Suril V. Shah
1
1
Inna Sharf
2
and Arun K. Misra
3
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2
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3
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This paper presents strategies for pointtopoint reactionless manipulation of a satellite
mounted dualarm robotic system for capture of tumbling orbiting objects, such as outof
commission satellites and space debris. Use of the dualarm robot could be more effective than
the single arm when there is no provision for a grapple fixture or the object is tumbling. The
dual arms can also provide dexterous manipulation. As the main objective in capture of orbital
objects is to move the endeffector from initial position to the grapple point with desired
velocity, the tasklevel reactionless constraints in terms of endeffector velocities are derived.
The trajectory planned using these constraints, however, results in several singular points
within the robot’s workspace. In order to overcome this shortcoming, three pointtopoint path
planning strategies are presented, which improve the reactionless operation of the dualarm
robot. The strategies are illustrated by carrying out simulations for a 6degreeoffreedom
(DOF) dualarm robotic system mounted on a satellite.
1
corresponding author
Reactionless Path Planning Strategies for Capture of Tumbling
Objects in Space Using a DualArm Robotic System
I. Introduction
Autonomous onorbit services, such as capture of orbiting objects, and refueling, repair and
refurbishment of disabled satellites, using a robot mounted on a service satellite will be one of
the important space operations in the future [13]. Particularly, active debris removal [3] has
gained a lot of attention in the recent years due to the increase in the number of debris. While
performing these onorbit services, it is desirable that the fuel consumption to overcome any
attitude disturbance of the base satellite is negligible, as limited fuel is mainly reserved for
orbital transfer maneuvers. The main motivation behind capturing space debris is to avoid
their possible collision with a working satellite in the same orbit. Some research efforts have
been directed towards achieving capture of a satellite with zero attitude disturbances to the
base. This is also commonly referred to as reactionless manipulation. Such reactionless
manipulation of a robot mounted on a satellite can translate into fuel savings and increase the
operating life of the servicing system.
In this regard, an optimization technique was proposed in [4] for minimization of the base
reactions, which did not lead to a satisfactory result on reactionless manipulation. The concept
of disturbance map was proposed in [5], which provided the minimum attitude disturbance
paths leading to lower fuel consumption. Later, a more effective extended disturbance map
was also proposed in [6]. These maps indeed help in reducing attitude disturbance, but may
not lead to nil attitude disturbance. A unique design of manipulator was provided in [7] that
led to reactionless manipulation. However, the major disadvantage of such a design is that it
makes the robot architecture very complex. A reaction null space (RNS) based path planning
was introduced in [8] for reactionless manipulation of a robot with flexible base. Later, in [9]
the RNS based approach was used for control of space robots. It was shown in [89] that the
joint velocities, obtained using the RNS formulation, result in zero reaction moments on the
satellitebase. Subsequently, the flight validation with ETSVII space robot and its extension
to a kinematically redundant arm, for the zero reaction maneuvers, were presented in [10]. It
was shown in [10] that the constraints for reactionless manipulation, in terms of joint
velocities, can be augmented with the tasklevel constraints in order to obtain desired motion
of the endeffector. The RNSbased concept was also used in [11] for capture of a tumbling
satellite. Moreover, the RNSbased approach with backward integration was attempted in [12]
for trajectory planning of 2link robot in the approach phase. Reactionless motion of a space
robot when capturing an unknown tumbling target was also presented in [13] based on the
momentum conservation equation and the recursive least squares method.
In the above mentioned studies, the focus was mainly on completing the task with a single
arm robot. However, when the orbiting object does not have provision for grapple or is
tumbling, the interception may be very difficult. In such cases, interception using a dualarm
robotic system can be appealing as this will increase the probability of grasp in comparison to
a singlearm robot. Use of a dualarm robot was described in [14], where one arm traced a
given path while the second arm worked both to control the base attitude and to optimize the
total operational torque of the system. The path planning of a planar dualarm freefloating
manipulator was also presented in [15]. In both [14] and [15], the second arm was only
involved in attitude control of the base satellite rather than capture of the object. An
autonomous approach for berthing of a moving satellite with two robots using a flexible wrist
mechanism and impedance control was proposed in [16]. Capture of a spinning object by two
flexible manipulators using hybrid position/force control and vibration suppression control
was also presented in [17]. A hardwareintheloop simulation of the spatial dualarm space
robot was presented in [18]. In [1618], the robot arms were manipulated without paying any
attention to the base attitude. More recently, in [19], the coordinated motion planning of a
spatial dualarm space robot for target capture was presented. In that work also, capture of the
target with both arms was carried out without regard to the base attitude.
It is worth noting that in the above cited works, either the dual arms capture the orbiting
object regardless of the attitude of the base satellite or the one arm captures the object while
the second arm is specifically used to control the attitude of the satellite. Thus, the reactionless
capture using a dualarm robotic system is least explored in the literature. The reactionless
trajectories have to be designed such that the two arms start from different initial
configurations and intercept the designated points on the object. It is also essential that both
endeffectors capture the tumbling object with velocity equal to that of the contact points in
order to avoid any significant impact. Hence, the major challenge in capture of a tumbling
object is pointtopoint reactionless manipulation of the robot arms with desired endeffector
velocities at the capture instant. This is a complex problem as the reactionless constraints are
nonholonomic and the resulting path has many singular points within the robot’s workspace
[10]. In comparison to the singlearm manipulation, the case of dualarm manipulation
requires that the paths have to be planned such that both arms stay away from singular
configurations, which themselves are path dependents.
Motivated by these facts, the reactionless pointtopoint path planning strategies are
proposed in this work for dualarm robotic systems for capture of a tumbling object. In the
present work, the two arms are moved so as to produce zero net reaction moment in order to
capture the tumbling target. Compared to the singlearm scenario, reactionless manipulation of
the dualarm may bring forth some interesting aspects of path planning. The pointtopoint
motion is achieved by deriving the tasklevel reactionless constraints for dualarm robotic
system by projecting the jointlevel reactionless constraints [8] using the Generalized Jacobian
Matrix [20]. As the resulting equations are highly constrained and have many singular points
within the robot’s workspace, three pointtopoint path planning strategies are also presented.
Extension of reactionless path planning to a dualarm robotic system and strategies to avoid
singular configurations are the main contributions of this work. Numerical illustrations are
provided using a 6DOF dualarm robotic system.
The rest of the paper is organized as follows: Some mathematical preliminaries are
provided in Section II. The reactionless manipulation of the dualarm robotic system is
presented in Section III, whereas several pointtopoint reactionless path planning strategies
are developed in Section IV. Finally, conclusions are given in Section V.
II. Preliminaries and Notation
In this section the equations of motion for dualarm robotic systems and constraints for
reactionless manipulation are derived as an extension of those given in [10] for a singlearm
robotic system.
A.Equations of motion
The equations of motion for an DOF robot mounted on a floatingbase can be written
similarly to those in [10] as:
$
$ $ $ $
$
+ = +
H H c F
x
J
F
H H c τ
φ
J
(1)
where H
∈
R
6×6
and H
$
∈
R
×
are the inertia matrices of the base and manipulator,
respectively, H
$
∈
R
6×
is the coupling inertia matrix,
x
∈
R
6
is the vector of linear and
angular accelerations of the base,
φ
∈
R
is the vector of joint accelerations, c
∈
R
6
and
c
$
∈
R
are the velocity dependent nonlinear terms of the base and manipulator, F
and F
∈
R
*
are the vectors of force and moment exerted on the centroid of the base and endeffector,
respectively, τ
$
∈
R
is the manipulator joint torque, J
∈
R
6×6
and J
$
∈
R
6×
are the Jacobian
matrices for the base and manipulator. For the dualarm robotic system, H
$
, H
$
,
φ
, c
$
, τ
$
,
J
, J
$
and F
can be written as follows:
[ ]
1 1 1
1 2
2 2 2
, , = , = ,
$ $ $
$ $ $ $ $
$ $ $
= =
H O φ c
H H H H φ c
O H φ c
1 1 1 1
2 2 2 2
= , = , = and =
$ $
$ $
$ $
τ J J O F
τ J J F
τ J O J F
(2a)
where the subscripts 1 and 2 represent arm1 and arm2, respectively. The floatingbase
module of the '"$+$ ("+$) [21], developed based on (12), is
used for the simulations carried out in this paper.
B.Constraints for reactionless manipulation
The matrices H
and H
$
, of (1), may also be expressed as
_
_ _
_
_ _
and
$ '
'
$
$
ω
ω
= =
H
H H
H H
H
H H
(3a)
Now, the constraints for reactionless manipulation can be written using those in [10] as
1
_ _ _ _
0 where
$ $ $ ' $ '
ω
= = −H φ H H H H H
(3b)
Equation (3b) represents the nonholonomic constraints, where
φ
belongs to the subspace of
reactionless motion of the robot. The above equation forms the constraint leading to zero
reaction moments but nonzero reaction forces. It is assumed that the satellite has reaction jets
or thrusters to take care of the base reaction forces. As in the previous literature, hereafter, the
term $# will imply manipulation with zero base moments only. For the
dualarm robotic system, (3b) can also be expressed as
1
1 2 1 1 2 2
2
0 or 0
$
$ $ $ $ $ $
$
= + =
φ
H H H φ H φ
φ
(4)
It can be seen from (4) that for the dualarm robot the sum of the coupling angular
momenta of both arms, not of the individual, has to be zero. Solution of (4) for
1
$
φ
and
2
$
φ
can be obtained using the pseudo inverse approach [8]. It is noted that (3b4) represent the
constraints as a function of joint velocities, and will be referred to as jointlevel reactionless
constraints.