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PoseGraph.m
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PoseGraph.m
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%PoseGraph Pose graph
% Copyright (C) 1993-2017, by Peter I. Corke
%
% This file is part of The Robotics Toolbox for MATLAB (RTB).
%
% RTB is free software: you can redistribute it and/or modify
% it under the terms of the GNU Lesser General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% RTB is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU Lesser General Public License for more details.
%
% You should have received a copy of the GNU Leser General Public License
% along with RTB. If not, see <http://www.gnu.org/licenses/>.
%
% http://www.petercorke.com
classdef PoseGraph < handle
properties
graph
ngrid
center
cellsize
end
methods
function pg = PoseGraph(filename, varargin)
% parse the file data
% we assume g2o format
% VERTEX* vertex_id X Y THETA
% EDGE* startvertex_id endvertex_id X Y THETA IXX IXY IYY IXT IYT ITT
% vertex numbers start at 0
opt.laser = false;
opt = tb_optparse(opt, varargin);
pg.graph = PGraph(3, 'distance', 'SE2');
fp = fopen(filename, 'r');
assert(fp > 0, 'Can''t open file %s', filename);
toroformat = false;
nlaser = 0;
% indices into ROBOTLASER1 record for the 3x3 info matrix in column major
% order
g2o = [6 7 8 7 9 10 8 10 11];
toro = [6 7 10 7 8 11 10 11 9];
% we keep an array pgi = vindex(gi) to map g2o vertex index to PGraph vertex index
tic
while ~feof(fp)
line = fgets(fp);
% is it a comment?
if line(1) == '#'
continue;
end
% get keyword
k = strfind(line, ' ');
% and deal with it
switch line(1:k-1)
case 'VERTEX_SE2'
% g2o format vertex
vertex = sscanf(line(k+1:end), '%d %f %f %f')';
v = pg.graph.add_node(vertex(2:4));
vindex(vertex(1)+1) = v;
vd.type = 'vertex';
pg.graph.setvdata(v, vd);
case 'VERTEX_XY'
vertex = sscanf(line(k+1:end), '%d %f %f')';
v = pg.graph.add_node(vertex(2:4));
vindex(vertex(1)+1) = v;
vd.type = 'landmark';
pg.graph.setvdata(v, vd);
case 'EDGE_SE2'
% g2o format edge
edge = sscanf(line(k+1:end), '%f')';
v1 = vindex(edge(1)+1);
v2 = vindex(edge(2)+1);
% create the edge
e = pg.graph.add_edge(v1, v2);
% create the edge data as a structure
% X Y T
% 3 4 5
ed.mean = edge(3:5);
% IXX IXY IXT IYY IYT ITT
% 6 7 8 9 10 11
ed.info = reshape(edge(g2o), [3 3]);
% and attach it
pg.graph.setedata(e, ed);
case 'VERTEX2'
toroformat = true;
vertex = sscanf(line(k+1:end), '%d %f %f %f')';
v = pg.graph.add_node(vertex(2:4));
vindex(vertex(1)+1) = v;
vd.type = 'vertex';
pg.graph.setvdata(v, vd);
case 'EDGE2'
toroformat = true;
edge = sscanf(line(k+1:end), '%f')';
v1 = vindex(edge(1)+1);
v2 = vindex(edge(2)+1);
% create the edge
e = pg.graph.add_edge(v1, v2);
% create the edge data as a structure
% X Y T
% 3 4 5
ed.mean = edge(3:5);
% IXX IXY IYY ITT IXT IYT
% 6 7 8 9 10 11
ed.info = reshape(edge(toro), [3 3]);
% and attach it
pg.graph.setedata(e, ed);
case 'ROBOTLASER1'
if ~opt.laser
continue;
end
% laser records are associated with the immediately preceding VERTEX record
[laser,n] = sscanf(line(k+1:end), '%f');
nbeams = laser(8);
vd.theta = [0:nbeams-1] * laser(4) + laser(2);
vd.range = laser(9:8+nbeams)';
vd.time = laser(21+nbeams);
pg.graph.setvdata(v, vd);
nlaser = nlaser + 1;
otherwise
error('RTB:posegraph:badfile', 'Unexpected line <%s> in %s', line(1:k-1), filename);
end
end
elapsed = toc;
fclose(fp);
if toroformat
fprintf('loaded TORO/LAGO format file: %d nodes, %d edges in %.2f sec\n', pg.graph.n, pg.graph.ne, elapsed);
else
fprintf('loaded g2o format file: %d nodes, %d edges in %.2f sec\n', pg.graph.n, pg.graph.ne, elapsed);
if nlaser > 0
fprintf(' %d laser scans: %d beams, fov %g to %g deg, max range %g\n', ...
nlaser, nbeams, [laser(2) sum(laser(2:3))]*180/pi, laser(5) );
end
end
end
function [r, theta] = scan(pg, n)
vd = pg.graph.vdata(n);
r = vd.range;
theta = vd.theta;
end
function [X,Y] = scanxy(pg, n)
vd = pg.graph.vdata(n);
[x,y] = pol2cart(vd.theta, vd.range);
if nargout == 1
X = [x; y];
elseif nargout == 2
X = x; Y = y;
end
end
function plot_scan(pg, n)
for i=n(:)'
[x,y] = pg.scanxy(i);
plot(x, y, '.', 'MarkerSize', 10);
pause
end
end
function xyt = pose(pg, i)
xyt = pg.graph.coord(i);
end
function t = time(pg, n)
t = pg.graph.vdata(n).time;
end
function plot(pg, varargin)
pg.graph.plot(varargin{:});
xlabel('x')
ylabel('y')
grid on
end
function world = scanmap(pg, varargin)
opt.center = [75 50];
opt.ngrid = 3000;
opt.cellsize = 0.1;
pg = tb_optparse(opt, varargin, pg);
h = waitbar(0, 'rendering a map');
world = zeros(pg.ngrid, pg.ngrid, 'int32');
for i=1:1:pg.graph.n
if rem(i, 20) == 0
waitbar(i/pg.graph.n, h)
end
xy = pg.scanxy(i);
[r,theta] = pg.scan(i);
xy(:,r>40) = [];
xyt = pg.graph.coord(i);
xy = SE2(xyt) * xy;
% start of each ray
[x1,y1] = pg.w2g(xyt(1:2));
for s=1:numcols(xy)
% end of each ray
[x2,y2] = pg.w2g(xy(:,s));
% all cells along the ray
p = bresenham(x1, y1, x2, y2);
try
k = sub2ind(size(world), p(:,1), p(:,2));
k1 = k(1:end-1); k2 = k(end);
world(k1) = world(k1) - 1;
world(k2) = world(k2) + 1;
catch me
% come here if any point on the ray is outside the grid
% silently ignore it
end
end
end
close(h)
%idisp(world)
end
function [gx,gy] = w2g(pg, w)
dd = 0.10;
w = w(:) + pg.center(:);
g = round(w/pg.cellsize);
gx = g(1); gy = g(2);
end
function plot_occgrid(pg, w)
x = [1:numcols(w)]*pg.cellsize - pg.center(1);
y = [1:numrows(w)]*pg.cellsize - pg.center(2);
w(w<0) = -1;
w(w>0) = 1;
w=-w;
idisp(w, 'nogui', 'xydata', {x, y})
xlabel('x'); ylabel('y');
end
% This source code is part of the graph optimization package
% deveoped for the lectures of robotics2 at the University of Freiburg.
%
% Copyright (c) 2007 Giorgio Grisetti, Gian Diego Tipaldi
%
% It is licences under the Common Creative License,
% Attribution-NonCommercial-ShareAlike 3.0
%
% You are free:
% - to Share - to copy, distribute and transmit the work
% - to Remix - to adapt the work
%
% Under the following conditions:
%
% - Attribution. You must attribute the work in the manner specified
% by the author or licensor (but not in any way that suggests that
% they endorse you or your use of the work).
%
% - Noncommercial. You may not use this work for commercial purposes.
%
% - Share Alike. If you alter, transform, or build upon this work,
% you may distribute the resulting work only under the same or
% similar license to this one.
%
% Any of the above conditions can be waived if you get permission
% from the copyright holder. Nothing in this license impairs or
% restricts the author's moral rights.
%
% This software is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied
% warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
% PURPOSE.
%ls-slam.m
%this file is released under the creative common license
%solves a graph-based slam problem via least squares
%vmeans: matrix containing the column vectors of the poses of the vertices
% the vertices are odrered such that vmeans[i] corresponds to the ith id
%eids: matrix containing the column vectors [idFrom, idTo]' of the ids of the vertices
% eids[k] corresponds to emeans[k] and einfs[k].
%emeans: matrix containing the column vectors of the poses of the edges
%einfs: 3d matrix containing the information matrices of the edges
% einfs(:,:,k) refers to the information matrix of the k-th edge.
%n: number of iterations
%newmeans: matrix containing the column vectors of the updated vertices positions
function g2 = optimize(pg, varargin)
opt.iterations = 10;
opt.animate = false;
opt.retain = false;
opt = tb_optparse(opt, varargin);
g2 = PGraph(pg.graph); % deep copy
eprev = Inf;
for i=1:opt.iterations
if opt.animate
if ~opt.retain
clf
end
g2.plot();
pause(0.5)
end
[vmeans,energy] = linearize_and_solve(g2);
g2.setcoord(vmeans);
if energy >= eprev
break;
end
eprev = energy;
end;
pg.graph = g2;
end
end % methods
end % classdef
%computes the taylor expansion of the error function of the k_th edge
%vmeans: vertices positions
%eids: edge ids
%emeans: edge means
%k: edge number
%e: e_k(x)
%A: d e_k(x) / d(x_i)
%B: d e_k(x) / d(x_j)
%function [e, A, B]=linear_factors(vmeans, eids, emeans, k)
function [e, A, B]=linear_factors(g, edge)
%extract the ids of the vertices connected by the kth edge
% id_i=eids(1,k);
% id_j=eids(2,k);
%extract the poses of the vertices and the mean of the edge
% v_i=vmeans(:,id_i);
% v_j=vmeans(:,id_j);
% z_ij=emeans(:,k);
v = g.vertices(edge);
v_i = g.coord(v(1));
v_j = g.coord(v(2));
z_ij = g.edata(edge).mean;
%compute the homoeneous transforms of the previous solutions
zt_ij=v2t(z_ij);
vt_i=v2t(v_i);
vt_j=v2t(v_j);
%compute the displacement between x_i and x_j
f_ij=(inv(vt_i)*vt_j);
%this below is too long to explain, to understand it derive it by hand
theta_i=v_i(3);
ti=v_i(1:2,1);
tj=v_j(1:2,1);
dt_ij=tj-ti;
si=sin(theta_i);
ci=cos(theta_i);
A= [-ci, -si, [-si, ci]*dt_ij; si, -ci, [-ci, -si]*dt_ij; 0, 0, -1 ];
B =[ ci, si, 0 ; -si, ci, 0 ; 0, 0, 1 ];
ztinv=inv(zt_ij);
e=t2v(ztinv*f_ij);
ztinv(1:2,3) = 0;
A=ztinv*A;
B=ztinv*B;
% %compute the homogeneous transforms of the previous solutions
% zt_ij=v2t(z_ij);
% vt_i=v2t(v_i);
% vt_j=v2t(v_j);
% % zt_ij = SE2(z_ij);
% % vt_i = SE2(v_i);
% % vt_j = SE2(v_j);
%
% %compute the displacement between x_i and x_j
% %f_ij=(inverse(vt_i)*vt_j);
% f_ij = vt_i.inv * vt_j;
%
% %this below is too long to explain, to understand it derive it by hand
% theta_i=v_i(3);
% ti=v_i(1:2);
% tj=v_j(1:2);
% dt_ij=tj-ti;
%
% si=sin(theta_i);
% ci=cos(theta_i);
%
% A= [-ci, -si, [-si, ci]*dt_ij; si, -ci, [-ci, -si]*dt_ij; 0, 0, -1 ];
% B =[ ci, si, 0 ; -si, ci, 0 ; 0, 0, 1 ];
%
% ztinv = inv(zt_ij);
% e = xyt(ztinv*f_ij);
% ztinv.t = 0;
% A = ztinv*A;
% B = ztinv*B;
end
%linearizes and solves one time the ls-slam problem specified by the input
%vmeans: vertices positions at the linearization point
%eids: edge ids
%emeans: edge means
%einfs: edge information matrices
%newmeans: new solution computed from the initial guess in vmeans
function [newmeans,energy] = linearize_and_solve(g)
tic
fprintf('solving');
% H and b are respectively the system matrix and the system vector
H=zeros(g.n*3,g.n*3);
b=zeros(g.n*3,1);
% this loop constructs the global system by accumulating in H and b the contributions
% of all edges (see lecture)
%for k=1:size(eids,2)
fprintf('.');
etotal = 0;
for edge = 1:g.ne
[e, A, B]=linear_factors(g, edge);
omega = g.edata(edge).info;
%compute the blocks of H^k
% not quite sure whey SE3 is being transposed, what does that mean?
b_i = -A'*omega*e;
b_j = -B'*omega*e;
H_ii = A'*omega*A;
H_ij = A'*omega*B;
H_jj = B'*omega*B;
v = g.vertices(edge);
id_i = v(1); id_j = v(2);
%accumulate the blocks in H and b
H((id_i-1)*3+1:id_i*3,(id_i-1)*3+1:id_i*3) = H((id_i-1)*3+1:id_i*3,(id_i-1)*3+1:id_i*3) + H_ii;
H((id_j-1)*3+1:id_j*3,(id_j-1)*3+1:id_j*3) = H((id_j-1)*3+1:id_j*3,(id_j-1)*3+1:id_j*3) + H_jj;
H((id_i-1)*3+1:id_i*3,(id_j-1)*3+1:id_j*3) = H((id_i-1)*3+1:id_i*3,(id_j-1)*3+1:id_j*3) + H_ij;
H((id_j-1)*3+1:id_j*3,(id_i-1)*3+1:id_i*3) = H((id_j-1)*3+1:id_j*3,(id_i-1)*3+1:id_i*3) + H_ij';
b((id_i-1)*3+1:id_i*3,1) = b((id_i-1)*3+1:id_i*3,1) + b_i;
b((id_j-1)*3+1:id_j*3,1) = b((id_j-1)*3+1:id_j*3,1) + b_j;
%NOTE on Matlab compatibility: note that we use the += operator which is octave specific
%using H=H+.... results in a tremendous overhead since the matrix would be entirely copied every time
%and the matrix is huge
etotal = etotal + e'*e;
end;
fprintf('.');
%note that the system (H b) is obtained only from
%relative constraints. H is not full rank.
%we solve the problem by anchoring the position of
%the the first vertex.
%this can be expressed by adding the equation
% deltax(1:3,1)=0;
%which is equivalent to the following
H(1:3,1:3) = H(1:3,1:3) + eye(3);
SH=sparse(H);
fprintf('.');
deltax=SH\b;
fprintf('.');
%split the increments in nice 3x1 vectors and sum them up to the original matrix
newmeans = g.coord()+reshape(deltax,3,g.n);
%normalize the angles between -PI and PI
for (i=1:size(newmeans,2))
s=sin(newmeans(3,i));
c=cos(newmeans(3,i));
newmeans(3,i)=atan2(s,c);
end
dt = toc;
fprintf('done in %.2g sec. Total cost %g \n', dt, etotal);
if nargout > 1
energy = etotal;
end
end
% This source code is part of the graph optimization package
% deveoped for the lectures of robotics2 at the University of Freiburg.
%
% Copyright (c) 2007 Giorgio Grisetti, Gian Diego Tipaldi
%
% It is licences under the Common Creative License,
% Attribution-NonCommercial-ShareAlike 3.0
%
% You are free:
% - to Share - to copy, distribute and transmit the work
% - to Remix - to adapt the work
%
% Under the following conditions:
%
% - Attribution. You must attribute the work in the manner specified
% by the author or licensor (but not in any way that suggests that
% they endorse you or your use of the work).
%
% - Noncommercial. You may not use this work for commercial purposes.
%
% - Share Alike. If you alter, transform, or build upon this work,
% you may distribute the resulting work only under the same or
% similar license to this one.
%
% Any of the above conditions can be waived if you get permission
% from the copyright holder. Nothing in this license impairs or
% restricts the author's moral rights.
%
% This software is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied
% warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
% PURPOSE.
%computes the homogeneous transform matrix A of the pose vector v
function A=v2t(v)
c=cos(v(3));
s=sin(v(3));
A=[c, -s, v(1) ;
s, c, v(2) ;
0 0 1 ];
end
%computes the pose vector v from an homogeneous transform A
function v=t2v(A)
v(1:2, 1)=A(1:2,3);
v(3,1)=atan2(A(2,1),A(1,1));
end