IEEE Robotics & Automation Magazine - December 2018 - 51

Fault Detection
As discussed in the section "Design and Implementation," one
of the advantages of drive trains incorporating magnetic
gears/couplings is their torque-limiting nature: an excessive
torque results in a pole-slipping condition, as opposed to the
mechanical damage characteristic of normal gearbox systems.
However, from a servo-control perspective, the effect of a
magnetic gear pole slipping is a loss of control of the load/
tool. Consequently, it is of interest to have a pole-slip detection method.
This can be accomplished by analyzing the absorbed
motor current I m . The algorithm used to identify the poleslipping condition is based on the grasp force reconstruction
algorithm presented in the section "Grasp Force Estimation."
This detection could trigger abort/survival modes or initiate a
software procedure to automatically reset the motor angular
position at rest ^q 0h and recover tool functionality.
Pole slipping can be induced even from the tool side of
the MC, e.g., if a traumatic event occurs at the terminal
device fingers. However, the finger's robust, compliant
nature helps in preventing such an event. The robust design
of both terminal devices, shown in Figure 6, allows various
kinds of finger deformations.
Experimental Results
The developed end effector was validated through both laboratory and field testing; the results are presented next.
Grasp Force Estimation
To aid the operator and/or automated control system of an
ROV/AUV, a disturbance observer [17] can be used for
grasp force estimation. Consider the following motor
dynamic equation:
J n qp = K tn I ref - x d = K tn I ref - x model - x int
= K tn I ref - x model - J (q)T w ext,

(2)

Figure 6. The terminal device deformations against sea stones
(top) and a table.

(mostly due to friction in the actuator gearbox). Considering that x g can be mostly neglected, especially for underwater
operations, and modeling x f with a Hayward-Dahl friction
model [19], x model is defined as
xf

x model

= Dqo + K 1 ^q - q 0h + K 2 ^q - q 0h q - q 0
+ K f ^q - q f h,

(3)

where q 0 is the motor angular position at rest (hand open), qo
is the motor velocity, D is the viscous damping, K 1 and K 2
are coefficients of a simplified elastic model ^ x te =
K e (q - q 0) - K 1 (q - q 0) + K 2 (q - q 0) q - q 0 h, K f i s
related to the friction coefficient, and q f is the adhesion point
of the Hayward model.
Assuming that the hand does not come in contact with the
object to be grasped [i.e., x int = 0 in (2)] during the calibration procedure, the hand-model torque can be computed
from the motor current and its motion response:
x model

= K tn I ref - J n qp .

(4)

Such a calculation requires motor current and acceleration
where qp , K tn, I ref , and J n denote the motor angular accelera- sensing. The latter would be sensitive to noise if computed
tion, torque constant, current, and inertia, respectively; J (q) from feedback position differentiation, so the equivalent
is the manipulator Jacobian that depends on motor position contribution determined by the proportional-integral difq; and w ext represents the wrench exerted by the end effector ferential that controls the actuator is computed in feedforon the environment (see, e.g., [18]). The disturbance torque ward instead.
x d combines all the internal and external disturbance
To identify the parameters of (3), the hand was driven with
torques and is assumed to be formed by two main compo- several velocity reference trajectories from fully open to fully
nents: the torque needed to close the hand x model when there closed and vice versa. Next, the resulting current, position,
is no interaction with the environment (i.e.,
without grasping any object) and the interaction torque x int .
Table 1. The numerical values of the parameters given
in the section "MC Control."
So the identification procedure aims at
x
,
obtaining an estimate of int relating it to the
Parameter
Value
Parameter
Value
current absorbed by the motor. To do so, a caliD
0.7719 mNms
Jn
2.44 Nms2
bration procedure is performed to identify the
K1
0.2619 mNm
K C,lin
14 Nm
term x model, which can be decomposed into
K2
JL
0.0002 mNm
3.25 × 10- 4 Nms2
three components: the elastic torque generated
by the hand tendons during closure x te, the
Kf
1,614 mNm
K tn
9.18 × 10- 3 Nm/A
x
,
gravitational effect g and the frictional torque
december 2018

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IEEE ROBOTICS & AUTOMATION MAGAZINE

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IEEE Robotics & Automation Magazine - December 2018

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