ACT GLOBAL OPTIMIZATION COMPETITION

Transcription

1 ACT GLOBAL OPTIMIZATION COMPETITION Page 1 Team 14: Alcatel Alenia Space Vincent Matinot Mission Analysis in the Science and Obsevation Diectoate Thiey Dagent Reseach goup on Platom & Satellite 02/02/2006, 1st ACT Global Tajectoy Optimiion Competition All ights eseved 2005, Alcatel Alenia Space

2 PROPOSED OPTIMIZATION METHOD Page 2 The poposed solution is based on T_3D, an intenal tool poviding solutions o the optimal obit tanse poblem. The theoy behind this tool is the application o the maximal pinciple and the utilization o continuation and smoothing techniques. To solve the poblem, the cost citeia has been intoduced in the sotwae by application o the maximal pinciple and the necessay conditions o optimality has been deived. NB: Multiple ly-by solution haven t been eally assessed in the time ame o the competition 02/02/2006, 1st ACT Global Tajectoy Optimiion Competition All ights eseved 2005, Alcatel Alenia Space

3 Tajectoy summay Page 3 The poposed solution has the ollowing eatues: Depatue date 21/04/ :00:00 Aival date 04/02/ :56:54 time o light yeas Vin Depatue 2.5 km/s Vin Aival km/s Satellite initial mass 1500 kg Satellite inal mass kg Total Thust duation J = m U. v el hous kg.km^2/s^2 02/02/2006, 1st ACT Global Tajectoy Optimiion Competition All ights eseved 2005, Alcatel Alenia Space

4 Tajectoy useul paamete Page 4 Satellite ellite sun Sun distance distance in AU in AU On/O on/o Thust thust in N in N Evolution o ellite sun distance in AU Time in Day om the 21/04/ Evolution o ellite Sun distance in AU Total Thust duation e+005 h Total impulse povide to the ellite m/s Time in Days om 21/04/2026 Thust law Thust law tavel days om 21/04/2026 Time in Days om 21/04/2026 The tajectoy has been computed with espect to the constaint on the minimum allowed heliocentic distance o 0.2 A.U. Without this constaint, the tend was to educe the peihelion as much as possible and peom a lage inclination change to invese the tajectoy 02/02/2006, 1st ACT Global Tajectoy Optimiion Competition All ights eseved 2005, Alcatel Alenia Space

5 Citeia intoduction The use o minimum pinciple implies deiving the necessay conditions on the cost citeia to calculate the tajectoy Cost citeia Constaints at t Augmented cost citeia with constaints J = ψ ( x( t m ), t U ) = X el. v X T Φ( x( t ), t ) = J +ν ψ ( x( t ), t ) Page 5 Necessay conditions at t Φ x = J x + X x m = v x T T ν = ( v v ).. v + ν v X x T λ Equation solved by T_3D X T v λ + m x λm X X. v. null = 0 x v ( v v ). Φ( x( t t Equation solved i t is ee + H ( x( t ),, ) u t = 0 ), t ) 02/02/2006, 1st ACT Global Tajectoy Optimiion Competition All ights eseved 2005, Alcatel Alenia Space

6 Optimization pocedue Page 6 A ist un has been peomed to coss the eoid with a minimum time poblem then: 1 st un with the cost citeia initialized with the min time poblem We ound that the geneal tend was to decease the peihelion as much as possible which violated the 0.2 AU constaint Need to intoduce the 0.2 AU state constaint on the path 2 nd un with a mass maximum poblem to impact in a tangential way the eoid at it peihelion and a ellite peihelion o 0.2 AU and the maximum time allowed (multiple case with multiple eoid peihelion in time window) 3 d un with the cost citeia and one intemediate ly path constaint at 0.2AU initialized by the best case o the second un This 3 d un is the solution povided to ACT o the competition 02/02/2006, 1st ACT Global Tajectoy Optimiion Competition All ights eseved 2005, Alcatel Alenia Space

7 Othe bette solution o diect EA Re-wok has been done ate the dead line Page 7 The analysis o the othe team esults on diect tanse (in paticula Team 9) has shown that the global optimization was not ound: many local optima the path constaint o 0.2 AU does help o an automatic scanning Re-wok o the initialization and intoduction o the 0.2 AU peihelion as a teminal condition and not as a ly path constaint Multiple stats with dieent initialization diectly with the inal cost citeia and playing with the smoothing paamete o the sotwae. Extaction o 2 o the best ound solutions 02/02/2006, 1st ACT Global Tajectoy Optimiion Competition All ights eseved 2005, Alcatel Alenia Space

8 EA sequence 2 Page 8 16 Inclinaison Inclinaison in Deg Duation in days Thust and engine on/o in N Thust poile Total thust duation e+005 h DV total m /s D u a tio n in d a y s Depatue date 20/04/ :24:00 Aival date 30/12/ :24:00 time o light yeas Vin Depatue 2.5 km/s Vin Aival km/s Satellite initial mass 1500 kg Satellite inal mass kg Total Thust duation J = m U. v el hous kg.km^2/s^2 02/02/2006, 1st ACT Global Tajectoy Optimiion Competition All ights eseved 2005, Alcatel Alenia Space

9 EA sequence 1 Page 9 16 Inclinaison Inclinaison in Deg Thust and engine on/o in N Thust law Total thust duation: e+005 h D V total m /s D uation in days Duation in days Depatue date 20/04/ :46:34 Aival date 16/01/ :46:34 time o light yeas Vin Depatue 2.5 km/s Vin Aival km/s Satellite initial mass 1500 kg Satellite inal mass kg Total Thust duation hous J = m U. v kg.km^2/s^2 el 02/02/2006, 1st ACT Global Tajectoy Optimiion Competition All ights eseved 2005, Alcatel Alenia Space

10 EA sequence 1 vesus 2 Page 10 Tajectoy in ecliptic plane 02/02/2006, 1st ACT Global Tajectoy Optimiion Competition All ights eseved 2005, Alcatel Alenia Space

11 Conclusion Page 11 Fo diect Eath-Asteoid tajectoy many solutions have been ound (thank to teams 9, 1 and 8) Ou actual best known solution has a cost citeia o kg.km^2/s^2, but has been obtained by putting the 0.2 AU constaint at teminal condition. Bette solutions may exist: thee is no insuance o global optimality The use o minimum pinciple coupled with smoothing technique is a good method to ind optimal contol bang-bang tajectoies in obit tanse It enables to ind athe quickly a pecise solution Fo global optimality the method use alone has some daw which have to be impoved by adding an uppe level algoithm dedicated to the eseach o good initial guess. We enjoyed the paticipation to ACT Global Optimiion Competition and we thank ESA and all the paticipants o this competition 02/02/2006, 1st ACT Global Tajectoy Optimiion Competition All ights eseved 2005, Alcatel Alenia Space