  Designing optimal soft modular robots is difficult, due to non-trivial
interactions between morphology and controller. Evolutionary algorithms (EAs),
combined with physical simulators, represent a valid tool to overcome this
issue. In this work, we investigate algorithmic solutions to improve the
Quality Diversity of co-evolved designs of Tensegrity Soft Modular Robots
(TSMRs) for two robotic tasks, namely goal reaching and squeezing trough a
narrow passage. To this aim, we use three different EAs, i.e., MAP-Elites and
two custom algorithms: one based on Viability Evolution (ViE) and NEAT
(ViE-NEAT), the other named Double Map MAP-Elites (DM-ME) and devised to seek
diversity while co-evolving robot morphologies and neural network (NN)-based
controllers. In detail, DM-ME extends MAP-Elites in that it uses two distinct
feature maps, referring to morphologies and controllers respectively, and
integrates a mechanism to automatically define the NN-related feature
descriptor. Considering the fitness, in the goal-reaching task ViE-NEAT
outperforms MAP-Elites and results equivalent to DM-ME. Instead, when
considering diversity in terms of "illumination" of the feature space, DM-ME
outperforms the other two algorithms on both tasks, providing a richer pool of
possible robotic designs, whereas ViE-NEAT shows comparable performance to
MAP-Elites on goal reaching, although it does not exploit any map.
