Optimization of Separated spacecraft Interferometer Trajectories in the Absence of A Gravity-Well Edmund M. Kong Prof david w. miller MIT Space Systems Laboratory 20th March 1998 Space Systems Laboratory Massachusetts Institute of Technology
Space Systems Laboratory Massachusetts Institute of Technology Optimization of Separated Spacecraft Interferometer Trajectories in the Absence of A Gravity-Well Optimization of Separated Spacecraft Optimization of Separated Spacecraft Interferometer Trajectories in the Interferometer Trajectories in the Absence of A Gravity Absence of A Gravity-Well Edmund M. Edmund M. Kong Prof David W. Miller David W. Miller MIT Space Systems Laboratory MIT Space Systems Laboratory 20th March 1998 March 1998
Objective Approach Objective: Determine the optimal synthetic imaging trajectory for a Separated Spacecraft Interferometer Image Quality Optimization Trajectory Optimization Mass metric Time metric Comparison with Other Alternatives Uniformly spaced DS3 U-v points Other considerations Optimal Systel Performance Metric Trade-offs Mass Space Systems Laboratory Massachusetts Institute of Technology
Space Systems Laboratory Massachusetts Institute of Technology Objective & Approach Objective & Approach Objective : Determine the optimal synthetic imaging trajectory for a Determine the optimal synthetic imaging trajectory for a Separated Spacecraft Interferometer Separated Spacecraft Interferometer Image Quality Optimization Image Quality Optimization Comparison with Other Alternatives Comparison with Other Alternatives Other Considerations Other Considerations Trajectory Optimization Trajectory Optimization Mass Metric Mass Metric Time Metric Time Metric Uniformly Spaced Uniformly Spaced U-V Points V Points DS3 Performance Metric Performance Metric Optimal System Optimal System Trade Mass Trade-offs
Image quality Model 2 Collector and 1 Combiner Interferometer (DS 3) Physics Average Image Intensity q,9)=∑ R I(+COSO)D(J1(X 丌 2Cos:(, xk+O, yR) a pixx+p yk cOS - Nominal Point Spread Function(2601 U-V Points) k=1(A Combiner 807 0.5 1.3 Collector Collector Psi milli-arcsecs -1.3-1.3 Psi milli-arcsecs Space Systems Laboratory Massachusetts Institute of Technology
Space Systems Laboratory Massachusetts Institute of Technology Image Quality Image Quality Model : 2 Collector and 1 Combiner Interferometer (DS 3) Physics : Average Image Intensity Combiner Collector Collector ∑ ∑ = = ⎟⎠⎞ ⎜⎝⎛ ⎟ + ⎠⎞ ⎜⎝⎛ ≈ ⎟⎠⎞ ⎜⎝⎛ + ⎟⎟⎠⎞ ⎜⎜⎝⎛ ⎟⎠⎞ ⎜⎝⎛ + = N k i k j k N k D i k j k D i j x y D N x y D J N I 1 2 2 1 2 sin sin 1 2 2 2 cos ( ) 1 2 2 cos ( ) 1 (1 cos ) ( ) ( , ) ϕ ϕ λ π λ π ϕ ϕ λ π λ π θ ϕ ϕ λ π θ λ π θ
Image Quality. Mean Square Error omo Minimize M△B=(-.) Best mse Performance 15r n×n Approach: Choose N subset of all points Compare with Nominal psf o Simulated Annealing c Optimization Technique Optimized MSE Imaging Locations(N= 201 Poir 500 05 100 200 300 400 No of Imaging Points Results Image quality increases with no of imaging points(N) 500 Diminishing rate of return X(m) Space Systems Laboratory Massachusetts Institute of Technology
Space Systems Laboratory Massachusetts Institute of Technology Image Quality Image Quality - Mean Square Error Mean Square Error Minimize : ( ) m m I I MSE m i m j o i j i j × − = ∑∑ = = 1 1 ( , ) ( , ) 2 ϕ ϕ ϕ ϕ 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 MSE, (W m-2 ) 2 (x 1 0-3 ) Best MSE Performance
Point spread Function Images MsE=14x103Wm2)2 MSE=2.97x 10-0Wm2 05 Psi, milli-arcsecs -1.3-1.3 Psik milli Psi milli-arcsec Psi mi‖ Arcsec 41 Imaging points 121 Imaging Points MsE=123×104wm2 MsE=572×105Wm2 907 05 milli-arcsecs 13-13 Psi milli-arcsecs -1.3-13 201 Imaging points 281 Imaging Points Space Systems Laboratory Massachusetts Institute of Technology
Space Systems Laboratory Massachusetts Institute of Technology Point Spread Function Images Point Spread Function Images 41 Imaging Points 201 Imaging Points 281 Imaging Points 121 Imaging Points
Trajectory optimization. Mass Metric Ako Minimize m felt Image Image ∑S1 Fuel Expended Per Image Assumptions Stop and Stare imaging mode 0.8 Trapezoidal velocity profile 06 Constant acceleration y Parameters Spacecraft masses L04 Collector= 150 kg Combiner= 250 kg 02 Cold Gas Propulsion p=62.5s,F=9mN 200 300 400 Constraint T Image 264 Hours No of Imaging Points Approach Traveling Salesman Result: Fuel mass increases with Algorithm no of imaging points(N Space Systems Laboratory Massachusetts Institute of Technology
Space Systems Laboratory Massachusetts Institute of Technology Trajectory Optimization Trajectory Optimization - Mass Metric Mass Metric Minimize : ⎟⎠⎞ ⎜⎝⎛ = ± − ∑=Ni si image image fuel fuel aN T T 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 Isp = 62.5 s, F = 9 mN Constraint : Timage = 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)
Trajectory Optimization-Time Metric/mo Minimize T Least Maneuvering Time Per Image va n=l 300 Assumptions: "Stop and Stare 250 imaging mode Triangular velocity 200 profile Small Integration Time 0工o Parameters Spacecraft masses Collector 150 k( Combiner 250 kg Pulse plasma thrusters 100 300 400 p=1000sF=14mN No of Imaging Points Constraint S/C Power 80 W Approach Traveling Salesman Result: Imaging time increases Algorithm with no of imaging points Space Systems Laboratory Massachusetts Institute of Technology
Space Systems Laboratory Massachusetts Institute of Technology Trajectory Optimization Trajectory Optimization - Time Metric Time Metric Minimize : = ∑ = N n si a T 1 2 0 100 200 300 400 0 50 100 150 200 250 300 No. of Imaging Points T i m e (Hrs ) 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 Isp = 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
Other alternatives Proposed ds3 Trajectory 67 Uniformly Spaced Imaging Points 500 500 米 φ中 0 500 500 X(m) X(m) Proposed DS3 Uniformly Spaced Reference. Linfield. JPL Space Systems Laboratory Massachusetts Institute of Technology
Space Systems Laboratory Massachusetts Institute of Technology Other Alternatives 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
PSF Comparison MSE=494x104Wm2)2 MsE=460×104Wm2 807 13 Psi( milli-arcsecs 1313 Psi, (milli-arcsecs Psi milli-arcsecs -13-13 Psi milll-arcsecs MSE=5.72x 10(Wm2y 231 Uniformly Spaced Proposed DS3 Imaging Point (261 Points) 07 205 281 Optimal mse Psi milli-arcsecs 13-13 Psi milli-arcsecs Imaging Points Space Systems Laboratory Massachusetts Institute of Technology
Space Systems Laboratory Massachusetts Institute of Technology PSF Comparison PSF Comparison 281 Optimal MSE Imaging Points Proposed DS3 (261 Points) 231 Uniformly Spaced Imaging Points
Fuel and Time Metrics vs MsE &ata Fuel Expended vs Image Quality Maneuvering Time vs Image Quality 350 1.2 300 250 Proposed DS3 Proposed DS3 08 3200 设 Uniform Spacing 0.6 g150 Uniform Spacing 0.4 100 Optimized MSI 02 Optimized MSE 0 0 10 10 MSF /A/ m-2:2 MSE AN m-22 Result: Better MSE with lower fuel consumption or shorter imaging time Space Systems Laboratory Massachusetts Institute of Technology
Space Systems Laboratory Massachusetts Institute of Technology Fuel and Time Metrics 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 urs ) Maneuvering Time vs Image Quality Proposed DS3 Uniform Spacing Optimized MSE Result : Better MSE with lower fuel consumption or shorter imaging time
