The excerpt note is about how to move the activity of pose cells according to the translational and rotational velocity in RatSLAM from Michael et al. 2008, 2004.

The new path integration method shifts existing pose cell activity rather than projecting a copy of the current activity forwards in time.

The path integration process projects the pose cell activity into cells slightly offset from the currently activated ones. If the robot is translating, the activity is shifted in the x, y plane; if the robot is rotating, activity is shifted in the direction.

The magnitude of the movement in the x, y plane is dependent on the translational velocity, v. The movement along the axis is dependent on the rotational velocity, .

When the rotational or translational velocity is becoming faster, the magnitude of the movement of activity should become bigger. The current activity will move faster forwarding to slightly offset cells when the slightly offset cells’ activity is becoming larger.

Posecells(:,:,dir_pc) = Posecells(:,:,dir_pc).*(1.0 - vtrans) + circshift(Posecells(:,:,dir_pc), [0 1]).*vtrans;

% given vtrans and the direction

% residue matrix
% formula 8.7 in Michael's book 2008
% ne [1 1] weight_ne = v * cos(th) * v * sin(th)   shift [1 1]
% se [1 0] weight_se = (1 - v * sin(th)) * v * cos(th)   shift [1 0]
% nw [0 1] weight_nw = (1 - v * cos(th)) * v * sin(th)   shift [0 1]
% sw [0 0] weight_sw = (1 - v * cos(th)) * (1 - v * sin(th)) = 1 - weight_ne - weight_se - weight_nw   shift [0 0]
% weight_ne = (v * cos(th)) * (v * sin(th))    
% weight_se = (1 - v * cos(th)) * v * sin(th)
% weight_nw = (1 - v * sin(th)) * v * cos(th)
% weight_sw = (1 - v * cos(th)) * (1 - v * sin(th)) = 1 - weight_sw - weight_se - weight_nw
% think in terms of NE divided into 4 rectangles with the sides

pca_new = pca_new.*weight_sw + circshift(pca_new, [0 1]).*weight_nw + circshift(pca_new, [1 0]).*weight_se + circshift(pca_new, [1 1]).*weight_ne;

For further more info, please read the Michael et al. 2008, 2004.

Michael Milford. Robot Navigation from Nature: Simultaneous Localisation, Mapping, and Path Planning Based on Hippocampal Models. Springer-Verlag Berlin Heidelberg Press, pp. 93-94, 2008.

Michael Milford, Gordon Wyeth, and David Prasser. “RatSLAM: a Hippocampal Model for Simultaneous Localization and Mapping.” In Robotics and Automation, 2004. Proceedings. ICRA’04. 2004 IEEE International Conference on, vol. 1, pp. 403-408. IEEE, 2004.