IEEE Robotics & Automation Magazine - December 2020 - 38

various actuation fields, multiphysics, nonlinearities, and
interactions with the environment.

constrained optimization problem. This geometry
approach suffers from the limitation that it is based on a
linear blending method; thus, it cannot well capture deformation with large strains.
To predict the dynamic behaviors of multiple bodies,
Macklin et al. [76] further developed a simulation framework
for hybrid rigid and soft bodies, in consideration of contacts
and frictions, using a nonsmooth Newton method to address
the underlying nonlinear complementarity problems. The
nonlinear dynamics models of different bodies were coupled
through a smooth isotropic friction model, and a complementarity preconditioner was applied to improve the convergence. To model the pressure loading, the authors adopted an
activation function that applies a uniform internal volumetric
stress to the domain of interest [Figure 6(c)]. However, more
physical experiments need to be conducted to validate the
computation framework.
Despite these attempts, there is no fast and effective
simulation tool for the computation of soft robots, and
this has been a major barrier to their design optimization.
Some portable solutions have been developed, but they do
not represent a universal solution. The ideal simulation
tool is expected to have high efficiency and acceptable
accuracy, robustness in a wide variety of problems,
numerical stability, and the capability of addressing

Optimization Method
The vast design space of soft robots is extremely difficult for
designers to manage. To explore the space and identify the
(locally) optimal design, one usually starts from an initial
guess and updates the existing design with a better one until
the algorithm converges to a feasible solution or the prescribed objective is fulfilled. The search direction is crucial,
and designers typically must conduct a sensitivity analysis. In
the strategy of line search or trust region, one may define the
direction of search based on the information of the objective
function and its gradients or Hessians, which require that the
problem is differentiable and twice differentiable, respectively. The gradient-based methods include the steepest descent
and conjugate gradient as employed in the works [9], [10],
[16], [17], [56], while Newton's method requires information
of the Hessian matrix.
Although gradient-based optimization algorithms tend to
get stuck in local optima, they have better scalability to the
number of variables, which is particularly advantageous for
handling large-scale problems. This is generally the case for
topology optimization of soft robots with an extremely large
number of design variables. There are numerous methods to

Body Element

Actuation
Element
Cable Actuation

(a)

Electrostatic
Actuation

Body
Element

Pneumatic
Actuation
Actuation
Φ
Element

Actuation
Element

(b)

(c)

Figure 6. The simulation of kinematics and dynamics of soft robots. (a) A physics-based simulation engine, SOFA, realizes real-time
simulation with a reduced model [74]. (b) A geometry approach to transforming the kinematics of soft robots into geometric change,
which incorporates cables, DEAs, and pneumatic actuations using varying line, area, and volume elements respectively [75]. (c) The
dynamics simulation of a soft gripper with robust contact coupling between the gripper and the object [76].

IEEE ROBOTICS & AUTOMATION MAGAZINE

DECEMBER 2020

IEEE Robotics & Automation Magazine - December 2020

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