Single-slew manoeuvres for spin-stabilized spacecraft 29 th March 2011 James Biggs Glasgow In collaboration with Nadjim Horri at the Surrey Space Centre 6 th International Workshop and Advanced School “Spaceflight Dynamics and Control”

Use an arrow like this to mark current section Introduction  Micro and nano spacecraft seen as viable alternatives to larger spacecraft for certain missions e.g. Enable rapid space access. 29th March James Biggs Introduction Motion Planning Reduction method Practical cost function Example Conclusion SSTL-150 UKube 1 – Clydespace and Strathclyde University

Use an arrow like this to mark current section 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. 29th March James Biggs Introduction Motion Planning Reduction method Practical cost function Example Conclusion

Use an arrow like this to mark current section 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. 29th March James Biggs Introduction Motion Planning Reduction method Practical cost function Example Conclusion

Use an arrow like this to mark current section 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. 29th March James Biggs Introduction Motion Planning Reduction method Practical cost function Example Conclusion

Use an arrow like this to mark current section 29 th March James Biggs Introduction Motion Planning Reduction method Practical cost function Example Conclusion

Use an arrow like this to mark current section 29 th March James Biggs Introduction Motion Planning Reduction method Practical cost function Example Conclusion

Use an arrow like this to mark current section 29 th March James Biggs Motion Planning using optimal control Kinematic constraint: Subject to the cost function: Introduction Motion Planning Reduction method Practical cost function Example Conclusion

Use an arrow like this to mark current section 29 th March Insert Name as Header & Footer Introduction Motion Planning Reduction method Practical cost function Example Conclusion

Use an arrow like this to mark current section 29 th March James Biggs Sketch of proof – Kinematic constraint Introduction Motion Planning Reduction method Practical cost function Example Conclusion

Use an arrow like this to mark current section 29 th March James Biggs Sketch of proof – Use a Lie group formulation Introduction Motion Planning Reduction method Practical cost function Example Conclusion

Use an arrow like this to mark current section 29 th March James Biggs Sketch of proof - Construct the left-invariant Hamiltonian (Jurdjevic, V., Geometric Control Theory, 2002) Introduction Motion Planning Reduction method Practical cost function Example Conclusion

Use an arrow like this to mark current section 29 th March James Biggs 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

Use an arrow like this to mark current section 29 th March James Biggs Sketch of proof. Lax Pair Integration: Solve for a particular initial condition Introduction Motion Planning Reduction method Practical cost function Example Conclusion

Use an arrow like this to mark current section 29 th March James Biggs PRACTICAL COST FUNCTION 1 Minimise the final pointing direction: Introduction Motion Planning Reduction method Practical cost function Example Conclusion

Use an arrow like this to mark current section 29 th March James Biggs 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:

Use an arrow like this to mark current section 29 th March James Biggs EXAMPLE Introduction Motion Planning Reduction method Practical cost function Example Conclusion SSTL-100

Use an arrow like this to mark current section 29 th March James Biggs EXAMPLE Introduction Motion Planning Reduction method Practical cost function Example Conclusion SSTL-100

Use an arrow like this to mark current section 29 th March Insert Name as Header & Footer Control Torque History (Nm) Introduction Motion Planning Reduction method Practical cost function Example Conclusion

Use an arrow like this to mark current section 29 th March James Biggs Introduction Motion Planning Reduction method Practical cost function Example Conclusion

Use an arrow like this to mark current section 29 th March James Biggs Introduction Motion Planning Reduction method Practical cost function Example Conclusion

Use an arrow like this to mark current section CONCLUSION 29 th March James Biggs 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