Control >> Finding object/goal >> Goal search

Goal search

In this section, we present a second series of experiments, in which a group of three s-bots has to find a goal item, which we refer to as the prey. We will shortly describe the controller in the following section. Afterwards, we detail the experimental setup. Finally, we discuss the results of our experiments.

Controller

In principle, the same behaviour based controller as described previously is also used for this experiment. For simplicity we have not mentioned before the behaviour in case an s-bot perceives the prey, which depends on the current state of the s-bot:

• Explorer: When detecting the prey, an explorer will attempt to connect to it by extending the chain it is currently moving along. It may only connect in case it perceives no more than one chain member and the prey.
• Chain member: A chain member that perceives the prey may not disaggregate from the chain.
• Lost: A lost s-bot perceives the prey as an obstacle and has to continue its random walk in order to regain contact to a chain.

Experimental setup

As shown in Figure 1, the experimental environment is the same as the one used for the previous experiment. As indicated on the top right corner of the image, a prey, which is represented by an s-bot with its red LEDs activated, is placed at a distance of 1.40 m from the nest. Note that the prey, by having the red LEDs activated, can be distinguished from a chain or the nest. The three s-bots have to find the prey and, by forming a chain, establish a connection between the prey and the nest. We define a connection as a chain of s-bots that allows other s-bots to navigate back and forth between nest and prey.

Figure 1. The experimental environment: a squared arena with a side length of 2.40 m with an s-toy, which represents the nest, placed in its center. In order to be recognized by the s-bots the blue LEDs of the s-toy are turned on. As indicated by the black and red dots around the nest, there are 40 different initial positions at three distances and 16 angles. At the beginning of an experiment an s-bot is randomly placed at one of them. Furthermore, an s-bot's initial orientation is determined randomly as well.

Given that an s-bot has a perceptual range of approximately 1 m to recognize red LEDs, it is sufficient that one s-bot starts a chain into the direction of the prey in order to perceive it. However, a chain of one s-bot is not yet sufficient to establish a connection between nest and prey because the perceptual range for the three other colours is approximately 50 cm.

Identical to the previous experiment, each trial is characterized by the values of the two control parameters P(expl->chain) and P(chain->expl), and by a seed that initializes a random number generator to determine the initial positions of the robots, and their probabilistic choices during an experiment. Again, for each of the two probabilities three different values are applied:

P(expl->chain) ∈ {0.01;0.1;1}

P(chain->expl) ∈ {0.001;0.01;0.1}.

For this experiment we have tested all nine possible combinations of the two parameters. For each combination, ten seeds are used to initialize an experiment. An experiment runs for 100 seconds.

Results

Figure 2 shows four screenshots of one successful trial where two s-bots are aggregated into a chain that establishes a connection between nest and prey which is exploited by the third s-bot to approach the prey.

Figure 2. Four screenshots of one successful trial: (a) the initial placement; (b) one s-bot connected itsself between nest and prey; (c) a second s-bot connected itsself; (d) the last s-bot moving along the established connection and approaches the prey.

In 81 of the 90 trials at least one s-bot has connected itsself between the nest and the prey within the time limit of 100 seconds. In 5 of the 9 unsuccessful trials the pobability set P(expl->chain)=0.01, P(chain->expl)=0.001 was used. In 75 trials at least two s-bots connected themselves between nest and prey, in this way establishing a connection between the two objects that can be used by other s-bots for the purpose of navigation. In 59 trials the third s-bot exploited the established connection to navigate towards the prey.

Figure 3 shows the completion times of the first, second and third s-bot to connect to the prey. We define the completion time as the time when an s-bot is aggregated into a chain between nest and prey. If no connection can be established, the value 100 is taken.

Figure 3(a)

Figure 3(b)

Figure 3(c). The completion times of the first, second and third s-bot to connect to the prey for (a) P(expl->chain)=0.01, (b) P(expl->chain)=0.1, and (c) P(expl->chain)=1. We define the completion time as the time when an s-bot is aggregated into a chain between nest and prey. If no connection can be established, the value 100 is taken. Errorbars indicate the standard deviation.

For this comparably simple setup a wide range of parameters leads to a similar successful performance. Therefore, it is not possible to determine which of the tested parameters is the best one. However, we observed that in general parameter sets with a very low probability to disaggregate from a chain are less successful than those with a higher value of P(chain->expl). This can be explained by the fact that a lower value of P(chain->expl) leads to a lower exploration rate. Once established, a chain has a longer lifetime and therefore no new chains are formed into unexplored areas, in this way blocking the exploration of the environment.