IEEE Robotics & Automation Magazine - December 2020 - 28

in free form is expected to imbue soft robots with programmable mechanical properties and desired responses to external stimuli, which unlocks new functionalities in the
paradigm of so-called morphological computation and
embodied intelligence [4], [5].
The transformative involvement of soft materials in
robots also poses unprecedented challenges. The increased
complexities of soft robotic systems, which may come from
geometry, material, actuation, and their intricate coupling,
are making conventional theories of robot design poorly
applicable. The difficulties come not only from the lack of
simulation and analysis tools to effectively and efficiently
predict complex mechanical behaviors of soft robots but
also from the lack of powerful optimization algorithms to
automate the design process. One must often rely on intuitions, experiences, or bioinspiration for soft robot design,
which can provide only limited scope. Research efforts have
increasingly been made toward a comprehensive design
paradigm to bridge the gap from theoretical and algorithmic perspectives.
In this article, instead of limiting the discussion to specific
applications, we articulate the fundamental concepts of design
optimization for soft robots. We exclude chemical- or material-level modifications but focus on mathematical design

approaches to soft robots based on widely available materials.
State-of-the-art progress is highlighted, with particular
emphasis on the methods to approach design problems and
their mathematical representation. The term optimization is
not necessarily limited to algorithms to solve a formulated
problem but more generally refers to innovations in any
design aspect leading to better performance of soft robots. We
conclude this review with a prospective look at future trends
for design optimization in soft robotics.
Design Architecture
The entire framework of design optimization for soft
robots is generally hierarchical and iterative, as presented
in Figure 1. A high-level task, such as locomotion and
grasping, can be decomposed into a sequence of motion
behaviors, including stretching, bending, twisting, or their
combination. For example, bending motions typically
dominate a grasping process, while alternating elongations
and compressions may dominate locomotion. Once the
desired mechanical behavior is determined, one may formulate it as an inverse design problem to be addressed by
mathematical programming.
The translation of the physical problem as a mathematical
optimization problem requires identifying and quantifying

Robot Task Space

Locomotion, Grasping, Swimming
Stretching, Bending, Twisting, Gaits

Motion Behavior Space
Design Optimization
Optimization Model
Design Objective
(Displacement and Force as
Functions of Time and Space)

Design Variable
(Geometry, Material, Actuation)

Mathematical Representation and Solution
Optimization Implementation

Design Variable
(Robot Composition)
Representation
Design Space

Design Analysis
(Robot Computation)

Discretization

Constraint
(Mass, Size, Stress, Manufacturing)
Optimization Method
(Robot Evolution)

Fabrication and Integration
(Casting, 3D Printing, and so on)

Figure 1. The architecture for design optimization of soft robots.

IEEE ROBOTICS & AUTOMATION MAGAZINE

DECEMBER 2020

Reasoning
Heuristics
Learning

Kinematics
Dynamics
Interactions

IEEE Robotics & Automation Magazine - December 2020

Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - December 2020