Control ofspacecraftswarmsoct01
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This document discusses using Coulomb forces for controlling spacecraft swarms by charging the spacecraft to different voltages. It finds that Coulomb forces can be comparable to state-of-the-art electric thrusters. Analysis shows stable orbital configurations exist for formations of 3 or 5 spacecraft oriented in different ways and separated by around 10 meters. Ongoing work includes examining formation stability, developing dynamic simulations, and formulating control laws to further explore using Coulomb forces for precision formation flying and space-based interferometry missions.
Control ofspacecraftswarmsoct01
- 1. Advanced Space P Propulsion Laboratory Control of Spacecraft Swarms Using Coulomb Forces Lyon B. King Gordon G. Parker Jer-Hong Chong Satwik Deshmukh Department of Mechanical Engineering This research made possible through funding from the NASA Institute for Advanced Concepts
- 2. Advanced Space P Propulsion Laboratory Motivation: Coulomb Clusters Laser-cooled trapped ion research at NIST “How to build a tractor beam Without gravitons” • Ions in 1/r2 confining potential form stable crystal formations • What would charged spacecraft do in a gravity potential?
- 3. Advanced Space P Propulsion Laboratory Presentation Overview • Introduction to formation flying • Space-based imaging and interferometry • Formation propulsion requirements • Spacecraft charging as control force • Coulomb force metrics • Coulomb formation orbital dynamics
- 4. Advanced Space P Propulsion Laboratory Space-based Imaging Concepts Space-based imaging problem: • Image resolution limited by size of aperture: θ=λ/d …but… • Spacecraft size limited by launch vehicle fairing (~ 4m) Solution #2: Separated Interferometer d effective Combiner Collector Collector Solution #1: Deployable structure d
- 5. Advanced Space P Propulsion Laboratory Interferometry Basics • Spatial frequencies in the image are given by u,v points • Each unique physical separation yields amplitude at one u,v point Two Spacecraft In physical plane (x1,y1) y (x2,y2) d Single amplitude In Fourier plane x (u1,v1) u v u = x2-x1/λ v = y2-y1/λ Inverting Spatial Frequency Spatial Amplitude Image To perform the inversion we need to fill the u,v plane
- 6. 3 Spacecraft 5 Spacecraft 7 Spacecraft 9 Spacecraft 11 Spacecraft Physical Plane Fourier Plane Finite apertures can fill-in Holes in u-v plane Consider single aperture As array of sub-apertures (xi, yi) •Kong, E.M., “Optimal Trajectories and Orbit Design for Separated Spacecraft Interferometry,” Master’s Thesis, MIT Dept. of Aeronautics and Astronautics, November, 1998. •Cornwell, T.J., “A Novel Principle for Optimization of the Instantaneous Fourier Plane Coverage of Correlation Arrays,” IEEE Trans. On Antennas and Propagation, Vol. 36, No. 8, 1165-1167.
- 7. Advanced Space P Propulsion Laboratory Interferometry for Formations All separations (u,v points) less Than d are covered by a single aperture (xi, yi) (xj, yj) d Separations (u,v points) greater than d Must come from separated spacecraft > d Implication: • To provide seamless u,v coverage spacecraft must fly within close proximity (~ d) of each other
- 8. Advanced Space P Propulsion Laboratory Formation Flying Introduction Optimal imaging configurations yield non-optimal orbital trajectories Rigid Formation Non-inertial Orbit Inertial Orbit Non-inertial Orbit • Requires constant thrust • Good imaging properties Dynamic Formation Family of inertial orbits Time-varying position About center satellite • Thrust only for error correction • Complicated imaging
- 9. Advanced Space P Propulsion Laboratory Propulsion Requirements Hill’s Equations for Formation F x F F y = − Ω − Ω 3 2 && & = + Ω && & For rigid formation: &x& = x& = &y& = y& = ... = 0 3 2 F x xm z = − Ω Fx ~ 16 μN 2 F = Ω zm Fz ~ 6 μN m = 100 kg x, z ~ 10 m z z m y x m x x y m z 2 2 2 = && +Ω Figure reprinted from Kong, E.M., “Optimal Trajectories and Orbit Design for Separated Ω = angular velocity (for GEO Ω =7.3x10-5 rad/sec) Spacecraft Interferometry,” Master’s Thesis, MIT Dept. of Aeronautics and Astronautics, November, 1998.
- 10. Advanced Space P Propulsion Laboratory Coulomb Control Forces • Engineering throttleable thrusters for 10 μN is tough • Current candidates (FEEP, Colloid) exhaust contaminants • Collisions are of paramount concern Is there a better way to control the formation? M YaEySb!e! 10-3 10-4 10-5 10-6 Coulomb Force (N) 10 20 30 40 50 60 70 Spacecraft Separation (m) 6 kV 8 kV 10 kV If the plasma Debye length is larger than spacecraft separation, Coulomb forces could be used 1 2 d Spacecraft 1 at Voltage Vsc1 Spacecraft 2 at Voltage Vsc2 Vsc1 = Vsc2 Spacecraft radius = 1 m GEO plasma conditions − = d F r r V V sc sc o d 1 2 1 2 d λ 4πε exp 2 1,2
- 11. Advanced Space P Propulsion Laboratory Spacecraft Charging Spacecraft Plasma e-current Plasma H+ current Photoelectron current e- Isc = Ie + Ii + Iph 1 I A en k T exp = sc e sc e k T B e B e e eV m 2 2 π − 1 I A en k T exp = − sc i sc i k T B i B i i eV m 2 2 π − = − I A eα I exp eV ph sc w pe k T sc B pe For equilibrium, Mother Nature adjusts spacecraft voltage such that net current is zero. Icontrol We can change the spacecraft voltage by creating a current imbalance 0 I I I sc e i ph πε 4 = + + I = = r C dV dt o + Icontrol 0
- 12. Advanced Space P Propulsion Laboratory Spacecraft Charge Control • Electron emission drives Vsc positive • Ion emission drives Vsc negative • Spacecraft potential control is naturally stable + + + + Vcontrol + + Vspacecraft V x Vplasma (God’s ground) Vspacecraft Vcontrol + + + Vcontrol Vspacecraft When Vsc = Vcontrol the emission Current is returned (Icontrol = 0) Vcontrol +
- 13. 1-m-radius spacecraft charging analysis for average GEO plasma environment 3000 2500 2000 1500 1000 500 I = P control V en k T eV en k T α e e I 4 π ε r 2 exp 2 I 4 π r I C dV dt 0 1 2 1 2 2 control sc − − + = = w ph i B i i sc B e B e e m k T m π π 0 0.00001 0.0001 0.001 0.01 0.1 Time (sec) Spacecraft Potential (Volts) P = 0.1 W P = 1 W P = 10 W control
- 14. Advanced Space P Propulsion Laboratory 1 2 2 2 F = πε r P o Total 2 2 control Coulomb d I F P Total sp =η Thruster 2 gI d FCoulomb FCoulomb 1 2 FThruster FThruster Coulomb Control Thruster Control Coulomb vs. Electric Propulsion 107 106 105 104 103 FCoulomb/FThruster at equivalent power Comparison of Coulomb Control for 1-m-radius Spacecraft in average GEO plasma with FEEP Thruster technology (Isp = 10,000 sec, η = 0.65) 1 mWatt 10 mWatts 100 mWatts 1000 mWatts 10 20 30 40 50 60 70 Spacecraft Separation (m)
- 15. Advanced Space P Propulsion Laboratory Mission design parameters for two-spacecraft flying in 20-m formation (located on Hill’s z-axis) COLLOID FEEP THRUSTER COULOMB MICROPPT CONTROL MEANS OF CONTROL SPECIFIC 1 x 107 500 1000 10000 IMPULSE (sec) I F sp & mg = EFFICIENCY 0.65 0.026 0.65 0.65 0.00003 0.089 0.045 0.004 (using H2 for Ion source) MASS OF FUEL FOR 10 YEARS (kg) INPUT POWER (W) 0.031 0.261 0.021 0.209 MASS/POWER 0.22 0.37 0.216 0.1125 RATIO (kg/W) INERT MASS (kg) 0.0068 0.097 0.005 0.024 TOTAL PROPULSION 0.00683 0.186 0.050 0.028 SYSTEM MASS (kg)
- 16. Advanced Space P Propulsion Laboratory Coulomb Orbit Dynamics Do formations exist for forces acting only along position vectors? Figure reprinted from Kong, E.M., “Optimal Trajectories and Orbit Design for Separated Spacecraft Interferometry,” Master’s Thesis, MIT Dept. of Aeronautics and Astronautics, November, 1998. • 3-spacecraft formations considered • 3 canonical orientations • Hill’s equations for relative motion • GEO orbit with 10-m separation x z y x z y x z y Along-track “leader-follower” Zenith-nadir “Coulomb tether” Z-axis stack
- 17. Advanced Space P Propulsion Laboratory 3-Spacecraft Orbital Analysis Equilibrium solutions to Hill’s equations V 1 q πε sc o sc sc o sc 4 = V r q r πε 4 = x z y x z y x z y Along-track “leader-follower” Zenith-nadir “Coulomb tether” Z-axis stack 0 2 1 0 1 2 0 1 2 Parameter Vscr is like equivalent charge:
- 18. x y z 10 m 10 m Spacecraft 1 Spacecraft 3 Spacecraft 2 Spacecraft 4 Spacecraft 0 4 collector + 1 combiner Imaging configuration
- 19. Advanced Space P Propulsion Laboratory 5-Spacecraft Formation 1 2 3 4 Solution Family 1 0 • Special case of 3-spacecraft z stack • Vehicle 2 and 4 remain neutral
- 20. Advanced Space P Propulsion Laboratory 1 2 3 4 0 5-Spacecraft Formation Solution Family 2 Spacecraft 1 & 3 Spacecraft 0 • All 5 Spacecraft charged • Minimum Vscr identified
- 21. Advanced Space P Propulsion Laboratory Phase I Summary Conclusions • Coulomb forces comparable with best thrusters • Continuous force dither/variation is possible • Required charge control demonstrated as early as 1979 (SCATHA) • Rich family of orbital solutions possible • Particularly suited to Fizeau interferometry (visible GEO imager?) • Coulomb control works best where thrusters work worst => synergistic control • Coulomb control can help with collision avoidance • Even if Coulomb is not used for control…… natural charging will be significant perturbation that must be addressed! On-going tasks • Examine formations for stability • Develop dynamic simulation • Formulate control laws • Search for more complicated formation solutions • Perform vehicle sizing analysis for canonical mission