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

first hg version after svn

+% We navigate a robot around a square using a fixed control policy and no noise.
+% We assume the robot observes the relative distance to the nearest landmark.
+% Everything is linear-Gaussian.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Create toy data set
+
+seed = 0;
+rand('state', seed);
+randn('state', seed);
+
+if 1
+  T = 20;
+  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)];
+else
+  T = 5;
+  ctrl_signal = repmat([1 0]', 1, T);
+end
+
+nlandmarks = 4;
+true_landmark_pos = [1 1;
+		     4 1;
+		     4 4;
+		     1 4]';
+init_robot_pos = [0 0]';
+
+true_robot_pos = zeros(2, T);
+true_data_assoc = zeros(1, 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'));
+  %nn = t; % observe 1, 2, 3
+  true_data_assoc(t) = nn;
+  true_rel_dist(:,t) = true_landmark_pos(:, nn) - true_robot_pos(:,t);
+end
+
+figure(1);
+%clf; 
+hold on
+%plot(true_landmark_pos(1,:), true_landmark_pos(2,:), '*');
+for i=1:nlandmarks
+  text(true_landmark_pos(1,i), true_landmark_pos(2,i), sprintf('L%d',i));
+end
+for t=1:T
+  text(true_robot_pos(1,t), true_robot_pos(2,t), sprintf('%d',t));
+end
+hold off
+axis([-1 6 -1 6])
+
+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 for inference
+
+% 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
+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
+
+%%%%%%%%%%%%%%%%%%%%%
+% Inference
+if 1
+[xsmooth, Vsmooth] = kalman_smoother(obs_rel_pos, A, C, Qbig, Rbig, init_x, init_V, ...
+				     'model', true_data_assoc, 'u', ctrl_signal, 'B', B);
+
+est_robot_pos = xsmooth(robot_block, :);
+est_robot_pos_cov = Vsmooth(robot_block, robot_block, :);
+
+for i=1:nlandmarks
+  bi = landmark_block(:,i);
+  est_landmark_pos(:,i) = xsmooth(bi, T);
+  est_landmark_pos_cov(:,:,i) = Vsmooth(bi, bi, T);
+end
+end
+
+
+if 0
+figure(1); hold on
+for i=1:nlandmarks
+  h=plotgauss2d(est_landmark_pos(:,i), est_landmark_pos_cov(:,:,i));
+  set(h, 'color', 'r')
+end
+hold off
+
+hold on
+for t=1:T
+  h=plotgauss2d(est_robot_pos(:,t), est_robot_pos_cov(:,:,t));
+  set(h,'color','r')
+  h=text(est_robot_pos(1,t), est_robot_pos(2,2), sprintf('R%d', t));
+  set(h,'color','r')
+end
+hold off
+end
+
+
+if 0
+figure(3)
+if 0
+  for t=1:T
+    imagesc(inv(Vsmooth(:,:,t)))
+    colorbar
+    fprintf('t=%d; press key to continue\n', t);
+    pause
+  end
+else
+  for t=1:T
+    subplot(5,4,t)
+    imagesc(inv(Vsmooth(:,:,t)))
+  end
+end
+end
+
+
+
+
+
+%%%%%%%%%%%%%%%%%
+% DBN inference
+
+if 1
+  [bnet, Unode, Snode, Lnodes, Rnode, Ynode, Lsnode] = ...
+      mk_gmux_robot_dbn(nlandmarks, Q, R, init_x, init_V, robot_block, landmark_block);
+  engine = pearl_unrolled_dbn_inf_engine(bnet, 'max_iter', 50, 'filename', ...
+					 '/home/eecs/murphyk/matlab/loopyslam.txt');
+else
+  [bnet, Unode, Snode, Lnodes, Rnode, Ynode] = ...
+      mk_gmux2_robot_dbn(nlandmarks, Q, R, init_x, init_V, robot_block, landmark_block);
+  engine = jtree_dbn_inf_engine(bnet);
+end
+
+nnodes = bnet.nnodes_per_slice;
+evidence = cell(nnodes, T);
+evidence(Ynode, :) = num2cell(obs_rel_pos, 1);
+evidence(Unode, :) = num2cell(ctrl_signal, 1);
+evidence(Snode, :) = num2cell(true_data_assoc);
+
+
+[engine, ll, niter] = enter_evidence(engine, evidence);
+niter
+
+loopy_est_robot_pos = zeros(2, T);
+for t=1:T
+  m = marginal_nodes(engine, Rnode, t);
+  loopy_est_robot_pos(:,t) = m.mu;
+end
+
+for i=1:nlandmarks
+  m = marginal_nodes(engine, Lnodes(i), T);
+  loopy_est_landmark_pos(:,i) = m.mu;
+  loopy_est_landmark_pos_cov(:,:,i) = m.Sigma;
+end
+
+