IEEE Robotics & Automation Magazine - December 2018 - 50

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

(m)

(n)

(o)

Figure 5. The tool change procedure phases: (a) tool A (the SoftHand), (b) the disengagement, (c) the switch, (d) the engagement,
and (e) tool B (the gripper). The respective tool change mechanism configuration in the (f)-(g) longitudinal and (k)-(o) frontal
planes. Note the mechanism spring position (in yellow) during the procedure. The springs, tool coupling device, and motor coupling
device are depicted with the same colors as in Figure 3(b). The tool change system's flanges are depicted with different colors
(light blue and green) to point out their different positions.

MC Control
MCs can be modeled by a two-bodies system (see, e.g., [16])
where, because of a magnetic spring element, a connection
exists. Such an elastic element may cause oscillations during
position control that could, in turn, degrade control performance. This high-compliance characteristic is known to represent a possible drawback when applied to robot motion
control, and it can limit the use of MC to systems with relatively low-bandwidth dynamic transients. Here, we verify that
the latter is our case, i.e., the oscillations provided by the MC
are negligible.
Consider the representation of our device shown in Figure 4(a), where the recalled two-bodies model has been
adopted for the MC. It is important to point out that this is
a roughly simplified model: damping or feedback control,
obviously present in the real system, are not taken into
account. In this manner, we are considering the worst operative conditions. The coupling behaves as a nonlinear soft
torsional spring that, if linearized about the origin as in
[16], has a stiffness coefficient K C, lin = pTmax, where p = 10
is the number of coupling magnetic poles and Tmax is its
maximum torque. The soft device equivalent stiffness coefficient is nonlinear and depends on the actual motor angle
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december 2018

q. Its linearized expression gives K L, lin (q) = K 1 + K 2 q,
where K 1 and K 2 are numerical parameters, previously
identified [see (2)]. This varying stiffness coefficient is
taken into account in the simplified subsystem, shown in
Figure 4(a), which is a harmonic oscillator with an impulse
response/transfer function:
H (s) =

H ( s)
1
= 1 2
.
J L s + 6K C, lin + K L, lin (q)@ J L
F (s)

(1)

Table 1 shows the numerical values of the quantities
defined here. We can evaluate (1) for each q 0 # q # q *,
where q 0 = 0 and q * are the motor angles that correspond
to an open hand and the hand max closure, respectively.
The resonance frequency ~ R (q) = 6K C, lin + K L, lin (q)@ J L
of the function from (1) is computed for increasing values
of q, and its trend is shown in Figure 4(b). We can see from
the figure that, even in the worst conditions where the
damping of the real system is neglected, the lower ~ R (q)
results in - 650 rad/s, so employing the motor under this
frequency will provide no sensible oscillations in position
control. In addition, ~ R (q) is almost constant, so it can be
filtered easily.
IEEE Robotics & Automation Magazine - December 2018

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