IEEE Robotics & Automation Magazine - December 2018 - 92

accuracy in both spacecraft attitude tracking and endeffector pose tracking. The tracking errors of spacecraft
attitude and hand orientation are kept within the magnitude of 10 -5 degrees, and the tracking error of the hand
position is kept within
10 -3 mm. Meanwhile,
Using AVSC, the end
smooth control torques
are provided. The value
effectors reach the desired of energy consumption
criteria E is 10 Nms.
pose much more quickly
Referring to Figure 5(f),
the smallest value of E
than with SQC2S.
under SQC2S is also
approximately 10 Nms.
However, to reach the
same tracking accuracy, energy consumption under
AVSC can be substantially reduced compared with that
under SQC2S.
Set-Point Control
As addressed in the "Adaptive Variable Structure Controller" section, AVSC is more advantageous when set-point
regulation is required for a robot. So it will be of interest to
investigate the system performance under SQC2S and
AVSC if no specific trajectory is defined. Instead, the system is fed with only the position of the desired touching
points, which are the same as that of the trajectory-tracking case. Because a large difference exists between the initial end-effector position and the final desired position, the
control torques may become saturated at the maximum
value, 1 Nm.

×

10-8
eγ

10
0
0

5

50

100
Time (s)
(a)
eθe1

× 10-5

150

0
-5

0

50

×

1

erex1
erey1

10-3

erex2
erey2

0.5
0
-0.5
-1

0

50

100
Time (s)
(b)

150

eθe2
Control
Torques (Nm)

Hand
Orientation (°)

Hand
Position (mm)

Attitude (°)

20

It turns out through simulation that the system will
become unstable with the SQC2S controller if the final target
position is fed to the system directly. To avoid instability, the
two straight lines that start from the initial position of the end
effectors and end by the target contact points have been evenly divided into ten segments. The input of the system is set as
the position of these ten points per 100 s. Such settings for the
input of the SQC2S system have been demonstrated to stabilize the system. A value of o = 0.1 is also set for the SQC2S to
avoid system instability caused by insufficient torques as well
as to save energy.
The system performance is shown in Figure 7. The red
lines in Figure 7(a)-(d) represent the system performance
under AVSC control, and the blue lines represent that under
SQC2S control. Only the pose of arm 1 is given because it has
been demonstrated that arm 2 shows the same trend as arm 1
in terms of comparing the two control methods.
Using AVSC, the end effectors reach the desired pose
much more quickly than with SQC2S. The spacecraft is successfully maintained at the desired orientation by the AVSC
control. Another detrimental effect from SQC2S is the
vibrations in the system states, which are caused by saturation of the control torques. The control torques [Figure 7(f)]
yield large values that originate from W max and become saturated. Thus, initially, the regulation errors present a
decreasing trend but start vibrating thereafter. The vibration
of the system states can result in undesirable physical contacts between the space robot and the target. In contrast,
AVSC can restrict the error dynamics in a parabolic trajectory, which is closer to the system's natural behavior, to eliminate the chattering effect. Meanwhile, the control gain is

100
Time (s)
(c)

150

0.06
0.04
0.02
0
-0.02
0

50

100
Time (s)
(d)

150

Figure 6. The system performance of AVSC: (a) the attitude-tracking error, (b) the tracking error of the hand position, (c) the tracking
error of the hand orientation, and (d) the control torques.

92

*

IEEE ROBOTICS & AUTOMATION MAGAZINE

*

december 2018
IEEE Robotics & Automation Magazine - December 2018

Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - December 2018
