At each time-step, a sonar scan is taken, the feed-forward inputs are cal culated, and the membrane potentials of all the neurons are updated. Any neurons which exceed their threshold will fire. The recurrent connections are then activated once, and a m ap is output on the basis of the neural firing pattern. The robot then makes a movement. After movement, the entire neu ral activation pattern, including sub-threshold potentials, is shifted through the distance the robot has moved, so it remains in an egocentric coordinate system. A new time-step then begins.
This allows the robot to integrate information from several viewpoints as follows: When the robot is initially placed in an environment all of the neurons
inputs to several neurons in the network. When the robot moves, this potential is transferred to the neurons corresponding to the new egocentric position of the features th at caused the initial sub-threshold potential, by the shifting mechanism ju st described. A second scan receiving reflections from the same features will activate these same neurons, allowing sonar information from several viewpoints to be integrated.
7.4
Experim ental Verification
In order to asses the performance of the above mapping system in comparison to other methods, we also implemented a Bayesian grid-based mapping system. The grid-based methods of Elfes (1987), Moravec (1988), and Cho (1990) per formed poorly on sonar data collected from our robot due to specular reflection from smooth wood walls in the environment. We therefore implemented the method of Lim and Cho (1992), which was designed to overcome the problems
of specular reflection. For the param eter C (unspecified by Lim and Cho), we
used the value 0.001, as we found this gave best resu!tst In order to produce output th at is visually comparable to th at produced by our model, we thresh- olded the occupancy probabilities. If a segment has occupancy probability less than 0.3, it is judged to be empty, if it has occupancy probability greater th at 0.7, it is judged occupied, otherwise it is marked unknown. Occupied cells were drawn on the output maps as line segments, with orientation given by the maximum of the orientation probability stored for the segment. We also compared the performance of our model to th at of the model of Lee and Recce
(Lee and Recce 1997; Lee 1996).
Figure 7.5 shows the maps produced 10 and 30 time-steps into a run in the environment shown in figure 7.4.
By 10 time-steps, all 3 systems produced a partial map of the environment, and by 30 time-steps, they produced a fairly complete map. The neural and Bayesian methods produce broadly similar maps. However, the effect of the lateral connections can be seen in the neural method. For example there is a
Plaster Brick Pillar Cardboard Box Rough Brick Smooth W ood ' 1 metre
Figure 7.4: The environment used to collect sonar data. The environment contains a mix of specular and non-specular surfaces.
greater coherence and collinearity of line segments th a t correspond to walls. Also in the Bayesian m ethod there are incorrectly identified line segments in the middle of free-space regions (see figure 7.5), th a t would cause the robot to make unneeded detours, and could make free space regions unreachable.
The feature-based m ethod is slightly slower than the other two a t accu m ulating a map, but is the most accurate at representing the positions of the walls. This is because of its non-probabilistic nature, whereby it must be sure of the existence of a feature before adding it to the map. For example, even by tim e 30, this m ethod has not detected the lines corresponding to the card board box or smooth plaster wall. Note th a t the smaller size of the free-space
F ig ure 7.5: T h e m ap s produced by th e neural m e th o d described in th is p ap er, th e B ayesian m e th o d of (Lim and Cho 1992), an d th e featu re-b ased m e th o d of (Lee an d Recce 1997), from th e sam e sonar d a ta , afte r 10 an d 30 tim e-steps. O pen circles rep resen t areas of space m arked as free, and line segm ents or lines rep resen t walls. T h e filled circle represents th e ro b o t position.
a rea w ith th is m e th o d is due to a ‘‘safety zone” of one ro b o t d ia m ete r placed a ro u n d th e walls by th e m apping softw are, ra th e r th a n a failure to d etect free space.
7.5
D iscussion
In th is ch ap ter, we described functional sim ilarities betw een grid-based m ap s for ro b o t so n ar an d artificial neural netw orks. M aking use of th is analogy, we p roposed a new grid -b ased m apping system m aking use of th e n eu ral concepts of receptive fields a n d la teral connections. N eurons w ith elo ng ated receptive fields d e te c t s tra ig h t walls in a sim ilar m a n n er to a H ough tran sfo rm . T h e la te ra l co nn ection s in th e netw ork are designed to reinforce m aps th a t rep resent co nfig uration s likely to occur in th e world, like s tra ig h t walls, an d in h ib it config uration s unlikely to occur, such as ran d o m sc atter.
T h e receptive fields of th e line neurons used in th e m odel have p ro p erties in com m on w ith th e ex perim entally observed receptive fields of som e n eu rons
cortex which m aintain the memory of an object through sustained activity (Miyashita 1988), similarly to the way cells in our network continue to code for features even when they are further from the robot th an the maximum sonar range.
Our network functions in egocentric coordinates, and therefore requires activation p attern s to be shifted after each robot movement. Droulez and Berthoz (1991) and Zhang (1996) have described neural mechanisms by which an entire neural activation p attern can be shifted to remain in egocentric co ordinates after movement. This shift of activity p attern is the equivalent of dead-reckoning in egocentric coordinates, as discussed in the last two chap ters. In the current im plementation we did not use a neural mechanism to perform the shift, b u t simply shifted the array of membrane potentials with a loop. Implementing a neural mechanism for this shift would make the network more biologically realistic but it would not contribute to its performance as an engineering m ethod for guiding the navigation of a robot.
We compared the new network to an established grid-based mapping sys tem, and to a feature-based m apping system, and found th a t the representation of walls by line segments is more coherent in the new neural m ethod than in the Bayesian m ethod, and th a t both the neural and Bayesian methods were faster at building a m ap than the feature-based method.
The new m ethod is based on the use of a single layer of neurons, and if implemented on parallel neural hardware, the m ap would updated one com putational tim e-step after the presentation of the new sensory input.
The current model represents only the first step in neural-based sonar map ping. The real strength of neural networks is their ability to learn using real world data. The net we described here, however, has fixed weights, and a large number of param eters whose values were not systematically optimised or derived from a m athem atical principle. A possibility for future work would be to incorporate learning into neural sonar mapping algorithms, and thereby reduce the num ber of free param eters.
system it is possible to derive mapping rules from a m athem atical principle, while keeping the benefits of the new system described in this chapter.