IEEE Robotics & Automation Magazine - December 2013 - 136

Physiologically-Based Potential Energy
As a consequence of the result reported in [20], which
guarantees the existence of an equivalent extended Jacobian
method for a given function p ($), the identified relationship suggests the possible explanation of the human arm's
natural posture by means of a physiologically-based potential energy u ^qh, as discussed, e.g., in [5]. The proposed
approach is therefore consistent with the approach by
Khatib, et al. [5], while presenting a simpler method more
suited for real-time implementation.

Elbow Swivel Angle (rad)

3
2.8
2.6
2.4
2.2
2
1.8
1.6

8 10
Time (s)

Elbow Swivel Angle (rad)

(a)
3.2
3
2.8
2.6
2.4
2.2
2
1.8
1.6
1.4
0

8 10
Time (s)
(b)

Elbow Swivel Angle (rad)

3.2
3
2.8
2.6
2.4
2.2
2
1.8
1.6

8 10 12 14 16
Time (s)
(c)

Figure 7. The swivel angle during some of the experiments: actual
(blue) and predicted (red). (a) Experiment A(5), volunteer 7.
(b) Experiment B(2), volunteer 5. (c) Experiment VA(2), volunteer 8.

136

IEEE ROBOTICS & AUTOMATION MAGAZINE

DECEMBER 2013

Methods Based on Correlation Analysis
In this method [13], an analysis has been performed that
resulted in a similar correlation between the hand pose and
the swivel angle. This correlation, however, did not take into
account a full representation of orientation, which is necessary for an accurate prediction. In fact, as reported in
Figure 3, which corresponds to experiment A(5), where volunteers were asked to reorient their hands while keeping the
wrist center almost fixed, a consistent variability in elbow
angle can be reported. This confirms that variables describing
the orientation of the hand have to be included to obtain an
effective correlation. In [12], the authors proposed a similar
method, applying their approach to a pointing task in the vertical plane, which somewhat limits its practical applicability.
Humanlike Trajectories for a Dual-Arm
Robotic Industrial Manipulator
The final objective of this article is to allow the robot to perform a natural execution of a given task by a proper exploitation of the kinematic redundancy. In the previous section,
"Redundancy Resolution in the Human Arm," we identified a
natural way that humans adopt to resolve arm redundancy.
This section describes the final step needed to achieve a
humanlike redundancy resolution for robotic manipulators.
We will make reference to a dual-arm redundant manipulator
called Frida.
Frida is an anthropomorphic robot developed by ABB
that aims at closing the gap between manual assembly and a
fully automatic assembly process. This concept robot suits
environments involving handling and assembly of small parts
in a line where both humans and robots work. The robot consists of a torso with an integrated controller, two 7-DoF arms,
and grippers capable of handling a wide range of parts. Each
arm has a reach similar to that of a small adult.
Adaptation to Robot Proportions
and Extension to the Left Arm
The motion-capture experiments on the human arm
described in the section "Redundancy Resolution in the
Human Arm" were performed without taking care of the
robot kinematic parameters and proportions. The identification problem was tackled considering the right arm only.
Therefore, the following two questions arise: 1) How do we
cope with arms with different proportions? 2) How does the
correlation identified apply to the left arm?
The answer to the first question is quite straightforward:
the only source of difference is the Cartesian variables x, y,
and z that depend on the human arm length, which might
differ from the length of the robot. However, thanks to a suitable choice of all the regressors in the identified relationship
(3), the value assigned to a depends on the ratio between the
Cartesian variables only and not on their absolute values.
This way, there is no particular issue in applying the identified model to a robot whose dimensions substantially differ
from those of the human arm. The problem concerning how
to modify the identified relationship to also suit the left arm

Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - December 2013