Gaits of controllers evolved by ENSO on flat ground. Both controllers in this video start moving with a pronk gait, which soon transitions into a trot and bound, respectively. Evolving the symmetries of the controllers systematically makes it possible for ENSO to produce such animal-like gaits with well-synchornized legs. These gaits are similar to those produced by controllers with handdesigned S4 and D2 symmetries.
S4 Symmetry
Gaits of controllers with handdesigned S4 symmetry evolved on flat ground. The first controller in this video produces a pronk gait, while the second controller produces a bound. These gaits are similar to those produced by ENSO.
D2 Symmetry
Gaits of controllers with handdesigned D2 symmetry evolved on flat ground. The first controller in this video produces a bound gait, while the second controller produces a trot. These gaits are similar to those produced by ENSO.
Random Symmetry Evolution
Gaits of controllers produced by random symmetry evolution on flat ground. Champion controllers of many evolutionary runs have the same S4 symmetry with which they were initialized, and therefore generate the same gaits as those with handdesigned S4 symmetry. However, other champions are less symmetric than those produced by ENSO, generating stumbling gaits, as shown in this video. Plotting leg angles as a function of time confirms that (1) legs are not well synchronized and (2) phase difference between legs does not divide the gait period evenly, producing the stumbling effect.
Direct Encoding
Gaits of controllers evolved with direct encoding. The lack of symmetry in this method makes it difficult to coordinate all four legs, producing ineffective gaits that utilize only a subset of the legs. For example, the gaits in this video utilize only the rear legs; the front legs just vibrate and remain non-functional. In contrast, the controllers evolved by the symmetry-based methods utilize all four legs effectively.