getLeftCircle(radius: Double): Circle = getTangentCircles(radius).first
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internal fun Pose2D.getRightCircle(radius: Double): Circle = getTangentCircles(radius).second
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internal fun Pose2D.getTangentCircles(radius: Double): Pair<Circle, Circle> {
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val dX = radius * cos(theta)
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val dY = radius * sin(theta)
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return Circle(Vector2D(x - dX, y + dY), radius) to Circle(Vector2D(x + dX, y - dY), radius)
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}
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internal fun leftOuterTangent(a: Circle, b: Circle) = outerTangent(a, b, SIDE.LEFT)
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internal fun rightOuterTangent(a: Circle, b: Circle) = outerTangent(a, b, SIDE.RIGHT)
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private fun outerTangent(a: Circle, b: Circle, side: SIDE): Straight {
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val centers = Straight(a.center, b.center)
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val p1 = when (side) {
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SIDE.LEFT -> Vector2D(
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a.center.x - a.radius * cos(centers.theta),
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a.center.y + a.radius * sin(centers.theta)
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)
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SIDE.RIGHT -> Vector2D(
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a.center.x + a.radius * cos(centers.theta),
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a.center.y - a.radius * sin(centers.theta)
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)
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}
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return Straight(
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p1,
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Vector2D(p1.x + (centers.end.x - centers.start.x), p1.y + (centers.end.y - centers.start.y))
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)
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}
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internal fun leftInnerTangent(base: Circle, direction: Circle) = innerTangent(base, direction, SIDE.LEFT)
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internal fun rightInnerTangent(base: Circle, direction: Circle) = innerTangent(base, direction, SIDE.RIGHT)
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private fun innerTangent(base: Circle, direction: Circle, side: SIDE): Straight? {
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val centers = Straight(base.center, direction.center)
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if (centers.length < base.radius * 2) return null
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val angle = theta(
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when (side) {
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SIDE.LEFT -> centers.theta + acos(base.radius * 2 / centers.length)
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SIDE.RIGHT -> centers.theta - acos(base.radius * 2 / centers.length)
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}
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)
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val dX = base.radius * sin(angle)
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val dY = base.radius * cos(angle)
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val p1 = Vector2D(base.center.x + dX, base.center.y + dY)
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val p2 = Vector2D(direction.center.x - dX, direction.center.y - dY)
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return Straight(p1, p2)
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}
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internal fun theta(theta: Double) = (theta + (2 * PI)) % (2 * PI)
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@ -29,7 +29,7 @@ class DubinsTests {
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val start = Pose2D.of(straight.end, straight.theta)
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val end = Pose2D.of(lineP1.start, lineP1.theta)
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val radius = 2.0
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val dubins = DubinsPathFactory(start, end, radius)
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val dubins = DubinsPath.all(start, end, radius)
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val absoluteDistance = start.distanceTo(end)
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println("Absolute distance: $absoluteDistance")
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@ -43,7 +43,7 @@ class DubinsTests {
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)
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expectedLengths.forEach {
|
||||
val path = dubins[it.key]
|
||||
val path = dubins.find { p -> p.type === it.key }
|
||||
assertNotNull(path, "Path ${it.key} not found")
|
||||
println("${it.key}: ${path.length}")
|
||||
assertTrue(it.value.equalFloat(path.length))
|
||||
|
||||
Loading…
Reference in New Issue
Block a user