卫星工程英文版（二）：l11_ff_1_imaging

Space Systems Laboratory Massachusetts Institute of Technology Optimization of Separated Spacecraft Interferometer Trajectories in the Absence of A Gravity-WellAbsence of A Gravity-Well Edmund M. Kong Prof David W. Miller MIT Space Systems Laboratory 20 th March 1998 Space Systems Laboratory Massachusetts Institute of Technology Objective & Approach Objective : Determine the optimal synthetic imaging trajectory for a Separated Spacecraft Interferometer Image Quality Optimization Comparison with Other Alternatives Other Considerations Trajectory Optimization Mass Metric Time Metric Uniformly Spaced U-V Points DS3 Performance Metric Optimal System Mass Trade-offs Space Systems Laboratory Massachusetts Institute of Technology Image Quality Model : 2 Collector and 1 Combiner Interferometer (DS 3) Physics : Average Image Intensity Combiner CollectorCollector ∑ ∑ = = ? ? ? ? ? ? + ? ? ? ? ? ? ≈ ? ? ? ? ? ? + ? ? ? ? ? ? ? ? ? ? ? ? ? ? + = N k kj k i N k kj k iD D ji y x D N y x JD N I 1 22 1 2 sin sin 1 2 2 )(cos2 21 )(cos2 )( )cos1(1 ),( ?? λ π λ π ?? λ π λ θπ ?? λ θπ λ θπ Space Systems Laboratory Massachusetts Institute of Technology Image Quality - Mean Square Error Minimize : () mm II MSE m i m j o jiji × ? = ∑∑ ==11 ),(),( 2 ???? Approach : Choose N subset of all points : Compare with Nominal PSF : Simulated Annealing Optimization Technique Results : Image quality increases with no. of imaging points (N) : Diminishing rate of return 0 100 200 300 400 0 0.5 1 1.5 No. of Imaging Points M SE, (W m -2 ) 2 (x 1 0 -3 ) Best MSE Performance Space Systems Laboratory Massachusetts Institute of Technology Point Spread Function Images 41 Imaging Points 201 Imaging Points 281 Imaging Points 121 Imaging Points Space Systems Laboratory Massachusetts Institute of Technology Trajectory Optimization - Mass Metric Minimize : ? ? ? ? ? ? ∑ ?±= = N i s i imageimage fuel fuel a N TT m m 1 4 2 2 & Assumptions : “Stop and Stare” imaging mode : Trapezoidal velocity profile : Constant acceleration Parameters : Spacecraft masses Collector = 150 kg Combiner = 250 kg : Cold Gas Propulsion I sp = 62.5 s, F = 9 mN Constraint : T image = 264 Hours Approach : Traveling Salesman Algorithm 0 100 200 300 400 0 0.2 0.4 0.6 0.8 1 No. of Imaging Points Fu e l (k g ) Fuel Expended Per Image Result : Fuel mass increases with no. of imaging points (N) Space Systems Laboratory Massachusetts Institute of Technology Trajectory Optimization - Time Metric Minimize : ∑ = = N n i s a T 1 2 0 100 200 300 400 0 50 100 150 200 250 300 No. of Imaging Points T i m e (H rs ) Least Maneuvering Time Per Image Assumptions : “Stop and Stare” imaging mode : Triangular velocity profile : Small Integration Time Parameters : Spacecraft masses Collector = 150 kg Combiner = 250 kg : Pulse Plasma Thrusters I sp = 1000 s, F = 1.4 mN Constraint : S/C Power 80 W Approach : Traveling Salesman Algorithm Result : Imaging time increases with no. of imaging points Space Systems Laboratory Massachusetts Institute of Technology Other Alternatives -500 0 500 -500 0 500 X (m) Y ( m ) 67 Uniformly Spaced Imaging Points -500 0 500 -500 0 500 X (m) Y ( m ) Proposed DS3 Trajectory Proposed DS3 Reference : Linfield, JPL Uniformly Spaced Space Systems Laboratory Massachusetts Institute of Technology PSF Comparison 281 Optimal MSE Imaging Points Proposed DS3 (261 Points) 231 Uniformly Spaced Imaging Points Space Systems Laboratory Massachusetts Institute of Technology Fuel and Time Metrics vs MSE 10 -5 10 -4 10 -3 10 -2 0 0.2 0.4 0.6 0.8 1 1.2 MSE (W m -2 ) 2 Fu e l ( k g ) Fuel Expended vs Image Quality Proposed DS3 Uniform Spacing Optimized MSE 10 -5 10 -4 10 -3 10 -2 0 50 100 150 200 250 300 350 MSE (W m -2 ) 2 T i m e (H o u rs ) Maneuvering Time vs Image Quality Proposed DS3 Uniform Spacing Optimized MSE Result : Better MSE with lower fuel consumption or shorter imaging time Space Systems Laboratory Massachusetts Institute of Technology Other Considerations Psi x Ps i y Main Lobe Comparison DS3 (261 Points) Uniformly Spaced (231 Points) Optimized MSE (281 Points) 0 50 100 150 200 250 300 350 0 1 2 Image Quality versus Fuel Trade-off No. of Imaging Points M SE, ( W m -2 ) 2 (x 1 0 -3 ) 0 0.5 1 Fu e l ( k g ) Main Lobe Comparison Trade-off -500 0 500 -500 0 500 X (m) Y ( m ) Imaging Time = 74 Hours “Image on the Fly” 2 3 4 5 6 7 5 7 9 11 500 1000 1500 No. of S/C Total System Mass Required (500 Images) No. of Cornwell Points M a ss ( k g ) Extension to N spacecraft Reference : Linfield, JPL Space Systems Laboratory Massachusetts Institute of Technology Conclusion ? Determined the optimal imaging locations ? Determined the optimal trajectories – Mass metric – Time metric 0 100 200 300 400 0 0.2 0.4 0.6 0.8 1 No. of Imaging Points Fue l ( k g) Fuel Expended Per Image 0 100 200 300 400 0 50 100 150 200 250 300 No. of Imaging Points T i m e (H rs ) Least Maneuvering Time Per Image ? Compared with other alternatives ? Future considerations – MSE versus Mass trade-off – MSE versus Time trade-off – Extension to N spacecraft – “Image on the Fly” mode – Other Metrics 10 -5 10 -4 10 -3 10 -2 0 50 100 150 200 250 300 350 MSE (W m -2 ) 2 T i m e (Ho u rs ) Maneuvering Time vs Image Quality Proposed DS3 Uniform Spacing Optimized MSE 2 3 4 5 6 7 5 7 9 11 500 1000 1500 No. of S/C Total System Mass Required (500 Images) No. of Cornwell Points Ma s s ( k g ) Space Systems Laboratory Massachusetts Institute of Technology Simulated Annealing ? Statistical Approach ? Randomly select a configuration and calculate cost, C r – If C r < C r-1 accept r th configuration – If C r > C r-1 accept r only if exp(-C r /T) > Random(0,1) – when C r is accepted, decrease T (system temperature) – Continue until system is frozen (no new solution accepted in N trials) ? Does not guarantee global minimum ? Quick and easy implementation ? Reasonable solution achieved in short computation time ? Reference: – S. Kirkpatrick, C. D., Gelatt, Jr., M. P. Vecchi, “Optimization by Simulated Annealing”, Science, Volume 220, Number 4598, 13 th May 1983.