www.strath.ac.uk/[email protected] single-slew manoeuvres for spin-stabilized spacecraft 29 th...
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www.strath.ac.uk/[email protected]
Single-slew manoeuvres for spin-stabilized spacecraft
29th March 2011
James Biggs
Glasgow
In collaboration with
Nadjim Horri at the Surrey Space Centre
6th International Workshop and Advanced School“Spaceflight Dynamics and Control”
Introduction
Micro and nano spacecraft seen as viable alternatives to larger spacecraft for certain missions e.g. Enable rapid space access.
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Introduction
Motion Planning
Reduction
method
Practical
cost function
Example
Conclusion
SSTL-150 UKube 1 – Clydespace andStrathclyde University
Attitude Modes
Two vital mission phases:-
• De-tumbling and stabilisation– initial tip-off speeds (worst case scenario for Ukube -5rpm in every axis .) Tumbling motion must be stabilised or mission will fail. B dot control has been demonstrated.
• Re-pointing and stabilisation – reorient spacecraft to target specific point (e.g. point antenna to ground station, point solar cells towards sun for maximum power.) Accurate re-pointing is yet to be realised .
This presentation proposes a method for re-pointing.
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Introduction
Motion Planning
Reduction
method
Practical
cost function
Example
Conclusion
Stabilization
Two conventional methods:-
• Spin stabilization – passive, re-pointing required.o Early satellites – NASA Pioneer 10/11, Galileo Jupiter orbiter
• Three axis-stabilization – active control.o Thrusters, reaction wheels on conventional spacecraft.
Spin stabilization is attractive for nano-spacecraft Enables temporary GNC switch off.
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Introduction
Motion Planning
Reduction
method
Practical
cost function
Example
Conclusion
Re-pointing spin stabilized spacecraft
Possibility:-
• Spin down, perform an eigen-axis rotation, spin up.
• Computationally easy to plan and track.
• may not be feasible with small torques of micro/nano spacecraft in a specified time.
Requires better planning/design of reference trajectory.
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Introduction
Motion Planning
Reduction
method
Practical
cost function
Example
Conclusion
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Introduction
Motion Planning
Reduction
method
Practical
cost function
Example
Conclusion
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Introduction
Motion Planning
Reduction
method
Practical
cost function
Example
Conclusion
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Motion Planning using optimal control
Kinematic constraint:
Subject to the cost function:Introduction
Motion Planning
Reduction
method
Practical
cost function
Example
Conclusion
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Introduction
Motion Planning
Reduction
method
Practical
cost function
Example
Conclusion
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Sketch of proof – Kinematic constraint
Introduction
Motion Planning
Reduction
method
Practical
cost function
Example
Conclusion
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Sketch of proof – Use a Lie group formulation
Introduction
Motion Planning
Reduction
method
Practical
cost function
Example
Conclusion
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Sketch of proof - Construct the left-invariant Hamiltonian (Jurdjevic, V., Geometric Control Theory, 2002)
Introduction
Motion Planning
Reduction
method
Practical
cost function
Example
Conclusion
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Sketch of proof - Construct the left-invariant Hamiltonian vector fields and solve:
Solve the differential equations:
Introduction
Motion Planning
Reduction
method
Practical
cost function
Example
Conclusion
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Sketch of proof.Lax Pair Integration:
Solve for a particular initial condition
Introduction
Motion Planning
Reduction
method
Practical
cost function
Example
Conclusion
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PRACTICAL COST FUNCTION 1Minimise the final pointing direction:
Introduction
Motion Planning
Reduction
method
Practical
cost function
Example
Conclusion
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PRACTICAL COST FUNCTION 2
Introduction
Motion Planning
Reduction
method
Practical
cost function
Example
Conclusion Minimize J by optimizing available parameters:
Minimize torque requirement amongst reduced kinematic motions:
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EXAMPLE
Introduction
Motion Planning
Reduction
method
Practical
cost function
Example
Conclusion
SSTL-100
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EXAMPLE
Introduction
Motion Planning
Reduction
method
Practical
cost function
Example
Conclusion
SSTL-100
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Control Torque History (Nm)
Introduction
Motion Planning
Reduction
method
Practical
cost function
Example
Conclusion
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Introduction
Motion Planning
Reduction
method
Practical
cost function
Example
Conclusion
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Introduction
Motion Planning
Reduction
method
Practical
cost function
Example
Conclusion
CONCLUSION
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• To realise nano-spacecraft as viable platforms for remote sensing precise attitude control is essential.
• Poses research challenges – low-computational methods for generating low-cost (zero fuel) motions.
• The presented method reduces the kinematics to a subset of feasible motions that can be defined analytically.
• Massive reduction in computation – reduced to parameter optimization.
• Can be extended to minimum time problems, three axis re-pointing i.e. No spinning constraint.
Introduction
Motion Planning
Reduction
method
Practical
cost function
Example
Conclusion
Thank You for your attention
Questions?
23