comparison toolboxes/FullBNT-1.0.7/bnt/examples/dynamic/SLAM/mk_linear_slam.m @ 0:e9a9cd732c1e tip

first hg version after svn

+function [A,B,C,Q,R,Qbig,Rbig,init_x,init_V,robot_block,landmark_block,...
+	  true_landmark_pos, true_robot_pos, true_data_assoc, ...
+	  obs_rel_pos, ctrl_signal] = mk_linear_slam(varargin)
+
+% We create data from a linear system for testing SLAM algorithms.
+% i.e. , new robot pos = old robot pos + ctrl_signal, which is just a displacement vector.
+% and  observation = landmark_pos - robot_pos, which is just a displacement vector.
+%
+% The behavior is determined by the following optional arguments:
+%
+% 'nlandmarks' - num. landmarks
+% 'landmarks' - 'rnd' means random locations in the unit sqyare
+%               'square' means at [1 1], [4 1], [4 4] and [1 4]
+% 'T' - num steps to run
+% 'ctrl' - 'stationary' means the robot remains at [0 0],
+%          'leftright' means the robot receives a constant contol of [1 0],
+%          'square' means we navigate the robot around the square
+% 'data-assoc' - 'rnd' means we observe landmarks at random
+%                'nn' means we observe the nearest neighbor landmark
+%                'cycle' means we observe landmarks in order 1,2,.., 1, 2, ...
+
+args = varargin;
+% get mandatory params
+for i=1:2:length(args)
+  switch args{i},
+   case 'nlandmarks', nlandmarks = args{i+1};
+   case 'T', T = args{i+1};
+  end
+end
+
+% set defaults
+true_landmark_pos = rand(2,nlandmarks);
+true_data_assoc = [];
+
+% get args
+for i=1:2:length(args)
+  switch args{i},
+   case 'landmarks',
+    switch args{i+1},
+     case 'rnd',   true_landmark_pos = rand(2,nlandmarks);
+     case 'square',   true_landmark_pos = [1 1; 4 1; 4 4; 1 4]';
+    end
+   case 'ctrl',
+    switch args{i+1},
+     case 'stationary', ctrl_signal = repmat([0 0]', 1, T);
+     case 'leftright', ctrl_signal = repmat([1 0]', 1, T);
+     case 'square',   ctrl_signal = [repmat([1 0]', 1, T/4) repmat([0 1]', 1, T/4) ...
+		    repmat([-1 0]', 1, T/4) repmat([0 -1]', 1, T/4)];
+    end
+   case 'data-assoc', 
+    switch args{i+1},
+     case 'rnd', true_data_assoc  = sample_discrete(normalise(ones(1,nlandmarks)),1,T);
+     case 'cycle', true_data_assoc = wrap(1:T, nlandmarks);
+    end
+  end
+end
+if isempty(true_data_assoc)
+  use_nn = 1;
+else
+  use_nn = 0;
+end
+
+%%%%%%%%%%%%%%%%%%%%%%%%
+% generate data
+
+init_robot_pos = [0 0]';
+true_robot_pos = zeros(2, T);
+true_rel_dist = zeros(2, T);
+for t=1:T
+  if t>1
+    true_robot_pos(:,t) = true_robot_pos(:,t-1) + ctrl_signal(:,t);
+  else
+    true_robot_pos(:,t) = init_robot_pos + ctrl_signal(:,t);
+  end
+  nn = argmin(dist2(true_robot_pos(:,t)', true_landmark_pos'));
+  if use_nn
+    true_data_assoc(t) = nn;
+  end
+  true_rel_dist(:,t) = true_landmark_pos(:, nn) - true_robot_pos(:,t);
+end
+
+
+R = 1e-3*eye(2); % noise added to observation
+Q = 1e-3*eye(2); % noise added to robot motion
+
+% Create data set
+obs_noise_seq = sample_gaussian([0 0]', R, T)';
+obs_rel_pos = true_rel_dist + obs_noise_seq;
+%obs_rel_pos = true_rel_dist;
+
+%%%%%%%%%%%%%%%%%%
+% Create params
+
+
+% X(t) = A X(t-1) + B U(t) + noise(Q) 
+
+% [L1]  = [1     ]  * [L1]       + [0]  * Ut  + [0   ]
+% [L2]    [  1   ]    [L2]         [0]          [ 0  ]
+% [R ]t   [     1]    [R ]t-1      [1]          [   Q]
+
+% Y(t)|S(t)=s  = C(s) X(t) + noise(R)
+% Yt|St=1 = [1 0 -1]  * [L1]  + R
+%                       [L2]    
+%                       [R ]    
+
+% Create indices into block structure
+bs = 2*ones(1, nlandmarks+1); % sizes of blocks in state space
+robot_block =  block(nlandmarks+1, bs);
+for i=1:nlandmarks
+  landmark_block(:,i) = block(i, bs)';
+end
+Xsz = 2*(nlandmarks+1); % 2 values for each landmark plus robot
+Ysz = 2; % observe relative location
+Usz = 2; % input is (dx, dy)
+
+
+% create block-diagonal trans matrix for each switch
+A = zeros(Xsz, Xsz);
+for i=1:nlandmarks
+  bi = landmark_block(:,i);
+  A(bi, bi) = eye(2);
+end
+bi = robot_block;
+A(bi, bi) = eye(2);
+A = repmat(A, [1 1 nlandmarks]); % same for all switch values
+
+% create block-diagonal system cov
+
+
+Qbig = zeros(Xsz, Xsz);
+bi = robot_block;
+Qbig(bi,bi) = Q; % only add noise to robot motion
+Qbig = repmat(Qbig, [1 1 nlandmarks]);
+
+% create input matrix
+B = zeros(Xsz, Usz);
+B(robot_block,:) = eye(2); % only add input to robot position
+B = repmat(B, [1 1 nlandmarks]);
+
+% create observation matrix for each value of the switch node
+% C(:,:,i) = (0 ... I ... -I) where the I is in the i'th posn.
+% This computes L(i) - R
+C = zeros(Ysz, Xsz, nlandmarks);
+for i=1:nlandmarks
+  C(:, landmark_block(:,i), i) = eye(2); 
+  C(:, robot_block, i) = -eye(2);
+end
+
+% create observation cov for each value of the switch node
+Rbig = repmat(R, [1 1 nlandmarks]);
+
+% initial conditions
+init_x = zeros(Xsz, 1);
+init_v = zeros(Xsz, Xsz);
+bi = robot_block;
+init_x(bi) = init_robot_pos;
+%init_V(bi, bi) = 1e-5*eye(2); % very sure of robot posn
+init_V(bi, bi) = Q; % simualate uncertainty due to 1 motion step
+for i=1:nlandmarks
+  bi = landmark_block(:,i);
+  init_V(bi,bi)= 1e5*eye(2); % very uncertain of landmark psosns
+  %init_x(bi) = true_landmark_pos(:,i);
+  %init_V(bi,bi)= 1e-5*eye(2); % very sure of landmark psosns
+end