Single-slew manoeuvres for spin-stabilized spacecraft

1. Glasgow In collaboration with Single-slew manoeuvres for spin-stabilized spacecraft 6th International Workshop and Advanced School “Spaceflight Dynamics and Control” James Biggs NadjimHorri at the Surrey Space Centre

2. Introduction Micro and nano spacecraft seen as viable alternatives to larger spacecraft for certain missions e.g. Enable rapid space access. Introduction Motion Planning Reduction method Practical cost function Example Conclusion UKube 1 – Clydespace and Strathclyde University SSTL-150 James Biggs

3. 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. Introduction Motion Planning Reduction method Practical cost function Example Conclusion James Biggs

4. Stabilization Two conventional methods:- • Spin stabilization – passive, re-pointing required. • Early satellites – NASA Pioneer 10/11, Galileo Jupiter orbiter • Three axis-stabilization – active control. • Thrusters, reaction wheels on conventional spacecraft. Spin stabilization is attractive for nano-spacecraft Enables temporary GNC switch off. Introduction Motion Planning Reduction method Practical cost function Example Conclusion James Biggs

5. 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/nanospacecraft in a specified time. Requires better planning/design of reference trajectory. Introduction Motion Planning Reduction method Practical cost function Example Conclusion James Biggs

6. Introduction Motion Planning Reduction method Practical cost function Example Conclusion James Biggs

7. Introduction Motion Planning Reduction method Practical cost function Example Conclusion James Biggs

8. Motion Planning using optimal control Kinematic constraint: Introduction Motion Planning Reduction method Practical cost function Example Conclusion Subject to the cost function: James Biggs

9. Introduction Motion Planning Reduction method Practical cost function Example Conclusion Insert Name as Header & Footer

10. Sketch of proof – Kinematic constraint Introduction Motion Planning Reduction method Practical cost function Example Conclusion James Biggs

11. Sketch of proof – Use a Lie group formulation Introduction Motion Planning Reduction method Practical cost function Example Conclusion James Biggs

12. Sketch of proof - Construct the left-invariant Hamiltonian (Jurdjevic, V., Geometric Control Theory, 2002) Introduction Motion Planning Reduction method Practical cost function Example Conclusion James Biggs

13. Sketch of proof - Construct the left-invariant Hamiltonian vector fields and solve: Introduction Motion Planning Reduction method Practical cost function Example Conclusion Solve the differential equations: James Biggs

14. Sketch of proof. Lax Pair Integration: Introduction Motion Planning Reduction method Practical cost function Example Conclusion Solve for a particular initial condition James Biggs

15. Minimise the final pointing direction: Introduction Motion Planning Reduction method Practical cost function Example Conclusion Practical cost function 1 James Biggs

16. Minimize torque requirement amongst reduced kinematic motions: Introduction Motion Planning Reduction method Practical cost function Example Conclusion Practical cost function 2 Minimize J by optimizing available parameters: James Biggs

17. Introduction Motion Planning Reduction method Practical cost function Example Conclusion example SSTL-100 James Biggs

18. Introduction Motion Planning Reduction method Practical cost function Example Conclusion example SSTL-100 James Biggs

19. Control Torque History (Nm) Introduction Motion Planning Reduction method Practical cost function Example Conclusion Insert Name as Header & Footer

20. Introduction Motion Planning Reduction method Practical cost function Example Conclusion James Biggs

21. Introduction Motion Planning Reduction method Practical cost function Example Conclusion James Biggs

22. 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 Conclusion James Biggs

23. Thank You for your attention Questions?