The external input Zi of a neuron is calculated as follows. The neuron receives
an excitatory contribution for every sonar return, and the contribution from all the sonar returns are added to produce the total input for the neuron. The contribution for a given sonar return is a function of the “sonar reflection point” of the return, defined to be the point the measured distance from the robot a t an angle equal to the beam centre direction. As we shall see in
chapter 8 this point may not be the actual physical location where the reflection
occurred - but we will continue to use the term in this chapter.
Example graphs of input contribution against reflection point position are shown in figure 7.2 for various neurons. A given neuron’s input is close to zero except in a certain region of space. Following the neuroscience literature, we
will call this region the receptive field of the neuron.
For a line neuron, the receptive field is elongated, directed along the neu rons preferred orientation. The exact formula for the input is a product:
feedforw ard input feedforw ard input
feedforw ard input feedforw ard input
F ig u re 7.2: R eceptive fields of various neurons. T h e figures show th e e x citato ry in p u t to th e n euron du e to a single so n ar re tu rn , as a fu n ctio n of so n ar beam reflection position. T h e le tte r “R ” deno tes th e p ositio n of th e ro b o t. T h e sq u are m esh has a 10cm spacing. A) R eceptive field of th e line neuron for th e grid segm ent 1 m east of th e ro b o t w ith n o rth -s o u th o rie n ta tio n . B) R eceptive field of th e line n eu ro n for th e grid segm ent 1.5m east of th e ro b o t w ith n o rth - so u th o rien tatio n . C) R eceptive field of th e line n euron for th e grid segm ent lm east of th e ro b o t w ith n o rth w est-so u th ea st o rien tatio n . D) R eceptive field of th e free-space n eu ron for th e grid segm ent l m east of th e ro b o t.
Zline C u n e ^ Fd o s X F 2ng X F R C F
Ciine is a c o n sta n t, equal to 0.5 for th e sim u latio n s describ ed below. Fpos
is a p o sitio n al facto r w hich gives th e receptive fields th e ir oblong shape. It is given by a double G aussian:
Z71 — p C p a r F ^ p a r ~ ^ ~ ^ 'p e r p F (^ p e r p)
J p o s — c
w here dpar is th e d ista n ce of th e so n ar reflection p o in t from th e line neuron p o sitio n in th e d irec tio n p arallel w ith th e n e u ro n ’s o rie n ta tio n , dperp is th e d ista n ce of th e so n ar reflection p o in t from th e line neuron p ositio n in th e
constant distances equal to 300mm and 40mm respectively.
Fang is an angular factor, to take into account the fact th a t sonar is prefer
entially reflected perpendicularly from specular walls by increasing the input of those line segments whose orientation is perpendicular to the reflected sonar beam. It is given by a Gaussian:
where A9 is the angular difference between the sonar beam angle and a
perpendicular to the neurons orientation, and u is the sonar beam half-width,
F r c f is a range confidence fa c to r (Lim and Cho 1992), whose purpose is to reduce the contribution of long range readings, which are more likely to be specular. It has the form
m ax -detect .range x range.w eight
where returning-range is the measured length of the sonar beam, m ax-detect-range
is the maximum measurable length (2.53m for our sensor), and range.w eight
and k are constants equal to 1.1 and 0.8 respectively (values given in Lim and
Cho 1992).
Figure 7.2a shows the input strength as a function of sonar reflection po sition, to a neuron from a grid segment lm to the east of the robot with orientation in the north-south direction. Figure 7.2b shows the input to a neuron 1.5m to the east of the robot, with the same orientation. The overall strength of input to this neuron is lower, due to the range confidence factor. Figure 7.2c shows the input strength to a neuron from the same grid segment as th a t in figure 7.2a, but oriented at a 45° angle. This neuron also has a lower overall input strength th an the neuron of figure 7.2a, due to the angular factor.
The length of a line neuron receptive field is much greater th an the grid size. The line neurons therefore perform line detection in a similar manner to
reflected from many points along the wall, all lying in a straight line, and will therefore give a large input to a line neuron whose orientation is collinear with the wall.
For a free-space neuron, the receptive field consists the region of space from which the sonar beam would not have been reflected if the the part of space the neuron corresponds to was occupied. This region consists of all points which are further away from the robot than the neuron, and whose bearing from the robot is less than one sonar beam width different from the neurons bearing. The strength of the input is given by:
Zfs — C fs X F p O S X FR C F
where C fs is a constant equal to 0.2, Frcf is as above, and Fpos is a
positional factor given by
F p o s = 1 - A</>2/ c j 2
where A(f> is the angular difference between the sonar beam and the bearing
to the neuron, and u is the beam half-width as above. An example of a free-
space neuron receptive field is shown in figure 7.2d.