From 42b31382ad25430e1db70dc438fd9f98e27d5ba1 Mon Sep 17 00:00:00 2001 From: zed Date: Fri, 21 Sep 2018 02:39:35 +0200 Subject: [PATCH] first commit --- Output/astar.jpg | Bin 0 -> 56561 bytes Output/dijkstra.jpg | Bin 0 -> 56623 bytes Output/dynamic.jpg | Bin 0 -> 57609 bytes Output/map.jpg | Bin 0 -> 36626 bytes Output/map_nodes.jpg | Bin 0 -> 53190 bytes addstartendpoint2ungraph.m | 38 ++++++++++++++++++++++++ astar.m | 56 ++++++++++++++++++++++++++++++++++++ costcal.m | 14 +++++++++ dijkstra.m | 45 +++++++++++++++++++++++++++++ drawRoute.m | 30 +++++++++++++++++++ dynamicpathplanning.m | 32 +++++++++++++++++++++ generate_node.m | 31 ++++++++++++++++++++ generate_undirected_graph.m | 36 +++++++++++++++++++++++ main.m | 56 ++++++++++++++++++++++++++++++++++++ map_definition.m | 45 +++++++++++++++++++++++++++++ pathcost.m | 7 +++++ sp_dp.m | 30 +++++++++++++++++++ 17 files changed, 420 insertions(+) create mode 100644 Output/astar.jpg create mode 100644 Output/dijkstra.jpg create mode 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zm(qi2?pcost); + % if new calculated is less than before one then set less one + Cost(T(I(J)))=cost(J); + % if new calculated way is less than the before one than set new route + % too + for j=1:length(J) + Route{T(I(J(j)))}=[cRoute T(I(J(j)))]; + end + % find minimum of normal cost plus heuristic cost of possible node + [mn cr]=min(Cost(T)+HCost(T)); + if isinf(mn) + i=n; + end + % set minimum total cost's node as current node + curr=T(cr); + cRoute=Route{curr}; + % add current node to tabu list to prevent loops + Tabu=[Tabu curr]; +end +% if current node is equal endnode means route is found +if curr ==endnode + route=cRoute; +else % i not means there is no way + route=[]; +end diff --git a/costcal.m b/costcal.m new file mode 100644 index 0000000..10cf0dc --- /dev/null +++ b/costcal.m @@ -0,0 +1,14 @@ +function sc=costcal(a,b) +tp=b-a; + +sc=sqrt(tp(:,1).^2+tp(:,2).^2); + + +% n=size(b,1); +% df=repmat(a,n,1)-b; +% df(:,3)=abs(df(:,3)); +% I=find(df(:,3)>pi); +% df(I,3)=2*pi-df(I,3); +% c=df(:,1).*df(:,1)+df(:,2).*df(:,2); +% sc=sqrt(sum(c,2))+df(:,3)+0.001; +% %sc=ones(n,1); \ No newline at end of file diff --git a/dijkstra.m b/dijkstra.m new file mode 100644 index 0000000..1fb0595 --- /dev/null +++ b/dijkstra.m @@ -0,0 +1,45 @@ +function [Route, Cost] = dijkstra(exbigraph,exbiloc,startnode) +% calculate route for given graph and starting point. +% this function finds all targets so you do not need to support end point + +graph=exbigraph; +Loc=exbiloc; +n=size(graph,1); +Cost=inf(n,1); +curr=startnode; +Route=cell(n,1); +Cost(curr)=0; +Tabu=[curr]; +cRoute=[curr]; +i=1; +% for number of nodes +while icost); + Cost(T(I(J)))=cost(J); + % update new comming node rote if the new cost is more efficient + for j=1:length(J) + Route{T(I(J(j)))}=[cRoute T(I(J(j)))]; + end + % find minimum costed node which is not visited yet in this iteration + [mn cr]=min(Cost(T)); + if isinf(mn) + i=n; + end + curr=T(cr); + % select selected route as forbitten route to not to select this nodes + % again + cRoute=Route{curr}; + Tabu=[Tabu curr]; +end + diff --git a/drawRoute.m b/drawRoute.m new file mode 100644 index 0000000..81e89fa --- /dev/null +++ b/drawRoute.m @@ -0,0 +1,30 @@ +function drawRoute(method,startnode,endnode,exnodelocation,exnodIndex,exunedges,rt,Cost) +% draw graph nodes and selected way. + +ns=size(exnodelocation,1); +map_definition(); +hold on; + +title([ method ' Cost:' num2str(Cost)]); +sn=exnodIndex(startnode); +en=exnodIndex(endnode); +plot(exnodelocation(1:ns,1),exnodelocation(1:ns,2),'b*'); +plot(exnodelocation(sn,1),exnodelocation(sn,2),'rx','markersize',10); +plot(exnodelocation(en,1),exnodelocation(en,2),'rx','markersize',10); + +for i=1:2:size(exunedges,1) + x1=exnodelocation(exunedges(i,1),1); + x2=exnodelocation(exunedges(i,2),1); + y1=exnodelocation(exunedges(i,1),2); + y2=exnodelocation(exunedges(i,2),2); + line([x1;x2],[y1;y2],'linewidth',0.1); +end + +for i=1:length(rt)-1 + x1=exnodelocation(exnodIndex(rt(i)),1); + x2=exnodelocation(exnodIndex(rt(i+1)),1); + y1=exnodelocation(exnodIndex(rt(i)),2); + y2=exnodelocation(exnodIndex(rt(i+1)),2); + line([x1;x2],[y1;y2],'color','r','linewidth',2); +end +hold off \ No newline at end of file diff --git a/dynamicpathplanning.m b/dynamicpathplanning.m new file mode 100644 index 0000000..f12cae0 --- /dev/null +++ b/dynamicpathplanning.m @@ -0,0 +1,32 @@ +function [parent, route, cost]=dynamicpathplanning(Graph,Loc,Ind,startnode,endnode) +% calculate minimum costs path with recursive manner. + +route=[]; +cost=0; +dist=[startnode 0]; +parent=[startnode nan]; +n=size(Graph,1); +deep=0; +% call main recursive function, this function will call itself and give us +% route +[ds dist parent ] = sp_dp(Graph, endnode, dist,parent,Loc,Ind,deep); + +Route=[]; +Route=[endnode ]; +next=1; +while Route(end)~=startnode && ~isnan(next) + curr=Route(end); + xx=find(parent(:,1)==curr); + next=parent(xx,2); + if ~isnan(next) + cost=cost+costcal(Loc(Ind(curr),:),Loc(Ind(next),:)); + Route=[Route next]; + end +end +if Route(end)==startnode + route=Route; +else + route=[]; + cost=inf; +end + diff --git a/generate_node.m b/generate_node.m new file mode 100644 index 0000000..4cfc307 --- /dev/null +++ b/generate_node.m @@ -0,0 +1,31 @@ +function [map, nodelocation]= generate_node(map,nnode) + +% merge vertices of all obstacle +obsx=map.pgx{1}; +obsy=map.pgy{1}; +for i=2:length(map.pgx) + obsx=[obsx NaN map.pgx{i}]; + obsy=[obsy NaN map.pgy{i}]; +end +map.obsx=obsx; +map.obsy=obsy; +% set nodelocation to all zero +nodelocation=zeros(nnode,2); +% generate nodes +n=1; +while (n<=nnode) + % generate random two number in range of map's border + rx=rand* (map.xrange(2)-map.xrange(1)) + map.xrange(1); + ry=rand* (map.yrange(2)-map.yrange(1)) + map.yrange(1); + state=0; + % if this node is not inside any obstacle + if ~inpolygon(rx,ry,obsx,obsy) + % add this location to nodelocation list + nodelocation(n,1)=rx; + nodelocation(n,2)=ry; + n=n+1; + end +end +hold on; +plot(nodelocation(:,1),nodelocation(:,2),'r*'); +hold off; \ No newline at end of file diff --git a/generate_undirected_graph.m b/generate_undirected_graph.m new file mode 100644 index 0000000..52d0719 --- /dev/null +++ b/generate_undirected_graph.m @@ -0,0 +1,36 @@ +function [undirectedGraph,unedges]=generate_undirected_graph(map,nodelocation) +% takes map and produce undirected map and its adge set + +% take number of node +nnode=size(nodelocation,1); +% set graph and edges as zero +undirectedGraph=zeros(nnode,nnode); +unedges=[]; + +%generate undirected graph + +for i=1:nnode-1 + for j=i+1:nnode + % take each pair of node^s location x and y + x1=[nodelocation(i,1);nodelocation(j,1)]; + y1=[nodelocation(i,2);nodelocation(j,2)]; + % check this two nodes intersect any obstacle or not + [xi,yi] = polyxpoly(x1,y1,map.obsx,map.obsy); + % if there is not any intersection + if length(xi)==0 + % connect this two nodes in graph + undirectedGraph(i,j)=1; + undirectedGraph(j,i)=1; + % add this connection to adge set + unedges=[unedges;i j;j i]; + end + end +end +% plot graph +hold on; +for i=1:2:size(unedges,1) + x1=[nodelocation(unedges(i,1),1);nodelocation(unedges(i,2),1)]; + y1=[nodelocation(unedges(i,1),2);nodelocation(unedges(i,2),2)]; + line(x1,y1); +end +hold off; \ No newline at end of file diff --git a/main.m b/main.m new file mode 100644 index 0000000..325c9cf --- /dev/null +++ b/main.m @@ -0,0 +1,56 @@ +clear +close all +clc + + +% number of nodes +ns=100; +map=map_definition(); +% +% generate random nodes +[map, nodelocation]= generate_node(map,ns); + + +% create undirected graph and its edges +[undirectedGraph,unedges]=generate_undirected_graph(map,nodelocation); + + +% define start and end point of simulation +startp=[5, 29]; +endp=[29, 20]; + +% add start and end location as a new 2 nodes in undirected map. +% n+1 th node is start point, n+2th node is end point +[extungraph,exnodelocation,exunedges ]=addstartendpoint2ungraph(map,undirectedGraph,nodelocation,unedges,startp,endp); +exundnodIndex=[1:ns+2]; +snodeund=ns+1; +enodeund=ns+2; + + +% optimal path with dijkstra on un-directional map +[Route Cost] = dijkstra(extungraph,exnodelocation,snodeund); +rt=Route{enodeund}; + +dijkstra_route=exnodelocation(rt,:); +cost=pathcost(dijkstra_route); +drawRoute('dijkstra on undirected map',snodeund,enodeund,exnodelocation,exundnodIndex,exunedges,rt,cost); + + + +% optimal path with astar on un-directional map +[Route] = astar(extungraph,exnodelocation,snodeund,enodeund); +astar_route=exnodelocation(Route,:); +cost=pathcost(astar_route); +drawRoute('Astar on undirected map',snodeund,enodeund,exnodelocation,exundnodIndex,exunedges,Route,cost); + + +% optimal path with dynamic programming on un-directional map +[parent, Route]=dynamicpathplanning(extungraph,exnodelocation,exundnodIndex,snodeund,enodeund); +dpundirected_route=exnodelocation(Route,:); +cost=pathcost(dpundirected_route); +drawRoute('Dynamic Programming on undirected map',snodeund,enodeund,exnodelocation,exundnodIndex,exunedges,Route,cost); + + + + + diff --git a/map_definition.m b/map_definition.m new file mode 100644 index 0000000..8a88927 --- /dev/null +++ b/map_definition.m @@ -0,0 +1,45 @@ +function map=map_definition() + +Npoly=13; +map.pgx{1}=[2 8.5 8.5 4 2 2 1 1 2 4 2]; +map.pgy{1}=[8 10 1 3 3 1 1 6 6 5 8]; +map.pgx{2}=[2 8 2 15 2 1 1 2 2]; +map.pgy{2}=[10 16 22 15.5 9 10 16 16 10]; +map.pgx{3}=[0 0 5 0]; +map.pgy{3}=[25 30 30 25]; +map.pgx{4}=[7 7 10 10 13 13 11 7]; +map.pgy{4}=[23 26 29 25 26 23 21 23]; +map.pgx{5}=[13 17 15 13]; +map.pgy{5}=[30 30 25 30]; +map.pgx{6}=[17 17 30 30 17]; +map.pgy{6}=[23 27 27 23 23]; +map.pgx{7}=[12 14 15 16 29 23 27 19 12]; +map.pgy{7}=[20 21 23 21.3 22 10 21.3 14 20]; +map.pgx{8}=[10 15 17.5 10 10]; +map.pgy{8}=[8 14 10 0 8]; +map.pgx{9}=[19 24 19 19]; +map.pgy{9}=[12.5 17 1 12.5]; +map.pgx{10}=[21 30 26 21]; +map.pgy{10}=[3 16 1 3]; +map.pgx{11}=[4 7 8 6 5 10 7 4 4]; +map.pgy{11}=[25 30 30 26 23 20 21 23 25]; +map.pgx{12}=[0 0 4 5 4 3 3 0]; +map.pgy{12}=[17 18 18 16 14 14 17 17]; +map.pgx{13}=[3 3 4 4 3]; +map.pgy{13}=[0 2 2 0 0]; +map.xrange=[0 30]; +map.yrange=[0 30]; + +figure; +plot([0 30 30 0 0],[0 0 30 30 0]); +hold on + +excluded_area=0; + +for ii=1:Npoly + excluded_area=excluded_area+polyarea(map.pgx{ii},map.pgy{ii}); + fill(map.pgx{ii},map.pgy{ii},'g') +end +hold off + + \ No newline at end of file diff --git a/pathcost.m b/pathcost.m new file mode 100644 index 0000000..a6278cb --- /dev/null +++ b/pathcost.m @@ -0,0 +1,7 @@ +function cost=pathcost(route) +% calculate route cost +cost=0; +for i=1:size(route,1)-1 + cost=cost+costcal(route(i,:),route(i+1,:)); +end + diff --git a/sp_dp.m b/sp_dp.m new file mode 100644 index 0000000..92d6c7f --- /dev/null +++ b/sp_dp.m @@ -0,0 +1,30 @@ +function [dst dist parent] = sp_dp(graph, v, dist,parent,Loc,Ind,deep) +% recursive function to solve dynamic programming for shortest path. + +deep=deep+1; +% find if coming node inside the already visited list +I=find(dist(:,1)==v); +if ~isempty(I) + % if it is tru then return its cost + dst= dist(I,2); +else + % if it is not true than add this node to the list + dist=[dist;v inf]; + parent=[parent;v nan]; + % find all connected nodes to the current node + u=find(graph(:,v)==1); + I=size(dist,1); + for i=1:length(u) + % find minimum distances way from nex connected node + [dst2 dist parent] =sp_dp(graph,u(i),dist,parent,Loc,Ind,deep); + % calculate begin to cuurent plus next to end cost + new_distance=costcal(Loc(Ind(u(i)),:),Loc(Ind(v),:))+ dst2; + % if this cost is less than before than update + if new_distance < dist(I,2) + dist(I,2)=new_distance; + parent(I,2)=u(i); + end + end + dst = dist(I,2); +end +