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, Germany2ASTRIUM 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

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 of a mass-spring-damper system caused by surface contact

Three-dimensional dynamics resulting from a misalignment of the two bodies

One-Dimensional Dynamics

Symbolic graphic of a representative system

Structural elasticity and damping in the surface contact create oscillating system

Elasticity and damping coefficients assumed to be very high( and )

In real system must be negative at all times to prevent separation

Graphic of the real system

One-Dimensional System Response to Rectangle Input

Input function (green) and qualitative system response

(blue) of representative system (low stiffness)

At the beginning of thrust profile the system oscillates about the new steady state with the amplitude A so that

When thrust ceases, Dx crosses into positive range. In real system this would mean separation

Rectangle profile

Dx

/ A

Time [sec]

Stored Potential Energy

Input function (green) and system response (blue) of representative

system

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:

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

Release of potential energy

Dx

/ A

Time [sec]

c

FU thrust

2

Stepwise Reduction of Thrust

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

System response to a stepwise reduction of the input by one half

Dx

/ A

Time [sec]

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, therefore off-modulation of OCT needed

While a maximum deviation of 5 cm is realistic, a deviation of 50 cm was assumed for this analysis

Position of System CoM and thrust force in a system with deviation

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

Simulation of modulated thrust profile for the four thrusters (ASTRIUM)

Condition on off-modulation to avoid separation

Three Dimensional Dynamics: Lateral Forces

Relation between different coordinate frames

Internal forces and torques between Chaser and Target are calculated using the accelerations the Target experiences

Angular velocity and acceleration of the system cause accelerations in the Target:

Centrifugal acceleration acts mainly in x-direction (direction of flight)

Euler acceleration acts mainly in y- and z-direction

Equations for the Balance of Forces on the Target

Six equations must be balanced, the sum of forces in three directions and the sum of torques in three directions

are the contact forces in x-direction transferred at the contact points

and are generalized terms for the lateral forces that are applied, either by friction or by the robot

is a torque about the x-axis provided either by friction or by the robot

At least contact forces are necessary to balance the system, additional forces create redundancy

and are balanced by contact forces, and by the robot or by friction

Effect of Friction in the Surface Contact

Friction is dependent on normal force and material specific coefficient:

In a configuration with six contact points each contact transfers a normal force of

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

Direction of inertial force in relation to external torque

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 and will even converge to zero deviation if damping is present

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 frame: m

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 z-direction 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 is constant when is positive and sinusoidal when is negative

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)