Gaits of controllers evolved by ENSO on inclined ground. These controllers typically have two types of modules that produce different leg behaviors useful for walking across the incline along the yellow line without slipping. 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.
S4 Symmetry
Gaits of controllers with handdesigned S4 symmetry evolved 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.
D2 Symmetry
Gaits of controllers with handdesigned D2 symmetry evolved 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.
Random Symmetry Evolution
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.