What is it about?

Optimizing over all degrees of freedom of an infinite-dimensional continuum elastic body such as a soft robot is computationally intractable, even when approximated with a large number of discrete elements. Lower-dimensional geometric representations are needed to allow for efficient shape exploration without sacrificing expressiveness. In this work, we propose a differentiable pipeline that co-designs a soft swimmer’s geometry and controller in simulation. This pipeline uses an algorithm that efficiently converges in a few minutes on novel swimmer designs that meet multiple specified performance objectives (especially compared to gradient-free solutions). Example objectives include fast, stable, and efficient swimming. The user starts by designing geometries that describe an arrangement of contracting units and deformable structures. Our algorithm interpolates between these shapes to generate hybrid designs. Next, the control of the swimmer's actuators is based on a trainable neural network, which takes the state of the swimmer and outputs control signals. The simulation of this robot then uses a differentiable finite element method (FEM) to model the movement. The use of projective dynamics as a computational ‘trick’ speeds up this simulation ten-fold compared to other methods.

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Why is it important?

Combining our design space with differentiable simulation and control, we can efficiently optimize a soft underwater swimmer's performance with fewer simulations than baseline methods. We demonstrate the efficacy of our method on various design problems such as fast, stable, and energy-efficient swimming and demonstrate applicability to multi-objective design. We show that our algorithm converges significantly faster than gradient-free optimization algorithms and strategies that alternate between optimizing geometric design and control. Our work opens up new possibilities for the creation of soft robots and deformable systems.


Our work proposes how to efficiently co-design both the shape and control of a soft robot. However, our simulation still does not properly model the fluidic forces that act on the swimmer, inaccurately describes large deformations, and oversimplifies the soft robot's actuator behavior. There is method yet on automating the design of interior muscle-based actuators for our soft swimmers. Our algorithm currently requires that base shapes themselves have to be chosen by hand — it would be interesting to investigate methods for extending the morphological search beyond the Wasserstein basis space. In the future, we will address these issues to enable our pipeline to realistically model the behavior and optimize the designs of soft robotic swimmers.

Robert Katzschmann
ETH Zürich, D-CHAB

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This page is a summary of: DiffAqua, ACM Transactions on Graphics, August 2021, ACM (Association for Computing Machinery), DOI: 10.1145/3476576.3476704.
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