ON-ORBIT ASSEMBLY OF LARGE STRUCTURES USING SPACE ROBOTS

Fatina Liliana Basmadji (1)

, Tomasz Rybus (2,1)

, Jerzy Sasiadek (3)

, Karol Seweryn (1)

(1)Space Research Centre of the Polish Academy of Sciences (CBK PAN), 18a Bartycka str., 00-716 Warsaw, Poland,

Email : fbasmadji@cbk.waw.pl, kseweryn@cbk.waw.pl (2)

Wroclaw University of Science and Technology, Wroclaw, Poland, Email: tomasz.rybus@pwr.edu.pl (3)

Carleton University, Ottawa, Canada, Email: Jurek.Sasiadek@carleton.ca

ABSTRACT

Large space structures are becoming popular as they can

be very useful in several application fields such

as telecommunication as well as deep space and Earth

observation missions. In this paper, the problem of

assembling two space modules using robots is

discussed. Two cases are considered: using two robots

with one manipulator each and using one robot with two

manipulators. A specialized simulation tool developed

at the Space Research Centre (CBK PAN) has been

extended to handle the problem of on-orbit assembly of

large structures using two multi arm / multi robot

solutions. Finally, simulations of large structure

assembly using space robots were conducted and the

results are presented in this paper.

1. INTRODUCTION

Concepts of large orbital structures are becoming

increasingly popular in recent years. Examples of such

structures include large space telescopes (e.g., [‎1]) and

space-based solar power satellites that would collect

solar power on-orbit and send it to Earth (e.g., [‎2]).

Today, large structures are built on Earth and they are

sent to an orbit in one piece. Size of the launcher limits

the possible size of the structure. One possible solution

is to fold the structure to the size with which it could be

stowed within the launcher fairing. In such case, after

reaching the orbit, this structure is unfolded to its full

size (the James Webb Space Telescope is an example of

such structure [‎3]). However, the mass is still a limit and

should be taken into consideration. Moreover, designing

a structure that can be folded is challenging and it is

difficult to ensure that the structure will be accurate and

will meet the predefined requirements when unfolded.

In addition, the unfolding process should be tested in the

same environment as the one where this process will

take place, i.e. the microgravity environment, which is

difficult to recreate on Earth [‎4].To overcome these

problems, smaller structures can be send to space

separately and then they can be assembled on-orbit. The

Mir Space Station and The International Space Station

are examples of very large structures constructed in this

way. However, astronauts were engaged in the assembly

process.

Several studies related to the problem of increasing the

automation degree in space are currently being

conducted. Some of these studies concern the problem

of building large structures using space robots instead of

astronauts [‎5]. In order to assemble modular structures

in space, robots would have to perform several tasks

such as grasping modules, connecting them, welding,

fastening or twisting. Application of space robots

reduces missions costs, in addition, they can be sent to

deep space or used in missions that are dangerous and

risky for humans [‎6]. Another advantage of space robots

is that they can work in hostile environment for a long

period of time and they are useful especially when it

comes to performing repetitive tasks. Therefore,

concepts of assembling large space telescopes on-orbit

using robots are considered in various studies (e.g., [‎7],

[‎8]).

However, there are several problems that need to be

solved. First of all, it is important to determine the type

of space robot that will perform the defined task. This

mainly concerns the number of manipulators that this

robot should have. Another question is whether one

space robot will be sufficient to perform the defined

task or a team of robots is required. If we assume that

during the assembly process the robots are not attached

to the structure, than control of such robots

is challenging, because motions of the manipulator’s‎

platform will influence position and orientation of the

robot [‎9]. Control problem of such space robot was

extensively investigated and there are several studies

devoted to the control and trajectory planning of robot

equipped with multiple manipulators [‎10]. The general

formulation of dynamic equations for multiple-arm

space robot can be found in [‎11], while application of

adaptive control for dual-arm robot can be found in

[‎12]. Significant changes of a robot position and

orientation caused by the reaction forces and reaction

torques induced by the motion of the manipulator could

make the grasping maneuver very difficult. Thus,

several techniques were proposed to overcome this

problem. These techniques allow to plan the

manipulator trajectory in such a way that the influence

of manipulator motion on the robot position and

orientation is minimized. Application of such technique

for the case of a robot equipped with two manipulator

can be found in [13]. In case of a robot equipped with at

least two manipulators one of these manipulators can be

used to ensure that the constant orientation of the robot

will be kept during the motion of the second

manipulator [‎14]. If a team of robots is used, their

motion must be coordinated. Control of a team of multi-

manipulator robots that assemble large structure is

considered in [‎15]. Several experiments concerning

assembly of a large structure by a team of multi-arm

robots were also performed on planar air-bearing

microgravity simulators [‎16].

In this paper, the problem of assembling two modules

using space robots is discussed. We consider two cases:

first case assumes that there are two space robots and

the task is to connect a module attached to the end

effector (EE) of the first robot manipulator with already

assembled structure. In this case, the first robot is

responsible for placing this module in its place within

the structure, while the second robot is responsible for

performing the connecting operation (either by welding,

fastening or twisting). The second case considers one

space robot with two manipulators. The first

manipulator is responsible for placing the module in its

position within the structure and the other manipulator

has to perform the connecting operation.

The paper is organized as follows. In section 2 we

present the kinematics and dynamics of free-floating

space robot with two manipulators. At the end of this

section we refer to problem of adding structure module

to the end effector. Simulation results of the chosen

scenario of connecting two modules using space robots

are presented in section 3. Finally, section 4 presents

conclusions and final remarks.

2. KINEMATICS AND DYNAMICS OF A FREE-

FLOATING SPACE ROBOT WITH TWO

MANIPULATORS

In this section, equations for the general case of two n-

DoF (degree of freedom) manipulators, with rotational

joints, mounted on the same space robot are introduced.

These equations are derived without the assumption of

zero momentum and angular momentum. We follow the

approach presented in [‎16,‎17] that involved one

manipulator and extent it to the case of two

manipulators mounted on the same robotic platform.

Equations presented in this section are expressed in the

inertial reference frame CSine.

First manipulator EE position is given as:

n

i

iqsee

1

111 lrrr

where rs is the position of the space robot center of mass

(CM), rq1 is the position of the first kinematic pair of the

first manipulator with respect to the robot (given in

CSine), and li1 is the position of the (i+1)th kinematic

pair of the first manipulator with respect to the ith

kinematic pair of the same manipulator, given in CSine.

Linear velocity of the first manipulator EE is expressed

as:

n

i

iieeiseessee

1

111111 rrkrrωvv

where vs and ωs are the linear and angular velocity of

the space robot, respectively, ki1 and ri1 are the unit

vector of angular velocity and position of the ith

kinematic pair of the first manipulator, respectively,

while 1i is the first derivative with respect to time of

the position of ith rotational joint of the first

manipulator and denotes the angular velocity of this

joint. The angular velocity of the first manipulator EE

can be expressed through angular velocities of the robot

and of the kinematic pairs:

n

i

iisee

1

111 kωω

Thus, the linear and angular velocity of the first

manipulator EE can be expressed using vector notation:

111

1

1θJ

ω

vJ

ω

v M

s

s

s

ee

ee

(4)

Where, vector 1θ contains angular velocities of the first

manipulator joints, whileJS1 is the Jacobian of the

satellite according to the first manipulator and is given

by the following 6 x 6 matrix:

I0

r~IJ

33

1

T

ee1_s

s

(5)

where ree1_s = ree1 – rs. Symbol ∼ denotes matrix which

is equivalent of a vector cross-product. I is the identity

matrix, and 0 denotes the zero matrix.JM1 is a standard

Jacobian of a fixed-base manipulator (in this case it

concerns the first manipulator) expressed in inertial

reference frame and is given by the following 6 x n

dimensional matrix:

111

11111111

1

n

neenee

Mkk

rrkrrkJ

(6)

The same approach could be used for the second

manipulator. The linear and angular velocity of the

second manipulator EE can be expressed as following:

222

2

2θJ

ω

vJ

ω

v M

s

s

s

ee

ee

(7)

Where, vector 2θ contains angular velocities of the

second manipulator joints, while JS2 is the Jacobian of

the satellite according to the second manipulator and is

given by the following 6 x 6 matrix:

I0

r~IJ _

33

2

2

T

see

s

(8)

where ree2_s = ree2 – rs. JM2 is a standard Jacobian of a

fixed-base manipulator (in this case it concerns the

second manipulator) expressed in inertial reference

frame and is given by the following 6 x n dimensional

matrix

212

22212212

2

n

neenee

Mkk

rrkrrkJ

(9)

where, ki2 and ri2 are the unit vector of angular velocity

and position of the ith kinematic pair of the second

manipulator, respectively.

The kinetic energy of the space robot with two

manipulators can be expressed as:

2

1

222

111

21

21

2

12

1

θ

θ

ω

v

N0FD

0NFD

FFEB

DDBA

θ

θ

ω

v

T

s

s

nn

TT

nn

TT

T

T

s

s

(10)

where the submatrices A, B, D, E, F and N are defined

in [18] for a system with one manipulator. For a system

with two manipulators, these submatrices were

determined for each manipulator. The subscript "1"

denotes the first manipulator, while the subscript "2"

denotes the second manipulator.

The angular momentum of the system is given by the

following equation:

PrLL s0 (11)

where L0 denotes the initial angular momentum. The

momentum P and the angular momentum of the system

with two manipulators can be expressed as:

am

m

s

s

s f

f

θ

θHH

ω

vH

PrL

P

2

1

32312

0

(12)

where:

BrEArB

BAH

ss

T ~~2(13)

11

1

31 ~DrF

DH

s

(14)

22

2

32 ~DrF

DH

s

(15)

fm and fam are time dependent functions that express the

change in momentum and the angular momentum of the

system respectively.

From Eq. 12, the robot linear and angular velocity can

be expressed as following:

2

1

3231

1

2θ

θHH

f

fH

ω

v

am

m

s

s (16)

Thus the relation between the EE velocity of the first

manipulator and joints velocities of both manipulators

can be expressed as:

232

1

21131

1

211

1

21

1

1θHHJθHHJJ

f

fHJ

ω

v

ssM

am

m

s

ee

ee

Similarly, the EE velocity of the second manipulator

could be expressed as following:

232

1

222131

1

22

1

22

2

2θHHJJθHHJ

f

fHJ

ω

v

sMs

am

m

s

ee

ee

(18)

Eqs.17-18 are simultaneous equations, and for a given

trajectories of both end effectors (defined by linear and

angular velocities), joints velocities of both

manipulators i.e. 1θ and

2θ could be determined. After

calculating joints velocities of both manipulators, robot

velocities could be obtained using the Eq.16.

Dynamics equations for the space robot with two

manipulators could be derived using Langrangian

formalism. In our case the potential energy might be

neglected and the generalized coordinates were chosen

in the following form:

2

1

θ

θ

Θ

r

qs

s

p

2

1

θ

θ

v

q

s

s

v

(20)

where Θs is the vector containing Euler angles that

describe the orientation of the space robot.

The generalized equations of motion for the whole

system can be expressed as:

,p v v p v Q M q q C q q q

where Q is the vector of generalized forces:

TT T

2

T

1s

T

s uuHFQ

(22)

where Fs and Hs are forces and torques acting on the

space robot. In this paper we assume that no forces and

torques are acting on the robot, thus:

dtsm Ff =0 (23)

dtsssam FrHf ~ =0 (24)

whileu1and u2 denote the vector composed of driving

torques applied in the first and second manipulator

joints respectively. In Eq. 21, M denotes the mass

matrix and C denotes the Coriolis terms. The Mass

matrix, M, is given by:

222

111

21

21

N0FD

0NFD

FFEB

DDBA

qM

nn

TT

nn

TT

T

p

while components of matrix C are calculated according

to Eq. 5.236 that is presented in [19]. Eq.21 can be used

then to determine control torques applied in manipulator

joints required to achieve the desired motion of the

system. For a system with one manipulator, more

information can be found in [18].

The problem of adding structure module to the EE

described in Fig.1requires considering its mass, inertia

tensor and the change of the centre of mass in the last

part of the manipulator to which it is added.

The manipulator used in this work has 7 DoF, thus, the

parameters of the 7th link of the manipulator to which

the module is attached will be as following:

moduleall mmm 77_ (26)

moduleall III _ 77 (27)

module

modulemoduleall

mm

mmcm

7

777

rr_

(28)

where, m7 and mmodule are the mass of the final part of

the manipulator and the mass of the added module

respectively. I7 and Imodule are the inertia tensor of the

final part of the manipulator and the inertia tensor of the

added module. The center of mass in the final part of the

manipulator with the added module is defined by

cm7_allwhile rn, rmodule are vectors from the origin of the

manipulator final link reference frame to the center of

mass of the manipulator final part and the module,

respectively. The same approach is used for a robot with

two manipulators.

Figure 1. Structure module attached to the EE

3. SIMULATION RESULTS

Simulations were conducted using a specialized

simulation tool that has been developed at the Space

Research Centre (CBK PAN) since 2009 and was

extended to handle the problem of on-orbit assembly of

large structures using two multi arm / multi robot

solutions. The scenario under consideration includes the

situation where a structure module needs to be

connected with already assembled structure. In this

case, the module has to be moved and placed in its

position within the structure first, then, an operation of

connecting it firmly with the structure (either by

welding, fastening or twisting) should be performed.

Simulations were carried out for both cases, the first one

concerns two space robots with one manipulator each

and the other case consider one space robot with two

manipulators. Mass and inertia parameters of the space

robot are presented in Tab.1. The products of inertia of

the robot are equal to zero. In the case of two space

robots, both of them have the same parameters.

Table 1. Space robot parameters

Mass

[kg] Inertia

[kg.m2]

Robot 100

Ixx= 2.83

Iyy= 6.08

Izz= 7.42

The parameters of each manipulator links are presented

in Tab. 2. In addition to the mass and inertia parameters,

the position of ith link with respect to the i-1th reference

frame is also presented. The position of ith link centre

of mass (cm) with respect to ith reference frame is also

given in Tab. 2. All reference frames are shown in Fig.

1. Tab 3. presents the parameters of the added module,

where the module cm position is given with respect to

the reference frame of the manipulator final part.

Table2. Manipulator links parameters

Link

“i” Mass

[kg] Inertia

[kg.m2]

cm

[m] Position

[m]

1 1.6188

Ixx= 0.0048

Iyy= 0.0036

Izz= 0.0048

xcg=0.0030

ycg=0.1079

zcg=0.0048

x=0

y=0.1226

z=0

2 4.212

Ixx= 1.2552

Iyy= 1.254

Izz= 0.0096

xcg=0.0001

ycg=0.0024

zcg=0.9124

x=0

y=0

z=1.5262

3 1.6188

Ixx= 0.0048

Iyy= 0.0036

Izz= 0.0048

xcg= -0.0030

ycg= 0.0788

zcg= 0.0048

x=0

y=0.0930

z= -0.1430

4 4.392

Ixx= 0.036

Iyy= 1.1484

Izz= 1.1232

xcg= 0.9026

ycg= -0.0011

zcg= 0.0467

x= 1.3808

y=0

z=0

5 1.6188

Ixx=0.0048

Iyy=0.0036

Izz= 0.0048

xcg= -0.0030

ycg= 0.0142

zcg= -0.0048

x=0

y=0

z=0

6 1.6188

Ixx= 0.0084

Iyy= 0.0084

Izz= 0.0036

xcg= 0.0030

ycg= 0.0096

zcg= 0.1349

x=0

y=0

z=0

7 0.1692

Ixx= 0.0001

Iyy=0.0001

Izz=0.0001

xcg=0

ycg=0

zcg=-0.1356

x=0

y=0

z=0.0002

Table3. Module parameters

Mass

[kg] Inertia

[kg.m2]

cm

[m] Position

[m]

module 5 Ixx= 0.4177

Iyy= 2.4010

Izz= 2.8167

xcg= -0.6

ycg=0

zcg=0

x=0

y=0

z=0

The EE trajectories were the same for both cases.

Simulation time was set up to 20 [sec] and it was

divided into two equal parts. In the first part, the

mission of the first manipulator EE was to place the

module in its position within the structure, while the

mission of the second manipulator EE was to reach the

position from which it will begin the connecting

operation. In the second part, the first manipulator EE

was responsible for keeping the module in its position,

while the second manipulator EE task was to perform

the connecting operation.

Each trajectory consists of three phases. In the first

phase, the motion of the manipulator EE (in the inertial

reference frame) is accelerated, then it is followed by

the second phase in which EE velocities are constant. In

the third phase, the motion is decelerated, and at the end

of this phase, accelerations, velocities and positions are

equal to a previously defined final conditions. In this

paper, final velocities and accelerations are assumed to

be equal to zero. Moreover, trajectories of each part are

assumed to be smooth.

Simulation results are presented in Fig.2-6for the case

of two robots and in Fig.7-13for the case of one robot

with two manipulators.

Figure 2. Manipulator reaction force

in respect to first robot cm

Figure 3. Manipulator reaction torque

in respect to first robot cm

Figure 4. Manipulator reaction force

in respect to second robot cm

Figure 5. Manipulator reaction torque

in respect to second robot cm

Figure 6. Space modules assembled by two space robots

Figure 7. Space modules assembled by a space robot

with two manipulators

Figure 8. First manipulator reaction force

in respect to robot cm

Figure 9. First manipulator reaction torque

in respect to robot cm

Figure 10. Second manipulator reaction force

in respect to robot cm

Figure 11. Second manipulator reaction torque

in respect to robot cm

Figure 12. Overall reaction force of both manipulators

mounted on the same robot

Figure 13. Overall reaction torque of both manipulators

mounted on the same robot

The changes of robots positions and orientations due to

manipulators motion are presented in Fig. 14,15.

Figure 14. Changes of robots positions

Figure 15. Changes of robots orientations

Simulations have shown that higher manipulator

reaction torques in respect to robot centre of mass are

reached when using two separate space robots. This is

due to the fact that in the case of two manipulators

mounted on the same robot, the reaction torques of the

first manipulator is partially compensated by the

reaction torque of the second manipulator.

4. CONCLUSIONS

In this paper, the problem on on-orbit assembly of large

structures using space robots was considered. Two cases

were investigated. The first case involved two space

robots with one manipulator each. The second case

involved two manipulators mounted on the same space

robot. The performed simulations have demonstrated

that both cases can be used to perform this task.

However, when using one robot with two manipulators,

smaller reaction torques can be achieved. In addition,

the usage of two space robots not always shortens the

operation time. In the case discussed above, the module

must be placed in the required position within the

structure first, then the connecting operation can be

performed. Moreover, there is a possibility of collision

between the two space robots. This situation does not

exist when using one space robot with two

manipulators. However, the collision possibility

between the two manipulators exists in both cases and

should be considered when planning manipulators

trajectories. Nevertheless, using a swarm of space

robots with two manipulators each, where each robot is

responsible for connecting different module to the

structure, could speed up the assembly process.

5. ACKNOWLEDGMENT

This work was financed by the Polish National Science

Centre under research grant 2015/17/B/ST7/03995.

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