Transcript DLR-Präsentation Raumfahrt 16:9 mit Kopf

Analysis of a Deorbiting Maneuver of a large Target Satellite
using a Chaser Satellite with a Robot Arm
Philipp Gahbler1, R. Lampariello1 and J. Sommer2
1DLR
Institute for Robotics and Mechatronics, Germany
2ASTRIUM Space Transportation GmbH, Bremen, Germany
ASTRA 2013
Motivation
The purpose of this work is to show that a Chaser satellite equipped with a
relatively weak robot arm is capable of deorbiting a large Target satellite.
The dynamics of the coupled system, consisting of the Chaser resting onto the
Target during the deorbiting, must be examined to ensure that the deorbiting
maneuver can be performed safely.
Key questions:
Is there risk of separation during deorbiting?
Do we need a clamp or does the robot have to exert high forces to avoid
separation?
Contents
Description of the system consisting of Chaser and Target
Identification of the critical dynamics
One-dimensional analysis of the surface contact dynamics
Three-dimensional analysis of the deorbiting dynamics and the robot internal forces
Validation with numerical simulations
Conclusions
Target
Very large object (e.g. 8 t)
Target needs to be deorbited
The satellite Envisat was used as an
example
Envisat
Chaser
Satellite with a mass of roughly 1 t
7 DoF robot arm for grasping
Chaser grasps the Target with robot
arm and rests onto it with six contact
points, arranged at a radius of 0.8 m
Model of a Chaser
System
Chaser positioned relative to Target
near the center of mass (CoM) of the
Target
Contact through a number of surface
contact points as well as robot arm
Surface contacts only exert force
during compression
Robot arm provides torques and lateral
forces
Combined System of Target and Chaser
Propulsion
Chaser accelerates system with four
orbit-control-thrusters (OCT)
Overall thrust typically 1500 N
Model of the Chaser
Critical Dynamics
One-dimensional dynamics of a
mass-spring-damper system
caused by surface contact
Three-dimensional dynamics
resulting from a misalignment of
the two bodies
System responds to changes in thrust
profile
Relative distance of surface contact
must be negative to prevent bumping
of masses
External torque occurs when thrust
vector doesn’t point through the
system CoM
The resulting angular acceleration
causes complex internal forces
One-Dimensional Dynamics
Structural elasticity and damping in the
surface contact create oscillating
system
Elasticity and damping coefficients
assumed to be very high
𝑁
(1.0 ∙ 108 𝑚
and 3.0 ∙ 105 𝑁𝑠
)
𝑚
Graphic of the real system
In real system ∆𝑥 = 𝑥𝑡𝑎 − 𝑥𝑐ℎ must be
negative at all times to prevent
separation
Symbolic graphic of
a representative system
One-Dimensional System Response to Rectangle Input
At the beginning of thrust profile the system
oscillates about the new steady state with the
amplitude A so that ∆𝑥𝑠𝑡𝑒𝑎𝑑𝑦 = −𝐴
When thrust ceases, Dx crosses into positive
range. In real system this would mean
separation
Dx / A
Rectangle profile
Time [sec]
Input function (green) and
qualitative system response
(blue) of representative system
(low stiffness)
Stored Potential Energy
2
Fthrust
U
c
Therefore high stiffness is desired, to minimize
the stored potential energy
Using the assumed values, the potential energy
is only 11.25 mJ, which the robot can easily
handle
Dx / A
Due to structural elasticity, potential energy is
stored in the structure, which is released at the
end of the thrust profile
The stored potential energy is given by the thrust
force, Fthrust, and the structural stiffness, c:
Release of
potential energy
Time [sec]
Input function (green) and system
response (blue) of representative
system
When thrust is reduced by a fraction of
the total, the system oscillates about
the new steady state by the difference
of the two states
If the reduction is by less than half of
the previous value, ∆x will always be
negative
Dx / A
Stepwise Reduction of Thrust
Time [sec]
System response to a stepwise reduction
of the input by one half
Three-Dimensional Dynamics: Disturbance Torque
External torques occur when the
deorbiting thruster force doesn’t point
through the CoM of the system
Deviation occurs when the Chaser and
the Target aren’t properly aligned,
especially when the precise location of
the Target CoM isn’t known
The attitude control system cannot
compensate for such high torques,
Position of System CoM and thrust force
therefore off-modulation of OCT needed
in a system with deviation
While a maximum deviation of 5 cm is
realistic, a deviation of 50 cm was
assumed for this analysis
Modulated Thrust Profile - Off Modulation
Attitude controller will selectively turn off
one or several of the four thrusters to
create torque, to account for
misalignments
Step width and sequence can be adjusted
in controller software
However, individual steps should only
change by one thrust level (e.g. 4 to 3 or 2
to 1) to avoid separation
Condition on off-modulation
to avoid separation
Simulation of modulated thrust profile for
the four thrusters (ASTRIUM)
Three Dimensional Dynamics: Lateral Forces
Internal forces and torques between
Chaser and Target are calculated using
the accelerations the Target experiences
Angular velocity 𝜔 and acceleration 𝜔 of
the system cause accelerations in the
Target:
𝑎𝑐𝑒𝑛𝑡 = 𝜔 × 𝜔 × 𝑟𝑠𝑡
𝑎𝐸𝑢𝑙 = 𝜔 × 𝑟𝑠𝑡
Centrifugal acceleration 𝑎𝑐𝑒𝑛𝑡 acts mainly
in x-direction (direction of flight)
Euler acceleration 𝑎𝐸𝑢𝑙 acts mainly in yand z-direction
Relation between different coordinate
frames
Equations for the Balance of Forces on the Target
Six equations must be balanced, the sum
of forces in three directions Σ𝐹𝑡 and the
sum of torques in three directions Σ𝜏𝑡
𝐹𝑐,1 , 𝐹𝑐,2 , … 𝐹𝑐,𝑛 are the contact forces in
x-direction transferred at the contact
points
𝐹𝑙,𝑦 and 𝐹𝑙,𝑧 are generalized terms for
the lateral forces that are applied, either
by friction or by the robot
𝜏𝑥 is a torque about the x-axis provided
either by friction or by the robot
At least 𝑛 = 3 contact forces are
necessary to balance the system,
additional forces create redundancy
𝐹𝑥 , 𝜏𝑦 and 𝜏𝑧 are balanced by contact
forces, 𝐹𝑦 , 𝐹𝑧 and 𝜏𝑥 by the robot or by
friction
Effect of Friction in the Surface Contact
Friction is dependent on normal force and material specific coefficient: 𝐹𝐹𝑟 = 𝜇 ∙ 𝐹𝑁
In a configuration with six contact points each contact transfers a normal force of
1309𝑁
=220𝑁
6
A typical value for the coefficient of friction is 0.5
Therefore, a lateral force of up to 650 N and a torque about the x-axis of 550 Nm
can be transferred
Frictionless Case
If friction is assumed to be zero, the robot can be used to compensate lateral
forces
System Stability
Given that most of the lateral forces are
caused by the angular acceleration
(Euler term), the relative acceleration
between the two bodies points opposite
to the deviation
This means that the angular acceleration
will bring the bodies to move to reduce
∆𝑦 and will even converge to zero
deviation if damping is present
Direction of inertial force in relation to
external torque
Numerical validation in SIMPACK
SIMPACK is a multi-body-simulation
software that allows the user to create
a model and integrate it numerically
Simpack program window
Assumed Grasping Point
Grasping point coordinates in Target
5
frame: 2.5 m
2
Combined System of Target and Chaser
Simulation Results of Case with Friction and no Off-modulation
Lateral forces follow the curves of the
angular acceleration, as expected
Lateral forces well in the range of what
friction can handle
Plot of the six contact forces (top) and the lateral
forces and torque about x-axis (bottom)
Simulation Results of Frictionless Case and no Off-modulation
Bodies oscillate relative to each
other in the y- and z-direction
Different damping coefficients
(provided by robot) in y- and zdirection to achieve similar
convergence time
Relative position (top) and velocity (bottom) of the two
bodies in y- and z-direction
Simulation Results of Frictionless Case and no Off-modulation
Lateral forces well in the range of
what robot can handle
Six contact forces (top), forces and torques provided by
robot (bottom)
Conclusions
The deorbiting of a heavy Target satellite is possible using a Chaser equipped with
only a robot arm
The system is threatened by separation when the thrust is reduced. If it is reduced
by less than half of its current value, the system stays in contact
At the end of a thrust profile potential energy is released, which however is low and
the resulting motion can be compensated by the robot
A misalignment of the thrust force causes rotational accelerations which result in
internal forces between the two bodies, but these can either be compensated by
friction or by the robot
Additionally, the system is stable, such that the misalignment will tend to decrease
It is planned to perform such a deorbiting maneuver within the DEOS project
Thank you!
Relative Motion Resulting from Excessive Reduction of Thrust
If the thrust is reduced by more than one
half, a relative motion occurs, in which
the two bodies separate and collide with
each other periodically
The acceleration ∆𝑥 = ∆𝑎 is constant
when ∆𝑥 is positive and sinusoidal when
∆𝑥 is negative
∆𝑥 has sinusoidal sections below zero
and parabolic sections above
Relative distance (blue) and relative
acceleration (green) of an oscillation with
separation
Simulation Results of Case with Friction and no Off-modulation
Constant angular acceleration due to
external torque from deviation of CoM
Torque is directed in y- and z-direction,
as expected, which causes the initial
angular acceleration about angles beta
and gamma
Over time the inertia tensor causes
rotation also about x-axis (alpha)
Of notice is the angular acceleration
profile, which determines the lateral
forces
Plot of angles Alpha (x), Beta (y) and Gamma (z) (top),
their velocities (middle) and accelerations (bottom)