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dstarlite.go
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dstarlite.go
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// Copyright ©2014 The Gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package dynamic
import (
"container/heap"
"fmt"
"math"
"gonum.org/v1/gonum/graph"
"gonum.org/v1/gonum/graph/path"
"gonum.org/v1/gonum/graph/simple"
)
// DStarLite implements the D* Lite dynamic re-planning path search algorithm.
//
// doi:10.1109/tro.2004.838026 and ISBN:0-262-51129-0 pp476-483
//
type DStarLite struct {
s, t *dStarLiteNode
last *dStarLiteNode
model WorldModel
queue dStarLiteQueue
keyModifier float64
weight path.Weighting
heuristic path.Heuristic
}
// WorldModel is a mutable weighted directed graph that returns nodes identified
// by id number.
type WorldModel interface {
graph.WeightedBuilder
graph.WeightedDirected
}
// NewDStarLite returns a new DStarLite planner for the path from s to t in g using the
// heuristic h. The world model, m, is used to store shortest path information during path
// planning. The world model must be an empty graph when NewDStarLite is called.
//
// If h is nil, the DStarLite will use the g.HeuristicCost method if g implements
// path.HeuristicCoster, falling back to path.NullHeuristic otherwise. If the graph does not
// implement graph.Weighter, path.UniformCost is used. NewDStarLite will panic if g has
// a negative edge weight.
func NewDStarLite(s, t graph.Node, g graph.Graph, h path.Heuristic, m WorldModel) *DStarLite {
/*
procedure Initialize()
{02”} U = ∅;
{03”} k_m = 0;
{04”} for all s ∈ S rhs(s) = g(s) = ∞;
{05”} rhs(s_goal) = 0;
{06”} U.Insert(s_goal, [h(s_start, s_goal); 0]);
*/
d := &DStarLite{
s: newDStarLiteNode(s),
t: newDStarLiteNode(t), // badKey is overwritten below.
model: m,
heuristic: h,
}
d.t.rhs = 0
/*
procedure Main()
{29”} s_last = s_start;
{30”} Initialize();
*/
d.last = d.s
if wg, ok := g.(graph.Weighted); ok {
d.weight = wg.Weight
} else {
d.weight = path.UniformCost(g)
}
if d.heuristic == nil {
if g, ok := g.(path.HeuristicCoster); ok {
d.heuristic = g.HeuristicCost
} else {
d.heuristic = path.NullHeuristic
}
}
d.queue.insert(d.t, key{d.heuristic(s, t), 0})
nodes := g.Nodes()
for nodes.Next() {
n := nodes.Node()
switch n.ID() {
case d.s.ID():
d.model.AddNode(d.s)
case d.t.ID():
d.model.AddNode(d.t)
default:
d.model.AddNode(newDStarLiteNode(n))
}
}
model := d.model.Nodes()
for model.Next() {
u := model.Node()
uid := u.ID()
to := g.From(uid)
for to.Next() {
v := to.Node()
vid := v.ID()
w := edgeWeight(d.weight, uid, vid)
if w < 0 {
panic("D* Lite: negative edge weight")
}
d.model.SetWeightedEdge(simple.WeightedEdge{F: u, T: d.model.Node(vid), W: w})
}
}
/*
procedure Main()
{31”} ComputeShortestPath();
*/
d.findShortestPath()
return d
}
// edgeWeight is a helper function that returns the weight of the edge between
// two connected nodes, u and v, using the provided weight function. It panics
// if there is no edge between u and v.
func edgeWeight(weight path.Weighting, uid, vid int64) float64 {
w, ok := weight(uid, vid)
if !ok {
panic("D* Lite: unexpected invalid weight")
}
return w
}
// keyFor is the CalculateKey procedure in the D* Lite papers.
func (d *DStarLite) keyFor(s *dStarLiteNode) key {
/*
procedure CalculateKey(s)
{01”} return [min(g(s), rhs(s)) + h(s_start, s) + k_m; min(g(s), rhs(s))];
*/
k := key{1: math.Min(s.g, s.rhs)}
k[0] = k[1] + d.heuristic(d.s.Node, s.Node) + d.keyModifier
return k
}
// update is the UpdateVertex procedure in the D* Lite papers.
func (d *DStarLite) update(u *dStarLiteNode) {
/*
procedure UpdateVertex(u)
{07”} if (g(u) != rhs(u) AND u ∈ U) U.Update(u,CalculateKey(u));
{08”} else if (g(u) != rhs(u) AND u /∈ U) U.Insert(u,CalculateKey(u));
{09”} else if (g(u) = rhs(u) AND u ∈ U) U.Remove(u);
*/
inQueue := u.inQueue()
switch {
case inQueue && u.g != u.rhs:
d.queue.update(u, d.keyFor(u))
case !inQueue && u.g != u.rhs:
d.queue.insert(u, d.keyFor(u))
case inQueue && u.g == u.rhs:
d.queue.remove(u)
}
}
// findShortestPath is the ComputeShortestPath procedure in the D* Lite papers.
func (d *DStarLite) findShortestPath() {
/*
procedure ComputeShortestPath()
{10”} while (U.TopKey() < CalculateKey(s_start) OR rhs(s_start) > g(s_start))
{11”} u = U.Top();
{12”} k_old = U.TopKey();
{13”} k_new = CalculateKey(u);
{14”} if(k_old < k_new)
{15”} U.Update(u, k_new);
{16”} else if (g(u) > rhs(u))
{17”} g(u) = rhs(u);
{18”} U.Remove(u);
{19”} for all s ∈ Pred(u)
{20”} if (s != s_goal) rhs(s) = min(rhs(s), c(s, u) + g(u));
{21”} UpdateVertex(s);
{22”} else
{23”} g_old = g(u);
{24”} g(u) = ∞;
{25”} for all s ∈ Pred(u) ∪ {u}
{26”} if (rhs(s) = c(s, u) + g_old)
{27”} if (s != s_goal) rhs(s) = min s'∈Succ(s)(c(s, s') + g(s'));
{28”} UpdateVertex(s);
*/
for d.queue.Len() != 0 { // We use d.queue.Len since d.queue does not return an infinite key when empty.
u := d.queue.top()
if !u.key.less(d.keyFor(d.s)) && d.s.rhs <= d.s.g {
break
}
uid := u.ID()
switch kNew := d.keyFor(u); {
case u.key.less(kNew):
d.queue.update(u, kNew)
case u.g > u.rhs:
u.g = u.rhs
d.queue.remove(u)
from := d.model.To(uid)
for from.Next() {
s := from.Node().(*dStarLiteNode)
sid := s.ID()
if sid != d.t.ID() {
s.rhs = math.Min(s.rhs, edgeWeight(d.model.Weight, sid, uid)+u.g)
}
d.update(s)
}
default:
gOld := u.g
u.g = math.Inf(1)
for _, _s := range append(graph.NodesOf(d.model.To(uid)), u) {
s := _s.(*dStarLiteNode)
sid := s.ID()
if s.rhs == edgeWeight(d.model.Weight, sid, uid)+gOld {
if s.ID() != d.t.ID() {
s.rhs = math.Inf(1)
to := d.model.From(sid)
for to.Next() {
t := to.Node()
tid := t.ID()
s.rhs = math.Min(s.rhs, edgeWeight(d.model.Weight, sid, tid)+t.(*dStarLiteNode).g)
}
}
}
d.update(s)
}
}
}
}
// Step performs one movement step along the best path towards the goal.
// It returns false if no further progression toward the goal can be
// achieved, either because the goal has been reached or because there
// is no path.
func (d *DStarLite) Step() bool {
/*
procedure Main()
{32”} while (s_start != s_goal)
{33”} // if (rhs(s_start) = ∞) then there is no known path
{34”} s_start = argmin s'∈Succ(s_start)(c(s_start, s') + g(s'));
*/
if d.s.ID() == d.t.ID() {
return false
}
if math.IsInf(d.s.rhs, 1) {
return false
}
// We use rhs comparison to break ties
// between coequally weighted nodes.
rhs := math.Inf(1)
min := math.Inf(1)
var next *dStarLiteNode
dsid := d.s.ID()
to := d.model.From(dsid)
for to.Next() {
s := to.Node().(*dStarLiteNode)
w := edgeWeight(d.model.Weight, dsid, s.ID()) + s.g
if w < min || (w == min && s.rhs < rhs) {
next = s
min = w
rhs = s.rhs
}
}
d.s = next
/*
procedure Main()
{35”} Move to s_start;
*/
return true
}
// MoveTo moves to n in the world graph.
func (d *DStarLite) MoveTo(n graph.Node) {
d.last = d.s
d.s = d.model.Node(n.ID()).(*dStarLiteNode)
d.keyModifier += d.heuristic(d.last, d.s)
}
// UpdateWorld updates or adds edges in the world graph. UpdateWorld will
// panic if changes include a negative edge weight.
func (d *DStarLite) UpdateWorld(changes []graph.Edge) {
/*
procedure Main()
{36”} Scan graph for changed edge costs;
{37”} if any edge costs changed
{38”} k_m = k_m + h(s_last, s_start);
{39”} s_last = s_start;
{40”} for all directed edges (u, v) with changed edge costs
{41”} c_old = c(u, v);
{42”} Update the edge cost c(u, v);
{43”} if (c_old > c(u, v))
{44”} if (u != s_goal) rhs(u) = min(rhs(u), c(u, v) + g(v));
{45”} else if (rhs(u) = c_old + g(v))
{46”} if (u != s_goal) rhs(u) = min s'∈Succ(u)(c(u, s') + g(s'));
{47”} UpdateVertex(u);
{48”} ComputeShortestPath()
*/
if len(changes) == 0 {
return
}
d.keyModifier += d.heuristic(d.last, d.s)
d.last = d.s
for _, e := range changes {
from := e.From()
fid := from.ID()
to := e.To()
tid := to.ID()
c, _ := d.weight(fid, tid)
if c < 0 {
panic("D* Lite: negative edge weight")
}
cOld, _ := d.model.Weight(fid, tid)
u := d.worldNodeFor(from)
v := d.worldNodeFor(to)
d.model.SetWeightedEdge(simple.WeightedEdge{F: u, T: v, W: c})
uid := u.ID()
if cOld > c {
if uid != d.t.ID() {
u.rhs = math.Min(u.rhs, c+v.g)
}
} else if u.rhs == cOld+v.g {
if uid != d.t.ID() {
u.rhs = math.Inf(1)
to := d.model.From(uid)
for to.Next() {
t := to.Node()
u.rhs = math.Min(u.rhs, edgeWeight(d.model.Weight, uid, t.ID())+t.(*dStarLiteNode).g)
}
}
}
d.update(u)
}
d.findShortestPath()
}
func (d *DStarLite) worldNodeFor(n graph.Node) *dStarLiteNode {
switch w := d.model.Node(n.ID()).(type) {
case *dStarLiteNode:
return w
case graph.Node:
panic(fmt.Sprintf("D* Lite: illegal world model node type: %T", w))
default:
return newDStarLiteNode(n)
}
}
// Here returns the current location.
func (d *DStarLite) Here() graph.Node {
return d.s.Node
}
// Path returns the path from the current location to the goal and the
// weight of the path.
func (d *DStarLite) Path() (p []graph.Node, weight float64) {
u := d.s
p = []graph.Node{u.Node}
for u.ID() != d.t.ID() {
if math.IsInf(u.rhs, 1) {
return nil, math.Inf(1)
}
// We use stored rhs comparison to break
// ties between calculated rhs-coequal nodes.
rhsMin := math.Inf(1)
min := math.Inf(1)
var (
next *dStarLiteNode
cost float64
)
uid := u.ID()
to := d.model.From(uid)
for to.Next() {
v := to.Node().(*dStarLiteNode)
vid := v.ID()
w := edgeWeight(d.model.Weight, uid, vid)
if rhs := w + v.g; rhs < min || (rhs == min && v.rhs < rhsMin) {
next = v
min = rhs
rhsMin = v.rhs
cost = w
}
}
if next == nil {
return nil, math.NaN()
}
u = next
weight += cost
p = append(p, u.Node)
}
return p, weight
}
/*
The pseudocode uses the following functions to manage the priority
queue:
* U.Top() returns a vertex with the smallest priority of all
vertices in priority queue U.
* U.TopKey() returns the smallest priority of all vertices in
priority queue U. (If is empty, then U.TopKey() returns [∞;∞].)
* U.Pop() deletes the vertex with the smallest priority in
priority queue U and returns the vertex.
* U.Insert(s, k) inserts vertex s into priority queue with
priority k.
* U.Update(s, k) changes the priority of vertex s in priority
queue U to k. (It does nothing if the current priority of vertex
s already equals k.)
* Finally, U.Remove(s) removes vertex s from priority queue U.
*/
// key is a D* Lite priority queue key.
type key [2]float64
// badKey is a poisoned key. Testing for a bad key uses NaN inequality.
var badKey = key{math.NaN(), math.NaN()}
func (k key) isBadKey() bool { return k != k }
// less returns whether k is less than other. From ISBN:0-262-51129-0 pp476-483:
//
// k ≤ k' iff k₁ < k'₁ OR (k₁ == k'₁ AND k₂ ≤ k'₂)
//
func (k key) less(other key) bool {
if k.isBadKey() || other.isBadKey() {
panic("D* Lite: poisoned key")
}
return k[0] < other[0] || (k[0] == other[0] && k[1] < other[1])
}
// dStarLiteNode adds D* Lite accounting to a graph.Node.
type dStarLiteNode struct {
graph.Node
key key
idx int
rhs float64
g float64
}
// newDStarLiteNode returns a dStarLite node that is in a legal state
// for existence outside the DStarLite priority queue.
func newDStarLiteNode(n graph.Node) *dStarLiteNode {
return &dStarLiteNode{
Node: n,
rhs: math.Inf(1),
g: math.Inf(1),
key: badKey,
idx: -1,
}
}
// inQueue returns whether the node is in the queue.
func (q *dStarLiteNode) inQueue() bool {
return q.idx >= 0
}
// dStarLiteQueue is a D* Lite priority queue.
type dStarLiteQueue []*dStarLiteNode
func (q dStarLiteQueue) Less(i, j int) bool {
return q[i].key.less(q[j].key)
}
func (q dStarLiteQueue) Swap(i, j int) {
q[i], q[j] = q[j], q[i]
q[i].idx = i
q[j].idx = j
}
func (q dStarLiteQueue) Len() int {
return len(q)
}
func (q *dStarLiteQueue) Push(x interface{}) {
n := x.(*dStarLiteNode)
n.idx = len(*q)
*q = append(*q, n)
}
func (q *dStarLiteQueue) Pop() interface{} {
n := (*q)[len(*q)-1]
n.idx = -1
*q = (*q)[:len(*q)-1]
return n
}
// top returns the top node in the queue. Note that instead of
// returning a key [∞;∞] when q is empty, the caller checks for
// an empty queue by calling q.Len.
func (q dStarLiteQueue) top() *dStarLiteNode {
return q[0]
}
// insert puts the node u into the queue with the key k.
func (q *dStarLiteQueue) insert(u *dStarLiteNode, k key) {
u.key = k
heap.Push(q, u)
}
// update updates the node in the queue identified by id with the key k.
func (q *dStarLiteQueue) update(n *dStarLiteNode, k key) {
n.key = k
heap.Fix(q, n.idx)
}
// remove removes the node identified by id from the queue.
func (q *dStarLiteQueue) remove(n *dStarLiteNode) {
heap.Remove(q, n.idx)
n.key = badKey
n.idx = -1
}