Multi-Objective Trajectory Optimisation

Transcription

1 Multi-Objective Trajectory Optimisation ESR: Elisabetta Iorfida Supervisors: Prof Phil Palmer, Prof Mark Roberts Surrey Space Centre, University of Surrey, UK University of Surrey, Guildford 2 nd 4 th December 2013

2 Personal Background Bachelor s degree (Laurea triennale), 2007 Aerospace Engineering, University of Pisa Thesis: Orbit models of electric sail space vehicles Master's degree (Laurea specialistica), 2011 Aerospace Engineering, University of Pisa MSc Thesis Project Astrodynamics & Satellite missions dept. Delft University of Technology Preliminary Design of Interplanetary Trajectories with Deep Space Manoeuvres 2

3 Personal Background Delft University of Technology project (TU Delft Astrodynamics toolbox) Tudat: a modular and robust astrodynamics Toolbox 5 th ICATT 2012, International Conference on Astrodynamics Tools and Techniques, 29 May 1 June 2012, ESA/ESTEC, Noordwijk, The Netherlands 3

4 PhD Researcher ESR Project Surrey Space Centre, University of Surrey (April 2012 Present) Multi-Objective Trajectory Optimisation Deep Space Manoeuvre (DSM): is a change in velocity at a specific time and position; is described by time (t DSM ), position (r DSM ) and velocity increment ( V DSM ): at least 4 dim space description. Advantage Drawback Decrease total cost ( V tot ) Increase search space complexity Distribution of local minima: a) without DSM and b) with DSM (Vasile and De Pascale, 2006). 4

5 ESR Project Primer Vector Theory/Method Lawden (1963) estimated the necessary conditions (NC) on the primer vector in the case of an optimal finite thrust, for the addition of DSM. Primer vector equation where. Current Approach Propagation along transfer orbit uses the state transition matrix, Drawbacks Propagation of the state transition matrix, that involves the integration of 36 differential equations. Initial condition of the PV can be computed only after the propagation of the STM along all the arc. 5

6 ESR Project Novel Approach New form of the Primer Vector equation: IN PLANE components OUT OF PLANE component Analytic solution for the out of plane component Analytic approximation for the propagation scheme of the in plane components using the Palmer coordinates,,,, (Palmer, 2007) Σ,, Σ 6

7 ESR Project Motivation: the boundary conditions on the primer vector depend only on the direction of the impulses Question: is it possible to fix the transfer orbit and analyse the stability of the trajectory just according to the direction of the Vs? Answer: Yes. Method Polar coordinates reference system: Δ Δ cos sin Δ Δ cos sin For a fixed transfer orbit it is possible to write the complete propagation of the primer vector as cos sin Φ, cos sin and analyse the stability of the orbit just as a function of the angles,, whereφ, is fixed and independent from and. 7

8 ESR Project 8

9 ESR Project 9

10 ESR Project Examples 10

11 Courses and Activities Confirmation Exam, 09 May 2013 Presentation and Viva Exam, Report title Modelling Multi-Objective Trajectory Optimisation, Supervisor Prof P. Palmer, Prof M. Roberts, Examiner Dr C. Tronci (Department of Mathematics, University of Surrey) AstroNet-II Schools - First AstroNet-II Training School, Rome January Second AstroNet-II Training School, Glasgow 3-7 June 2013 Workshops for Post Graduate fellows organized by the University of Surrey - Welcome to Your PhD (FEPS), 24/04/ Engaging with Your Literature, 14/05/ When Do I Start Writing and How?, 14/06/ The PhD Confirmation Process (aka Transfer / Upgrade Exam), 22/11/ Confirmation, Academic Writing: Getting Started, 06/02/ Confirmation Report Writing, 18/02/ Using different tenses effectively in doctoral writing, 20/06/ Removing ambiguity from your doctoral writing: understanding modifiers, 03/07/2013 Outreach activities - SATRO Festival of Science and Engineering at Brooklands Museum, Weybridge (UK), 26/06/2013. Surrey Space Centre - Weekly meetings (Astrodynamics group, one-to-one supervisors meetings) - Monthly Reports - Annual and 6 months reviews (October 2012, May 2013, October 2013) - Open Student Presentation (03/10/ /05/ /10/2013) 11

12 Workshops/Conferences Workshops - Surveillance of Space and Astrodynamics Academic Workshop, 20 th February 2013 International Space Innovation Centre (ISIC), Harwell - 1 st UK Workshop on Optimisation in Space Engineering (OSE), 5 th 6 th November 2013, Birmingham Conference - Celmec VI, Sixth Meeting on Celestial Mechanics, San Martino al Cimino (Viterbo, Italy), 2-6 September Presented a talk and an abstract with the title Modelling mid-course Corrections of Interplanetary Trajectory 12

13 Future Work/Collaboration Journal Papers Paper on the novel propagation method of the primer vector (1),Celestial Mechanics and Dynamical Astronomy Paper on the novel propagation method of the primer vector (2) Paper on the application of the novel propagation method Conference ICNPAA congress: Mathematical problems in engineering, aerospace and sciences, Narvik University, Norway, July 15-18, Internship Companies of the Network, e.g. Thales, ESA or Astrium Collaboration Universities of the Network, e.g. IEEC or Universita di Roma Tor Vergata 13

14 Thank you for your attention! Any questions? 14