Control >> Cooperative transport >> Different shapes and sizes

Transport by a group of pre-attached s-bots

This section details the experimental work concerning the transport module that is used to control s-bots which are capable of localizing the target location.

Controller

  1 α = 0
  2 repeat
  3 α* = computeTargetDirection( ambient light sensors )
  4 α = (α* + 3 α) / 4
  5 if (torque problem on turret or tracks) then
  6 execute recovery move
  7 else
  8 setTurretOrientation(α)
  9 if (soft alignment sufficient) then
10 move and softly re-align towards α
11 else
12 turn on the spot towards target
13 endif
14 endif
15 until (timeout reached)

Algorithm 1: Transport module

Algorithm 1 describes the control module for the transport. The basic concept of the control has been validated already in simulation: the s-bot aligns its chassis towards the direction in which the target is perceived, and moves towards it.

Experimental Setup

The task is to transport a prey towards a light source. The prey has a mass of 813g and is initially put in a fixed location, at a distance of 250cm to the light source. The s-bots start being attached to the prey, either directly or within a chain formation. They are supposed to transport the prey within a time period of 15 seconds for as far as possible towards the target location.

Figure 1: Spatial arrangement of 1-3 s-bots (white) around a prey (gray). In each case, the transport target (not indicated) is a light source, 250cm to the right side of the prey.

In this study, 1 to 3 s-bots are used. The number of different spatial arrangements has been limited to the discrete set illustrated in Figure 1. All arrangements fulfill the condition that every s-bot is initially arranged in such a way that no obstacle (prey or teammate) is shadowing the light source.

We examine the performance of the system in two different types of environments:

• Environment A: a polyvinyl-chloride-based ground. In this environment, the friction coefficient between the prey and the ground is about 0.46. The friction coefficient between the tracks and the ground is about 0.57 in the lateral direction and 0.58 in the frontal direction.
• Environment B: a polystyrene-like ground. In this environment, the friction coefficient between the prey and the ground is about 0.41. The friction coefficient between the tracks and the ground is about 1.3 in the lateral direction, and more than 1.8 in the frontal direction.

The force necessary to move the prey in Environment A is similar to the one in Environment B. For Environment A, we consider the magnitude of friction between the tracks and the ground as moderate. For Environment B, there is so much friction between the tracks and the ground that if a lateral force is applied to the s-bot, it will either topple down or it will be displaced by a sequence of irregular movements. Environment B is considered as a very difficult test-bed, since a group of s-bots connected to each other and/or the prey might easily get stuck, if not coordinated properly.

Results

To assess the performance of the s-bots in Environment A and B, in total more than 500 trials have been performed. The performance metric we use is the distance gain, that is, the distance the prey has gained with respect to the light source within the time period of 15 seconds.

The distance an s-bot with the speed constraints we set can cover in Environment A or B during the time frame of 15 seconds is about 232cm. In Environment type A, an s-bot attached to a prey can pull it for about 8cm by moving backwards, while a chain of two s-bots can pull the prey for about 210cm. Since a group cannot transport the prey faster than its members can move, two s-bots are sufficient for reaching almost optimal performance in this case.

Figure 2: Transport performance of 1-3 s-bots in Environment A and B. Observations per box (from the left to the right): 42, 75, 90, 120, 105 and 105.

The white boxes in Figure 2 refer to the transport performance of 1 to 3 s-bots for Environment A. If there is only one s-bot, the distance covered is low and we observed that it depends mostly on the particular spatial arrangement used. For the arrangements A1 and A2 the force the s-bot exerts on the prey does initially not act through the center of the prey, thus the prey is rotated for almost 90 degrees and thereby it is moved for a few cm more. A similar behavior had been observed in simulation.

As expected for Environment A, one s-bot was nearly incapable of moving the prey in all trials. On the contrary, two and three s-bots have transported the prey during each of the 90 trials for more than 60cm. The whiskers cover observations in the intervals [2, 13], [75, 193] and [71,190].

The gray boxes of Figure 2 refer the transport performance of 1 to 3 s-bots in Environment B. The whiskers cover observations in the intervals [6, 138], [39, 163] and [7,163].

Due to the better grip the tracks have on the ground of Environment B, a single s-bot itself is already capable of transporting the prey. Nevertheless, for the group sizes 2 and 3, the system performs better in Environment A. Note that the force necessary to move the prey in Environment A is slightly bigger than for Environment B.

As discussed previously, the task can be solved almost optimal by two s-bots. For Environment A, there seems to be no gain in performance by adding the third s-bot. On the other hand, the third s-bot seems not to disrupt the performance either.

Figure 3: Transport performance for different spatial arrangements of 3 s-bots and the prey (15 observations per box).

In the following we examine the results for groups of three s-bots in more detail. The box-plot in Figure 3 groups observations belonging to the same spatial arrangement. The white boxes refer to trials performed in Environment A, while the gray ones refer to trials performed in Environment B. For all different spatial arrangements, the median performance in Environment A is superior to the median performance in Environment B. Thus, although the performance of a single s-bot is superior in the Environment B which provides the s-bot's tracks with better grip, a group of s-bots performs superior in Environment A. We believe that due to the very high friction in Environment B, a precise alignment of all s-bots' tracks in the same direction is required to let successfully combine the forces to start moving the heavy prey.

By comparing the patterns of the white and gray boxes, it can be recognized that the type of spatial arrangement affects the performance. Overall, it seems that the arrangement C0, C3 and C6, which are the ones in which at least one s-bot is located on the left and right side of the prey (wrt the target) lead to a better performance than the others. This is plausible, since in such arrangement less energy is required to reach a stable configuration during transport.

In the symmetric case (arrangement C0), the lowest transport distance observed over all trials in Environment A (B) is still 67% (54%) of the distance a single s-bot moving straight without any load can cover within the same amount of time.

Example movies:

• Cooperative Transport, 3 s-bots, terrain with moderate friction (Quicktime, 2.2 MB).
• Cooperative Transport, 3 s-bots, terrain with high friction (Quicktime, 2.3 MB).

References

• Groß R. and Dorigo M. Group Transport of an Object to a Target that Only Some Group Members May Sense, In Yao X., Burke E., Lozano J. A., Smith J., Merelo-Guervós J. J ., Bullinaria J. A., Rowe J., Tiňo P., Kabán A., and Schwefel H.-P., editors, Parallel Problem Solving from Nature - 8th International Conference, PPSN VIII, volume 3242 of Lecture Notes in Computer Science, pages 852-861. Springer Verlag, Berlin, Germany, 2004