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The Crane: Triangle

Figure 2.25: Crane with a diagonal crane arm: intermediate (top) and final (bottom) stages.

The diagonal crane arm experiment had a slightly more complicated fitness function than the previous bridge experiment. Here the aim was to evolve a structure capable of holding a 250g payload up and away from a fixed base. The size of the external load is fixed but not its position (fig. 2.26).
Figure 2.26: Crane arm experiment


We built by hand a crane base with motors for rotating the arm and pulling the hook. The evolved crane arm needed to attach to this base, so the experimental setup had 5 ``fixed bricks'' where the rest of the structure was allowed to attach. The fitness value is the horizontal length x of the arm, but if the maximum load M supported at the tip is less than 250 g then xis multiplied by M/250, thus reducing the fitness (table 2.11). The arm has to go up and away at the same time, because the space is restricted to the diagonal semiplane -x>y.

Table 2.11: Setup of the diagonal crane arm experiment.
Bricks {4,6,8,10,12,16}
Max Bricks 127
Base (0,-1)-(-16,-1)
x Range (-50,22)
y Range (-1,40)
xy Restriction y > -x
Fixed Bricks 6 at (6,0)
  4 at (12,0)
  4 at (12,1)
  4 at (12,2)
  4 at (12,3)
Fitness \( 1+(-x)\alpha \)
  x = position of the tip
  \( \alpha \) = fraction of 250g supported

We observed a curious phenomenon about the way a triangular solution appeared. Soon the crane evolved a counterbalance, located at the top, to act against the massive external load. This counterbalance took the shape of a bar going back from the tip of the crane -- where the load is located, with a pile of bricks at the other end to act against the weight. This counter-weight could not be too heavy, for the crane is required to support its own weight before adding the external load (fig.2.27).

Figure 2.27: Three stages on the evolution of the diagonal crane arm: counterbalance, closer to triangle, closed triangle.




With the tendency to reuse useful parts that had already been observed in the long bridge experiment, the counterbalance at the tip, with its ``J'' shape, reappeared at a lower position, creating an arm counterbalanced at two points. The fact that these two counterbalances ended up connecting to each other and touching down at the base was a fortuitous event that created a new stronger synthesis: a triangular shape which supports more weight than the original counterbalancing bar, by tensioning the vertical column. At the same time the triangle supports all this counterbalancing apparatus (by compression) when the crane is not lifting a load. This is a change of use, as discussed in section 2.6.2, only in a much larger scale.

next up previous
Next: Optimization Up: Artificial Evolution Re-Discovers Building Previous: Exaptations, or `change of
Pablo Funes