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00:39
Flat: ENSO
Gaits of controllers produced 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.
00:39
Flat: S4 Symmetry
Gaits of controllers with handdesigned S4 symmetry 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.
00:39
Flat: D2 Symmetry
Gaits of controllers with handdesigned D2 symmetry 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.
00:39
Flat: Random
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.
00:39
Incline: ENSO
Gaits of controllers produced by ENSO on inclined ground. These controllers are less symmetric than those evolved on flat ground, and typically have two types of modules that produce different leg behaviors useful for walking effectively on inclined ground. In this video, two (or three) legs of the same module type remain nearly stationary to provide the support necessary for maintaining the robot's forward orientation, while the other legs make a full circle, propelling the robot forward without slipping.
00:39
Incline: S4 Symmetry
Gaits of controllers with handdesigned S4 symmetry on inclined ground. These gaits are similar to those on flat ground because the possible gaits are constrained by symmetry. The first controller in this video implements a gait similar to the walk (i.e. legs are quarter-period separated in phase), while the second controller implements a transverse gallop (i.e. left legs have opposite phase and right legs are one-tenth of a period ahead of their respective left legs in phase). However, these gaits are not as effective on inclined ground. In contrast, ENSO produces significantly faster gaits by evolving the symmetries appropriate for inclined ground.
00:39
Incline: D2 Symmetry
Gaits of controllers with handdesigned D2 symmetry on inclined ground. These gaits are similar to those on flat ground because the possible gaits are constrained by symmetry. The controllers in this video implement a trot gait and a bound gait respectively. However, these gaits are not as effective on inclined ground. In contrast, ENSO produces significantly faster gaits by evolving the symmetries appropriate for inclined ground.
00:39
Incline: Random
Gaits of controllers produced by random symmetry evolution on inclined ground. The unsystematic symmetry mutations of random symmetry evolution are detrimental on inclined ground as well, resulting in many of the champion controllers retaining their original S4 symmetry, and therefore producing the same gaits as those with handdesigned S4 symmetry. However, other champions (such as in this video) can have symmetries that generate faster gaits than those produced by S4 symmetry, but these gaits are often not as effective as those produced by ENSO.
