Hybrid Force and Position Control Strategy of Robonaut Performing Object Transfer Task

Abstract

This paper proposes a coordinated hybrid force/position control strategy of robonaut performing object transfer operation. Firstly, the constraint relationships between robonaut and object are presented. Base on them, the unified dynamic model of the robonaut and object is established to design the hybrid force/position control method. The movement, the internal force and the external constraint force of the object are considered as the control targets of the control system. Finally, a MATLAB simulation of the robonaut performing object transfer task verifies the correctness and effectiveness of the proposed method. The results show that all the targets can be control accurately by using the method proposed in this paper. The presented control method can control both internal and external forces while maintaining control accuracy, which is a common control strategy.

Full text

Hybrid Force and Position Control Strategy of Robonaut Performing Object
Transfer Task
Gang Chen, Yu-Qi Wang , Qing-Xuan Jia and Pei-Lin Cai
School of Automation, Beijing University of Posts and Telecommunications, Beijing 100876, China
Abstract. This paper proposes a coordinated hybrid force/position control strategy of robonaut perform ing object transfer
operation. Firstly, the constraint relationships between robonaut and object are presented. Base on them, the unified dynamic
model of the robonaut and object is established to design the hybrid force/position control method. The movement, the
internal force and the external constraint force of the object are considered as the control targets of the control system.
Finally, a MATLAB simulation of the robonaut performing object transfer task verifies the correctness and effectiveness of
the proposed method. The results show that all the targets can be control accurately by using the method proposed in this
paper. The presented control method can control both internal and external forces while maintaining control accuracy, which
is a common control strategy.
1 Introduction
The complexity and difficulty of space missions increase
alongside the deepening of human exploration about
space. Therefore, a new type of space robot called
robonaut is designed to deal with this situation, and it can
be used to assist or replace the human astronauts to carry
out the on-orbit operation tasks in order to reduce the
astronauts’ working pressure and the cost of space
operations. The robonaut consist of three branches, in
which one is generally called the coupled torso while the
other two are robot arms. Due to the existence of
redundant arms, its flexibility, operation ability, operating
range and other aspects of performance are far better than
single arm robot, and its coordination ability and control
accuracy are significantly improved compared with the
multi robot because of the existence of coupled torso. The
robonaut, with its strong collaboration and wide operating
range, can efficiently and reliably assist astronauts in
performing many on-orbit operations, including mating,
twisting, handling, complex parts assembling and space
station maintenance etc. As a typical dual arm
coordination task, object transfer is representative in orbit
operation, so it is of great significance to study the
coordinated operation method in the process of object
transfer.
The position control strategy is difficult to meet the
requirements of the interaction between the robot and the
environment when the robonaut performs coordinated
manipulation tasks. To finely perform the given task,
compliance control method is necessary which means it is
vital to control the necessary operation force in the
coordinated manipulation tasks, as well as limit the
undesirable force to the system meanwhile. There are
several main manners of dual-arm coordinate operate
control technique, such as impedance control[1-2], hybrid
force/position control [3-4], intelligent control[5-6]. The
hybrid force/position control method is relatively simple
and does not rely on environmental information. Besides,
the accuracy of this method is relatively higher than other
methods. Given this, the hybrid force/position control
method is adopted in this paper.
A number of relevant researches have been carried
out which concerning the hybrid force/position control
during the processes of object transfer. C. V. Albrichsfeld
[7] analyzed the relationship in two robots holding a
single object by introducing a concept of ‘virtual stick’,
and then they presented a symmetric non-master/slave
hybrid position/force coordinated control scheme using
the equations which derive from virtual stick. A. I.
Tuneski [8] extended an active compliance control
scheme which is capable of adjusting its parameters to
the unknown system compliance. Furthermore, a general
model was derived by discussing different contact cases
of the object. However, all the methods mentioned above
existing the following deficiencies: firstly, these articles
could not achieve the external force compliance control
only considering the internal force when the object is
subjected to external force, which may cause the failure
of compliance control. Secondly, some of the methods
directly divide the object into two parts and then fixed on
the end of each manipulator. In this way, a rather better
simulation results can be obtained, but these methods are
limited to theoretical analysis and are not suitable for
practical operation.
For the deficiencies above, more specific study will
be carried out in subsequent chapters. Specifically, in
chapter II, the constraint relationships between robonaut
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and object will be presented. Then, in chapter III, the
unified dynamic model of the robonaut and object is
going to be established to design the hybrid force/position
control method. Moreover, a simulation study will be
implemented to verify the algorithm control in chapter IV.
Finally, the comprehensive review and summary will be
done in the final chapter.
2 Dynamic modeling
The structure of robonaut studied in this paper is shown
in Figure 1. It consists of three branches: the coupled
torso branch (branch 1) and two arm branches (branch 2
and branch 3). Generally, one end of the coupled torso
branch is fixed at the base, the other end is connected
with the root of the two arm branches. The ends of the
arms are free to move to complete the operational tasks.
Assume that branch 1 has
1
DOFn
, branch 2 and
branch 3 have
2
DOFn
and
3
DOFn
respectively.
1
q
0
x
0
z
0

2
q
1
n
q
1
( 1)ln
q

branch2
12
( 1)ln n
q

12
()ln n
q

0
y
el
z
el
y
el
x
el

1
( 1)
rn
q

13
( 1)rn n
q
13
()
rn n
q

er

er
z
er
x
er
y
et

et
y
et
x
branch1
branch3
base
Figure 1. The structure of robonaut
2.1 Constraint relationships
Figure 2 shows the coordinated model of object transfer
operation. Point
c
O
is the mass of the object and the
object frame is attached at it. For simplicity, let us ignore
the size of object, and translate the origins of the left and
right arms end frames to the point
c
O
, named as
 
,
ew
O w lr
.
When we assume that the stiffness of the object is
large enough to ignore the deformation, the pose
constraint between robonaut and object can be written as
00 0
clr
lr
c lc r c
 


 


PPP
RRRRR
(1)
The velocity constraint can be written as
clr
 

XXX
(2)
The acceleration constraint can be written as
clr
 
  
XXX
(3)
The force constraint relationship is shown in Figure 3.
The output forces of left and right arms, the external
constraint force of robonaut system are
 
T
TT
,,
w ww
w lr f

 

F fn
， and translate them to
the point
c
O
, named as
 
T
TT
,,
cw cw cw
w lr f

 

F fn
.
The resultant force of the object can be expressed as
c e cf
 F WF F
(4)
where
 
66
W EE
,
T TT
[, ]
e cl cr
F FF
.
c
p
X0
Y0
Z0
O0
er
O
l
p
r
p
el
O
c
O
left right
Figure 2. The coordinated model of object transfer operation.
X
0
Y
0
Z
0
O
0
l
f
l
n
r
f
r
n
f
f
f
n
c
n
c
f
left right
constraint
c
p
cl
p
cr
p
cf
p
el
O
er
O
c
O
ef
O
Figure 3. The force model of object transfer operation.
2.2 Dynamic models
In this paper, we intend to use the movement, the internal
force and the external constraint force of the object as the
control targets of the control system. Firstly, the dynamic
models of the object and the robonaut are established.
Base on them, the unified dynamic model is constructed,
which means the object and the robonaut as a whole.
2.2.1 Object dynamic model
The dynamic equation of object is given by using the
Newton-Euler equation
 
cc c
cc c cc c
m


 




vf
I In
  
(5)
where
c
m
,
c
I
represent the object’s mass and inertia
tensor, respectively.
Equation (5) can be rewritten as
c cc c
 

F MX C
(6)
where
3 33
33
c
c
c
m





0
0
E
MI
,
 
31
c
c cc





0
CI
 
.
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2.2.2 Robonaut dynamic model
The velocity of the ends of the arms can be written as
 
T
TT
,,
w ww
w lr

 


Xv

, where
w
v
and
w

are the
linear and angular velocity respectively. By differential
kinematics, it can be obtained that
 
 
T TT
12
T TT
13
[, ] ,
[, ] ,
l l l ll l l l
r r r rr r r r
 

 




X v =Jq J J q
X v =Jq J J q


(7)
where
 
,
w
w lrJ
represent the Jacobian matrixes of
the left and right manipulators respectively.
According to equation (7), the kinematics equation
can be thus written as
3
2
1 26
16 3
ll n
l
e
r nr
r




  





0
0



JJ
X
X q Jq
JJ
X
(8)
where
 
123
12 nnn 
RJ
represents the Jacobian matrix of
the robonaut.
From equation (8), we can get
 
e
e

 

 


   
 
 
X Jq Jq
q J X Jq
(9)
where

J
represents pseudo-inverse of
J
.
By using Lagrange-Euler method, the dynamics of the
robonaut in joint space coordinates suggested in this
paper can be described as follows
       
2T
2mn e
  
   
Aqq Bqqq Cqq Dq J F

(10)
where
 
Aq
is an
nn
symmetric positive definite
inertia matrix.
 

Aqq
represents the inertia forces vector.
 
Bq
is an
 
1 /2n nn


Coriolis matrix.
 
2
mn

Bqqq
represents the Coriolis forces vector.
 
Cq
is an
nn
centrifugal matrix.
 
2

Cqq
represents the
centrifugal forces vector.
 
Dq
is an
1n
gravitational
matrix. In addition,
123
nn n n
.
Substituting (9) to(10), the dynamics of the robonaut
in Cartesian space coordinates can be described as
ee
 

MX C F U
(11)
Where
 
     
T
T2
T
2mn






  





  
M J AqJ
C J Bqqq Cqq Dq MJq
UJ

2.2.3 Robonaut system unified dynamic model
From(4), the output force of robonaut can be obtained as
 
 
 
12
l
e c cf
r
c c c cf i i



  

  

F W F F E WW
W M X C W F WF


(12)
① The first term on the right side of the equation,
represents the driving force of robonaut on the object,
where
T
[ ]2
66
,

W EE
.
② The second term on the right side of the equation,
represents the external constraint force of robonaut
system.
③ The third term on the right side of the equation,
 
12

E WW
represents the null space of
W
,
 
,
w
w lr

represents any
61
vector. Due to the
characteristics of null space, we can get that
 
T
TT
12 6 1
,
lr





0W E WW
 
. So, this part of force
produces the internal force of the object. Also,
T
66i,

 

WE E
,
 
2
i lr
 F
 
.
Substituting (3), (12) to (11), the unified dynamic
model is constructed as
s c s cf i i

  

U M X C W F WF
(13)
where：
sc
sc


 

 


M M WM
C C WC
(14)
3 Control algorithm
In this paper, the internal force, the movement and the
external constraint force of the object are considered as
the control targets of the hybrid force/position control
system. To simplify the problem, the internal force at the
mass center of the object can be chosen in object transfer
operation task.
The position control law of object can be designed as
 
 
c cd d cd c p cd c

   

   
XSXKXXKXX
(15)
where
cd
X
,
cd

X
and
cd

X
represent the desired pose,
velocity and acceleration respectively.
p
K
,
d
K
are
derivative and proportional feedback gains respectively.
S
is an
66
position-selecting matrix.
The external constraint force control law of the
robonaut system can be designed as
 
 
cf cfd pf cfd cf df cfd cf

   


FSFKFF KFF
(16)
where
cfd
F
represent the desired external constraint force.
pf
K
,
df
K
are derivative and proportional feedback gains
respectively.
S
is an
66
force-selecting matrix.
3
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cd
X

cd
X
cd
X




c
X

cfd
F

differential

-
df
K
id
F

differential

-
cf
F
i
F

Robot
systems
m
q
m
q

i
F
cf
F
forward
kinematics
,
lr
XX
,
lr
XX

Speed
constraints
c
X

Position&
orientation
constraint
c
X
-
-
pf
K
df
K
i
W
p
K
d
K
J
S
S
s
M
W


T
J
 
,
s
C qq

pf
K
Figure 4. Hybrid force/position control structure of robonaut.
7l
Z
7l
X
6l
Z
6l
X
5l
X
4l
X
3l
X
2l
X
1l
X
5l
Z
4l
Z
3l
Z
2l
Z
1l
Z
1r
Z
2r
Z
3r
Z
4r
Z
5r
Z
6r
Z
7r
Z
1r
X
2r
X
3r
X
4r
X
5r
X
6r
X
7r
X
er
O
el
O
2
X
1
X
0
X
1
Z
2
Z
0
Z
0
Y
0
O
0

el

er

Figure 5. D-H frames of robonaut in simulation.
The internal force control law of the object can be
designed as
 
 
ic id pi id i di id i
  

FFKFF KFF
(17)
where
id
F
represent the desired internal force.
Substituting(15), (16) (17) to (13) it can be obtained
that the control joint torque
 
 
 
 
 
 
 
 
 
T
s cd d cd c p cd c
s cfd pf cfd cf df cfd cf
i id pi id i di id i


   

    

    
  


JMSXKXXKXX
CWSFKFF KFF
WFKFFKFF

(18)
The proposed control structure is shown in Figure 4.
4 Simulation Study
The robonaut involved in this simulation is shown in
Figure 5. The coupled torso has 2 rotation joints and the
two arms both have 7 rotation joints. The D-H parameters
of the robonaut are listed in Table 1.
Table 1. D-H parameters of the robonaut in simulation.
1/ rad
i


1/m
i
a
/ rad
i

/m
i
d
t1 0 0 0 0.45
t2 -π/2 0 -π/2 0
al1 π 0.3 -π 0.2
al2 π/2 0 π/2 0.15
al3 π/2 0 0 0.15
al4 0 0.5 0 0.15
al5 0 0.5 0 0.15
1
/ rad
i


1/m
i
a
/ rad
i

/m
i
d
al6 -π/2 0 -π/2 0.15
al7 -π/2 0 -π 0.2
ar1 0 0.3 π 0.2
ar2 -π/2 0 -π/2 0.15
ar3 -π/2 0 0 0.15
ar4 0 0.5 0 0.15
ar5 0 0.5 0 0.15
ar6 π/2 0 π/2 0.15
ar7 π/2 0 π 0.2
The task involved in this simulation is that the
robonaut holds an object to terminal point along a desired
arc trajectory on the constraint surface. Assuming that the
radius of the arc is 0.1m, and the object must remain in
contact with the constraint surface during the movement.
Set the total control time to be 10s.
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Assuming that the constraint surface is parallel to the
inertial frame yOz plane. The origin of the constraint
frame is set at the center of the arc trajectory. Then the
homogeneous transformation matrixes representing the
poses of constraint frame with respect to inertial frame is
0c
R
=[0, 0, -1; 1, 0, 0; 0, -1, 0].
The initial position of object is
c_int
P
=[-0.5m, 0.1m,
1.5m], the corresponding joint angle is
0t
q
=[-1.34°, -
15.88°],
0l
q
=[47.09°, -131.02°, 186.84°, -94.48°,
157.38°, 161.55°, 38.06°],
0r
q
=[-53.89°, 142.63°,
-194.46°, 90.40°, -152.17°, -164.75°, -50.64°].
The desired internal force is set as
61
0
, the desired
external constraint force is set as
61
0
.
Apply the algorithm mentioned above to this case,
then the trajectory , the internal force and the external
constraint force of the object result to be Figure 6, Figure
7 and Figure 8 respectively, which verifies the
effectiveness of the algorithm discussed in this paper.
Figure 6. The trajectory of the object.
Figure 7. The internal force of the object.
Figure 8. The external force of the object.
5 Conclusion
This paper proposes the coordinated hybrid force/position
control strategy of robonaut performing object transfer
operation. The constraint relationship between two
manipulators and object is presented at first. Afterward
the unified dynamic model of the robonaut and object is
established to design the hybrid force/position control
method of the robonaut. The movement, the internal force
and the external constraint force of the object are
considered as the control targets of the control system,
thereby achieving simultaneous control of the internal
force and the external force of the object. Finally a
simulation study verifies the effectiveness of the
algorithm.
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