  Soft robots have gained significant attention due to their flexibility and
safety, particularly in human-centric applications. The co-design of structure
and controller in soft robotics has presented a longstanding challenge owing to
the complexity of the dynamics involved. Despite some pioneering work dealing
with the co-design of soft robot structures and actuation, design freedom has
been limited by stochastic design search approaches. This study proposes the
simultaneous optimization of structure and controller for soft robots in
locomotion tasks, integrating topology optimization-based structural design
with neural network-based feedback controller design. Here, the feedback
controller receives information about the surrounding terrain and outputs
actuation signals that induce the expansion and contraction of the material. We
formulate the simultaneous optimization problem under uncertainty in terrains
and construct an optimization algorithm that utilizes automatic differentiation
within topology optimization and neural networks. We present numerical
experiments to demonstrate the validity and effectiveness of our proposed
method.
