  Deformable robots are notoriously difficult to model or control due to its
high-dimensional configuration spaces. Direct trajectory optimization suffers
from the curse-of-dimensionality and incurs a high computational cost, while
learning-based controller optimization methods are sensitive to hyper-parameter
tuning. To overcome these limitations, we hypothesize that high fidelity soft
robots can be both simulated and controlled by restricting to low-dimensional
spaces. Under such assumption, we propose a two-stage algorithm to identify
such simulation- and control-spaces. Our method first identifies the so-called
simulation-space that captures the salient deformation modes, to which the
robot's governing equation is restricted. We then identify the control-space,
to which control signals are restricted. We propose a multi-fidelity Riemannian
Bayesian bilevel optimization to identify task-specific control spaces. We show
that the dimension of control-space can be less than $10$ for a high-DOF soft
robot to accomplish walking and swimming tasks, allowing low-dimensional MPC
controllers to be applied to soft robots with tractable computational
complexity.

Robotics