ELSE uses a slightly modified version of the NEAT (NeuroEvolution of Augmented Topologies) algorithm developed by Kenneth Stanley at University of Texas at Austin.
I've experimented with several different algorithms for evolving neural networks, including fixed topology, the GNARL algorithm from Peter Angeline, and an evolved version of echo state networks from Herbert Jaeger from the Fraunhofer Institute. At this point, none of the other approaches have matched NEAT's speed and robustness (how likely a given run is to result in walking behavior).
I'm currently working on evolving steering behavior. That is, providing an input (or two) that suggest a direction to walk. Results are mixed, but I'm hopeful with some subtle changes to the fitness measure they will improve.
I'm also very interested in the notion of "neutral mutations" and the subset of space of that neutral mutations can explore. I've not done much with this, but an early result can be (possibly) viewed in these terms. At first, each organism was given several trials to measure its fitness-- the idea being that random fluxations in starting conditions and the physics simulation could compound to yield different fitnesses and this might skew the results. However, removing the multiple evaluations per fitness actually increased the speed of the algorithm, even ignoring the cost of the multiple runs. It is possible that the added randomness serves to broaden a kind of neutral network and improve the speed of exploration of the genome space.
Currently, all the implementations use Sigmoidal neurons. Many suggest that more advanced neural models, like leaky integrators, will ease the finding of cyclical behavior and improve results. I'm mostly finished with integrating leaky neurons into the NEAT code, but have a bit more work to do.
Occasionally, the controllers sometimes evolved behaviors that achieved a good fitness quickly, but had limited ability to improve. One example is seen in this animation (DivX, 93KB) of a "standing long-jump". Note that the evolved behavior here manages a jump of about 3.3m, which is just about the gold-medal range for Olympic standing-long jumpers-- a good indication that the actuator strength was mismatched in this run.
Reil, Biologically Inspired Control of Bipeds