IEEE Robotics & Automation Magazine - December 2018 - 93

6

80
SQC2S
AVSC

0

0

50

100
150
Time (s)
(a)

0

200

SQC2S
AVSC
0

50

100
150
Time (s)
(b)

SQC2S
AVSC

0
0

50

100
150
Time (s)
(d)

200

SQC2S
AVSC
0

50

100
150
Time (s)
(c)

200

0

50

100
150
Time (s)
(f)

200

1

0.5
0
-0.5
-1

1
0

200

t-SQC2S (Nm)

t-AVSC (Nm)

0.5

1.5
0.5

1

1
erey1 (m)

40
20

1.5

-0.5

2

60

-2
-4

2.5
erex1 (m)

2

eθ1 (°)

eγ (°)

4

0

50

100
150
Time (s)
(e)

200

0.5
0
-0.5
-1

Figure 7. The set-point control under SQC2S and AVSC: the (a) spacecraft attitude, (b) end-effector orientation of arm 1, (c) endeffector position along the x direction of arm 1, (d) end-effector position along the y direction of arm 1, (e) control outputs of
AVSC, and (f) control outputs of SQ2CS. Note: For (a)-(d), red lines represent AVSC performance and blue lines represent SQC2S
performance.

adapted based on error dynamics to avoid inducing excessive control outputs.
Therefore, the control torques generally vary within the
available value and avoid becoming saturated. As a result,
the regulation errors decrease monotonically to zero. For
the previously mentioned reasons, the SQC2S-controlled
system consumes much more energy (E = 258 Nms) than
the AVSC-controlled system (16 Nms). The simulated
course of the dual-arm space robot's postural change
under AVSC control is illustrated in Figure 8 for a setpoint regulation case. The first arm arrives at the first
touching point almost in a straight line, while several turning points appear for the second arm. This is understandable because the control torques in Figure 7(e) become
saturated several times.
Robustness Investigation
Sliding mode controllers are well known to be capable of
dealing with system uncertainties, and the AVSC controller can regulate its control gain to adapt to such uncertainties. In space missions where a space robot is used, the
dynamic parameters of the space robot system can change
due to fuel consumption, structural reconfiguration, or
manipulation of an unknown target. Therefore, in this section, we investigate system performance under AVSC and
SQC2S in a scenario where the system dynamic model is
not known precisely.
On the basis of the derivation of the space robot, matrices A and B in (1) depend on the physical parameters
(which have practical limits) and the motion parameters of
the spacecraft. As a result, the change of spacecraft

parameters will be reflected in the change of A and B in the
dynamic model of the simulation. Thus, to create a condition where system dynamics are not known a priori, matrices A and B in the dynamic model are set as different
values from those used in the controller. In the simulation
model, At and Bt are used in the controller block, while
A = (1 + d) At and B = (1 + d) Bt are used in the dynamic
model block, d ! " - 0.3, - 0.2, - 0.1, 0, 0.1, 0.2, 0.3 , . In

Figure 8. The course of the space robot in set-point regulation
for AVSC.

december 2018

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