Symmetry is useful as a constraint in designing complex systems such
as distributed controllers for multilegged robots. However, it is
often difficult to determine which symmetries are appropriate. It
is therefore desirable to design such systems automatically, e.g.
by utilizing evolutionary algorithms that produce symmetry through
developmental mechanisms. The success of these algorithms depends
on how well they explore the space of valid symmetries. This paper
presents an approach called Evolution of Network Symmetry and
mOdularity (ENSO) that utilizes group theory to search the space of
symmetries effectively. This approach was evaluated by evolving
neural network controllers for a quadruped robot in physically
realistic simulations. On flat ground, the resulting controllers
are as fast as those having hand-designed symmetry, and
significantly faster than those without symmetry. On inclined
ground, where the appropriate symmetries are difficult to determine
manually, ENSO produced significantly faster gaits that also
generalize better than those of other approaches. On robots with a
more complicated structure including knee joints, ENSO resulted in
more regular gaits than the other approaches. These results suggest
that ENSO is a promising approach for evolving complex systems with
modularity and symmetry.
Videos of the evolved robot walking behaviors