IEEE Robotics & Automation Magazine - December 2020 - 34

[41] proposed a method to design deformable objects with
spatially varying microstructures using 3D printing. Optimization was conducted to design tiled microstructures
by interpolating families of related structures to smooth--
ly vary the material properties over a wide range [Figure 4(f )]. However, the microstructure configurations
were limited by the prescribed family. The microstructure
design may further benefit from unconstrained topology optimization with natural interconnections [51]
and consideration of large deformation [52] and buckling
phenomena [53].
Design Variable: Actuation
Actuation plays an equally important role in design
approaches for soft robots by directly determining the external stimuli. From the perspective of mechanics, actuators
define the form, magnitude, and direction of the
input loads applied to a
Soft robots provide
soft robot. Various actuation technologies in soft
excellent examples
robotics introduce new
opportunities and chalof design-dependent
lenges. Unlike rigid ro--
bots, where the input
problems, where the
force and torques are ap--
plied only at the joints,
actuation is typically
soft robots can be driven
by mechanical loads and
coupled with soft bodies.
more often by active ma--
terials that are responsive
to multiple physical fields,
which offers designers more freedom to modulate the actuation fields.
Cable tension and pneumatics represent the traditional
actuation technologies in soft robots. Skouras et al. [54]
developed a method to automate the design of cable-driven deformable characters that exhibit the desired deformation behaviors. The locations of cables on the character
and material distribution were simultaneously optimized,
which made the character deform to the target shape [Figure 5(a)]. Hiller and Lipson [33] proposed the concept of
volumetric actuation materials for a pneumatic locomotive soft robot. Evolutionary algorithms were used, the fitness function taken to be the moving distance of the
center of mass.
Dielectric elastomer actuators (DEAs), which form a
classic category of electric active polymers, can generate
large deformation when subjected to external high voltages [59]. Due to their advantages of large deformability and
rapid response, DEAs have been widely used in soft
robotic systems [60], [61]. However, current DEA design
paradigms are mostly based on people's intuition or experiences, and a systematic mathematical modeling and
optimization methodology is still lacking to exploit their
actuation potentials for the desired motion tasks.
34

IEEE ROBOTICS & AUTOMATION MAGAZINE

DECEMBER 2020

Hajiesmaili and Clarke [55] made a first attempt by
applying gradient electric fields to DEAs along the thickness direction through a layer-by-layer fabrication, and
voltage-tunable negative and positive Gaussian curvatures were produced [Figure 5(b)].
More generally, Chen et al. [56] recently developed
an automatic design methodology to maximize the
displacements of interest of DEAs by topology optimization of the spatially varying electric fields. The optimized design remarkably improved the output
displacements by up to 75% compared to their intuitive counterparts, with applications in triggering
planar sheets to shape-morph into the desired 3D configurations [Figure 5(c)]. A density-based topology
optimization method was applied to the automatic
design of DEAs by Wang et al. [62]. In addition, metastructures encoded with designable anisotropies can
be combined with DEAs to produce programmable
deformations, as demonstrated by a unidirectional actuator in [63].
Magnetic fields are also widely used to drive soft
robots by providing a far-field actuation controlled in
an untethered manner, and their advantages are longrange, dexterous, precise, fast, and robust characteristics. The magnetically responsive materials are expected
to largely deform, navigate in complex workspaces, and
perform specific tasks. To program their deformations,
a popular avenue is to embed magnetic particles into a
soft matrix to create spatially varying magnetic actuations and lead to the desired motions. Kim et al. [64]
offered a delicate fabrication solution by directly encoding the layout of ferromagnetic particles in the printing
process. Lum et al. [57] developed a design methodology to automatically generate the required magnetization
profile and actuating fields, so that a soft cantilever
deformed to the desired shapes [Figure 5(d)]. Recently,
Tian et al. [58] employed a topology optimization
approach to automate the layout design of the ferromagnetic domain. The objective function consists of
subobjective functions for kinematics and stiffness
requirements. The optimization method was verified on
a gripper [Figure 5(e)].
Integrated Design
Although we have classified the optimization model of
soft robots in terms of design variables, including geometry, material, metamaterial, and actuation, the boundaries among these variables are not clear. A metamaterial
deals with both geometry and material at a small scale. A
spatially varying actuation field is usually embodied
within the geometry or material. This is the case for
pneumatic actuation, where the pressurization is closely
associated with the chamber geometry, and magnetic
actuation, where the external magnetic field is distributed on the 3D distributed ferromagnetic domain.
Thus, an integrated strategy for design optimization is

IEEE Robotics & Automation Magazine - December 2020

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