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Dstar.m
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Dstar.m
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%Dstar D* navigation class
%
% A concrete subclass of the abstract Navigation class that implements the D*
% navigation algorithm. This provides minimum distance paths and
% facilitates incremental replanning.
%
% Methods::
% Dstar Constructor
% plan Compute the cost map given a goal and map
% query Find a path
% plot Display the obstacle map
% display Print the parameters in human readable form
% char Convert to string% costmap_modify Modify the costmap
%--
% modify_cost Modify the costmap
%
% Properties (read only)::
% distancemap Distance from each point to the goal.
% costmap Cost of traversing cell (in any direction).
% niter Number of iterations.
%
% Example::
% load map1 % load map
% goal = [50,30];
% start=[20,10];
% ds = Dstar(map); % create navigation object
% ds.plan(goal) % create plan for specified goal
% ds.query(start) % animate path from this start location
%
% Notes::
% - Obstacles are represented by Inf in the costmap.
% - The value of each element in the costmap is the shortest distance from the
% corresponding point in the map to the current goal.
%
% References::
% - The D* algorithm for real-time planning of optimal traverses,
% A. Stentz,
% Tech. Rep. CMU-RI-TR-94-37, The Robotics Institute, Carnegie-Mellon University, 1994.
% https://www.ri.cmu.edu/pub_files/pub3/stentz_anthony__tony__1994_2/stentz_anthony__tony__1994_2.pdf
% - Robotics, Vision & Control, Sec 5.2.2,
% Peter Corke, Springer, 2011.
%
% See also Navigation, DXform, PRM.
% 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
% Implementation notes:
%
% All the state is kept in the structure called d
% X is an index into the array of states.
% state pointers are kept as matlab array index rather than row,col format
%TODO use pgraph class
% pic 7/09
classdef Dstar < Navigation
properties (SetAccess=private, GetAccess=private)
G % index of goal point
% info kept per cell (state)
b % backpointer (0 means not set)
t % tag: NEW OPEN CLOSED
h % distance map, path cost
validplan % a plan has been computed for current costmap
% list of open states: 2xN matrix
% each open point is a column, row 1 = index of cell, row 2 = k
openlist
openlist_maxlen % keep track of maximum length
% tag state values
NEW = 0;
OPEN = 1;
CLOSED = 2;
end
properties (SetAccess=private, GetAccess=public)
niter
costmap % world cost map: obstacle = Inf
end
methods
% constructor
function ds = Dstar(world, varargin)
%Dstar.Dstar D* constructor
%
% DS = Dstar(MAP, OPTIONS) is a D* navigation object, and MAP is an
% occupancy grid, a representation of a planar world as a
% matrix whose elements are 0 (free space) or 1 (occupied).
% The occupancy grid is coverted to a costmap with a unit cost
% for traversing a cell.
%
% Options::
% 'goal',G Specify the goal point (2x1)
% 'metric',M Specify the distance metric as 'euclidean' (default)
% or 'cityblock'.
% 'inflate',K Inflate all obstacles by K cells.
% 'progress' Don't display the progress spinner
%
% Other options are supported by the Navigation superclass.
%
% See also Navigation.Navigation.
% invoke the superclass constructor
ds = ds@Navigation(world, varargin{:});
% init the D* state variables
ds.reset();
if ~isempty(ds.goal)
ds.goal_change();
end
ds.reset();
end
function reset(ds)
%Dstar.reset Reset the planner
%
% DS.reset() resets the D* planner. The next instantiation
% of DS.plan() will perform a global replan.
% build the matrices required to hold the state of each cell for D*
ds.b = zeros(size(ds.costmap), 'uint32'); % backpointers
ds.t = zeros(size(ds.costmap), 'uint8'); % tags
ds.h = Inf*ones(size(ds.costmap)); % path cost estimate
ds.openlist = zeros(2,0); % the open list, one column per point
ds.openlist_maxlen = -Inf;
ds.occgrid2costmap(ds.occgridnav);
ds.validplan = false; % plan doesn't match costmap
end
function s = char(ds)
%Dstar.char Convert navigation object to string
%
% DS.char() is a string representing the state of the Dstar
% object in human-readable form.
%
% See also Dstar.display, Navigation.char.
% most of the work is done by the superclass
s = char@Navigation(ds);
% Dstar specific stuff
if ~isempty(ds.costmap)
s = char(s, sprintf(' costmap: %dx%d, open list %d', size(ds.costmap), numcols(ds.openlist)));
else
s = char(s, sprintf(' costmap: empty:'));
end
if ds.validplan
s = char(s, sprintf(' plan: valid'));
else
s = char(s, sprintf(' plan: stale'));
end
end
function plot(ds, varargin)
%Dstar.plot Visualize navigation environment
%
% DS.plot() displays the occupancy grid and the goal distance
% in a new figure. The goal distance is shown by intensity which
% increases with distance from the goal. Obstacles are overlaid
% and shown in red.
%
% DS.plot(P) as above but also overlays a path given by the set
% of points P (Mx2).
%
% See also Navigation.plot.
plot@Navigation(ds, varargin{:}, 'distance', ds.h);
end
% invoked by Navigation.step
function n = next(ds, current)
if ~ds.validplan
error('Cost map has changed, replan');
end
X = sub2ind(size(ds.costmap), current(2), current(1));
X = ds.b(X);
if X == 0
n = [];
else
[r,c] = ind2sub(size(ds.costmap), X);
n = [c;r];
end
end
function plan(ds, varargin)
%Dstar.plan Plan path to goal
%
% DS.plan(OPTIONS) create a D* plan to reach the goal from all free cells
% in the map. Also updates a D* plan after changes to the costmap. The
% goal is as previously specified.
%
% DS.plan(GOAL,OPTIONS) as above but goal given explicitly.
%
% Options::
% 'animate' Plot the distance transform as it evolves
% 'progress' Display a progress bar
%
% Note::
% - If a path has already been planned, but the costmap was
% modified, then reinvoking this method will replan,
% incrementally updating the plan at lower cost than a full
% replan.
% - The reset method causes a fresh plan, rather than replan.
%
% See also Dstar.reset.
opt.progress = true;
opt.animate = false;
[opt,args] = tb_optparse(opt, varargin);
% was a goal given here
if ~isempty(args) && isvec(args{1},2)
goal = args{1};
ds.setgoal(goal);
ds.reset();
end
% check we have a goal
assert(~isempty(ds.goal), 'RTB:Dstar:plan', 'no goal specified here or in constructor');
goal = ds.goal;
% keep goal in index rather than row,col format
ds.G = sub2ind(size(ds.occgridnav), goal(2), goal(1));
ds.INSERT(ds.G, 0, 'goalset');
ds.h(ds.G) = 0;
ds.niter = 0;
if opt.progress
% for replanning we don't really know how many iterations, so scale it to
% the worst case, a full replan
hprog = Navigation.progress_init('D* planning');
end
% number of free cells, upper bound on number of iterations, trapped free
% cells will never be reached
nfree = prod(size(ds.occgridnav)) - sum(sum(ds.occgridnav > 0));
nupdate = round(nfree/100);
while true
ds.niter = ds.niter + 1;
if opt.progress && mod(ds.niter, nupdate) == 0
Navigation.progress(hprog, ds.niter/nfree);
if opt.animate
Navigation.show_distance(ds.h);
end
end
if ds.PROCESS_STATE() < 0
break;
end
end
if opt.progress
Navigation.progress_delete(hprog);
end
ds.validplan = true;
fprintf('%d iterations\n', ds.niter)
end
function set_cost(ds, costmap)
%Dstar.set_cost Set the current costmap
%
% DS.set_cost(C) sets the current costmap. The cost map is the same size
% as the occupancy grid and the value of each element represents the cost
% of traversing the cell. A high value indicates that the cell is more costly
% (difficult) to traverese. A value of Inf indicates an obstacle.
%
% Notes::
% - After the cost map is changed the path should be replanned by
% calling DS.plan().
%
% See also Dstar.modify_cost.
if ~all(size(costmap) == size(ds.occgridnav))
error('costmap must be same size as occupancy grid');
end
ds.costmap = costmap;
ds.validplan = false;
end
function modify_cost(ds, xy, newcost)
%Dstar.modify_cost Modify cost map
%
% DS.modify_cost(P, C) modifies the cost map for the points described by
% the columns of P (2xN) and sets them to the corresponding elements of C
% (1xN). For the particular case where P (2x2) the first and last columns
% define the corners of a rectangular region which is set to C (1x1).
%
% Notes::
% - After one or more point costs have been updated the path
% should be replanned by calling DS.plan().
%
% See also Dstar.set_cost.
function modify(ds, x, y, newcost)
X = sub2ind(size(ds.costmap), y, x);
ds.costmap(X) = newcost;
if ds.t(X) == ds.CLOSED
ds.INSERT(X, ds.h(X), 'modifycost');
end
end
if all(size(xy) == [2 2]) && numel(newcost) == 1
% a rectangular region is specified
for xx=xy(1,1):xy(1,2)
for yy=xy(2,1):xy(2,2)
modify(ds, xx, yy, newcost);
end
end
elseif numcols(xy) == numel(newcost)
% a set of column vectors specifying the points to change
for i=1:numcols(xy)
modify(ds, xy(1,i), xy(2,i), newcost(i));
end
else
error('number of columns of P and C must match');
end
ds.validplan = false;
end
end % public methods
methods (Access=protected)
function occgrid2costmap(ds, og, cost)
if nargin < 3
cost = 1;
end
ds.costmap = og;
ds.costmap(ds.costmap==1) = Inf; % occupied cells have Inf driving cost
ds.costmap(ds.costmap==0) = cost; % unoccupied cells have driving cost
end
% The main D* function as per the Stentz paper, comments Ln are the original
% line numbers.
function r = PROCESS_STATE(d)
%% states with the lowest k value are removed from the
%% open list
X = d.MIN_STATE(); % L1
if isempty(X) % L2
r = -1;
return;
end
k_old = d.GET_KMIN(); d.DELETE(X); % L3
if k_old < d.h(X) % L4
d.message('k_old < h(X): %f %f\n', k_old, d.h(X));
for Y=d.neighbours(X) % L5
if (d.h(Y) <= k_old) && (d.h(X) > d.h(Y)+d.c(Y,X)) % L6
d.b(X) = Y;
d.h(X) = d.h (Y) + d.c(Y,X); % L7
end
end
end
%% can we lower the path cost of any neighbours?
if k_old == d.h(X) % L8
d.message('k_old == h(X): %f\n', k_old);
for Y=d.neighbours(X) % L9
if (d.t(Y) == d.NEW) || ... % L10-12
( (d.b(Y) == X) && (d.h(Y) ~= (d.h(X) + d.c(X,Y))) ) || ...
( (d.b(Y) ~= X) && (d.h(Y) > (d.h(X) + d.c(X,Y))) )
d.b(Y) = X; d.INSERT(Y, d.h(X)+d.c(X,Y), 'L13'); % L13
end
end
else % L14
d.message('k_old > h(X)');
for Y=d.neighbours(X) % L15
if (d.t(Y) == d.NEW) || ( (d.b(Y) == X) && (d.h(Y) ~= (d.h(X) + d.c(X,Y))) )
d.b(Y) = X; d.INSERT(Y, d.h(X)+d.c(X,Y), 'L18'); % L18
else
if ( (d.b(Y) ~= X) && (d.h(Y) > (d.h(X) + d.c(X,Y))) )
d.INSERT(X, d.h(X), 'L21'); % L21
else
if (d.b(Y) ~= X) && (d.h(X) > (d.h(Y) + d.c(Y,X))) && ...
(d.t(Y) == d.CLOSED) && d.h(Y) > k_old
d.INSERT(Y, d.h(Y), 'L25'); % L25
end
end
end
end
end
r = 0;
return;
end % process_state(0
function kk = k(ds, X)
i = ds.openlist(1,:) == X;
kk = ds.openlist(2, i);
end
% add node to open list
function INSERT(ds, X, h_new, where)
% where is for diagnostic purposes only
ds.message('insert (%s) %d = %f\n', where, X, h_new);
i = find(ds.openlist(1,:) == X);
if length(i) > 1
error('D*:INSERT: state in open list %d times', X);
end
if ds.t(X) == ds.NEW
k_new = h_new;
% add a new column to the open list
ds.openlist = [ds.openlist [X; k_new]];
elseif ds.t(X) == ds.OPEN
k_new = min( ds.openlist(2,i), h_new );
elseif ds.t(X) == ds.CLOSED
k_new = min( ds.h(X), h_new );
% add a new column to the open list
ds.openlist = [ds.openlist [X; k_new]];
end
if numcols(ds.openlist) > ds.openlist_maxlen
ds.openlist_maxlen = numcols(ds.openlist);
end
ds.h(X) = h_new;
ds.t(X) = ds.OPEN;
end
% remove node from open list
function DELETE(ds, X)
ds.message('delete %d\n', X);
i = find(ds.openlist(1,:) == X);
if length(i) ~= 1
error('D*:DELETE: state %d doesnt exist', X);
end
if length(i) > 1
disp('hello')
end
ds.openlist(:,i) = []; % remove the column
ds.t(X) = ds.CLOSED;
end
% return the index of the open state with the smallest k value
function ms = MIN_STATE(ds)
if isempty(ds.openlist)
ms = [];
else
% find the minimum k value on the openlist
[~,i] = min(ds.openlist(2,:));
% return its index
ms = ds.openlist(1,i);
end
end
function kmin = GET_KMIN(ds)
kmin = min(ds.openlist(2,:));
end
% return the cost of moving from state X to state Y
function cost = c(ds, X, Y)
[r,c] = ind2sub(size(ds.costmap), [X; Y]);
dist = sqrt(sum(diff([r c]).^2));
dcost = (ds.costmap(X) + ds.costmap(Y))/2;
cost = dist * dcost;
end
% return index of neighbour states as a row vector
function Y = neighbours(ds, X)
dims = size(ds.costmap);
[r,c] = ind2sub(dims, X);
% list of 8-way neighbours
Y = [r-1 r-1 r-1 r r r+1 r+1 r+1; c-1 c c+1 c-1 c+1 c-1 c c+1];
k = (min(Y)>0) & (Y(1,:)<=dims(1)) & (Y(2,:)<=dims(2));
Y = Y(:,k);
Y = sub2ind(dims, Y(1,:)', Y(2,:)')';
end
end % protected methods
end % classdef