IEEE Robotics & Automation Magazine - March 2016 - 69

Table 1. A comparison between the CT,
AE, and CE of the EP-based (Th = 4 mm)
and standard controllers.

X Axis-EP Controller
Reference, G(TjO t)
Filter Output, B(tO t)
Ball Position, B(t)
Hand Position, H(t)

0.4
0.2
0

-0.2

Algorithm

0.97e-4 sec

9.30e-3 m

3.37e2 (m/s)2

Standard

3.08e-4 sec

6.70e-3 m

3.99e2 (m/s)2

0.4
Position (m)

350
300
250
200

15
20
Time (s)
(a)

X Axis-Standard Controller
Reference, G(TjO t)
Filter Output, B(tO t)
Ball Position, B(t)
Hand Position, H(t)

Control Energy-Motor Commands

400
Energy ((m/s)2)

Conclusions
In this article, a bioinspired predictive controller based on
internal models has been implemented and compared with a
standard predictive controller. The EP concept was used to
create a predictive control system able to anticipate the
dynamics of an external object. The experiments conducted
on the iCub robot show
that the system is able to
The EP-based controller
predict the future target
trajectory and anticipate
uses the sensory prediction
the target dynamics moving the robot hand to the
to skip some of the
predicted goal position.
The EP-based controller is
computations done on
less time-consuming and
more energy efficient
sensory processing and
than a standard controller.
Although the position
kinematics solving.
error of the standard controller is lower, the position error of the EP-based
controller can be kept within limits by defining the EP threshold. In our case, we have set a tracking error of 1 cm according to the task and mechanical precision limits of the robot.
The internal simulation of the target motion makes it possible

Position (m)

In Figure 6, the results on the AE are shown. It is possible to
notice that the EP-based controller error grows monotonically
for small values of the threshold. Due to the initial observation
period D obs of three oscillations, the system's average prediction
errors start with values close to 1 cm (1.06 cm to be precise).
The control energy is shown in Figure 7. The ﬁgure
shows decreasing control energy with increasing thresholds. This behavior is due to the fact that as fewer updates
of the target trajectory are executed, the less movement the
iCub arm performs. The control energy stabilizes for
threshold values bigger than or equal to 1 cm. This happens
because all the cases with thresholds bigger than 1 cm execute only a few trajectory predictions per oscillation, keeping the arm behavior similar.
Therefore, the EP-based controller resounds to the need of
consuming less energy and sparing CT. Based on our results, a
general rule is to set the EP threshold as high as possible while
keeping the system error lower than a predeﬁned limit. This
can be done empirically, by determining the threshold value by
experiments, or automatically, by changing the threshold
dynamically. In our case we can decide a maximal error and
initialize the threshold accordingly. In this case, we are not
interested in the maximal system error but, for example, in the
maximal update frequency, we can decide to dynamically
change the threshold based on the update frequency.
Let us assume that for a successful grasp a reasonable limit
for the hand position error is 1 cm. Among the EP-based systems with errors lower than 1 cm, the one with the threshold
value of 4 mm is the one with lower CE and CT. The results
on the x-axis for the two controllers are shown in Figure 8
and summarized in Table 1.

0.2
0

-0.2

02
0.
00
4
0.
00
6
0.
00
8
0.
01
0.
01
2
0.
01
4
0.
01
6
0.
01
8
0.
02

0.
0

150

15
20
Time (s)
(b)

Threshold (m)
Figure 7. The CE changes as the threshold is varied. The plot
represents the EP-based controller results. The standard
controller corresponds to the point with Th = 0 m. The mean and
standard deviations on 20 sequences are shown.

Figure 8. The behavior of the two algorithms during an oscillation
sequence. The EP controller has a Th = 4 mm. Results on the axis
are shown in steps of 2 mm.

march 2016

IEEE ROBOTICS & AUTOMATION MAGAZINE

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