IEEE Robotics & Automation Magazine - September 2022 - 49

remain level. Nevertheless, it is worth noting how other
parameters (e.g., the changing stiffness in the plots) influence
the shape of the function and position of the plateau.
The behavior of the linear quadratic (LQ) cost in row 2,
which is commonly used to design optimal LQ regulator control
feedback [34], is similar to the previous one but not quite
the same. For the most common actuator architectures, the
LQ cost tends to decrease with larger damping values,
although without reaching a plateau. Notably, in some architectures,
the cost function has a minimum, which depends on
the system stiffness. The presence of a definite minimum is a
characteristic we meet again when looking at the maximum
force transmitted by a robot in case of an unexpected impact,
60
50
40
30
20
10
a critical factor for the safety of collaborative robots [35]. Nevertheless,
if we look at the force transmitted to the actuator
gearbox, which characterizes the impact resilience of a robot
[36], the effect of the architecture topology can make it differ
from the seemingly identical previous one (see the " Topology "
section for an explanation).
Finally, not all cost functions improve with the introduction
of damping. The last row of the table is a glaring example
of this phenomenon, happening for the amount of energy dissipated
during cyclic and rebound tasks. This parameter,
which impacts the efficiency of walkers [37] and robots executing
cyclic tasks in general, is destined to worsen with the
addition of dissipative elements. An example of the complex
Semiactive
Passive
1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015 2017 2019
(a)
Weight
(b)
(c)
(d)
Figure 1. (a) The trend in the study of damping systems in the actuation of compliant robots. The bars are proportional to the number
of published papers about damping in soft actuation. Information from the database (see the " Database Identification " section) has
been cross-checked to count the papers according to their control (b) A compact Arm from [26] (license 5210131303438). (c) A
viscoelastic liquid-cooled actuated leg testbed from [27] (license 5210131175828). (d) Blue, a bipedal robot with variable stiffness
and damping from [6] (license 5210131223138).
SEPTEMBER 2022 * IEEE ROBOTICS & AUTOMATION MAGAZINE *
49

IEEE Robotics & Automation Magazine - September 2022

Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - September 2022

Contents
IEEE Robotics & Automation Magazine - September 2022 - Cover1
IEEE Robotics & Automation Magazine - September 2022 - Cover2
IEEE Robotics & Automation Magazine - September 2022 - Contents
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