Copernicus, A Generalized Trajectory Design and Optimization System Greg Johnson Sebastian Munoz The University of Texas at Austin November 25, 2003

Overview What is trajectory design and optimization? What makes this problem so difficult? The necessity for a generalized trajectory system Existing systems The Copernicus trajectory system Conclusions

What is trajectory design and optimization? Finding the best trajectories for a given mission Example: Moon Capture Earth/Moon trajectory Ballistic 3rd body perturbation Trajectory produced with Copernicus, created in SOAP by Sebastian Munoz

What makes this problem so difficult? What is the best trajectory? Minimized parameters Total ΔV Time of flight Maximized parameters Payload capacity Excess fuel Finding a trajectory with optimal values for one or all of these parameters

The necessity of a general system “Not limited in scope, area or application” –The American Heritage Dictionary of the English Language Capabilities of a general system ΔV minimization Time of flight minimization Payload maximization Excess fuel maximization Multiple segments for a trajectory Such a system would satisfy the needs for any mission, including complex interplanetary trajectories

Some other systems VARITOP CHEBYTOP MIDAS SEPSPOT GESOP & ASTOS Strengths and weaknesses

VARITOP “General two-body, sun-centered trajectory design and optimization program” Low thrust trajectories only

CHEBYTOP “General two-body, sun-centered trajectory design and optimization program” Computationally quick, but inaccurate Quick mission planning, but future analysis required

MIDAS “Patched-conic interplanetary trajectory solver” Minimizes ΔV and mass, not time Difficult to use, large input files Created to verify the validity of results from other programs

SEPSPOT Computes trajectories for electrically propelled spacecraft Considers wide range of forces Only minimizes time Good for Orbital eccentricities less than .65

GESOP & ASTOS “Graphical Environment for Simulation and OPtimization” Can simulate any dynamical system Uses ASTOS application for spacecraft trajectory optimization Requires large amount of input Result accuracy may be affected by broadness of problems it can solve

Inspiration Copernicus developed to combine capabilities of other programs, without their weaknesses Development began Fall 2001 by Dr. Cesar Ocampo

Copernicus Trajectory System Goals Solve any type of trajectory problem Initial and final states Fixed or variable Parameters to minimize or maximize Any or all Methods used “Basic” trajectory segment Ocampo, Cesar, “An Architecture for a Generalized Spacecraft Trajectory Design and Optimization System,” The University of Texas at Austin, Austin, TX, 2003.

The Trajectory Segment Allows boundary conditions to be specified Allows discontinuities Fixed/free parameters Numerical methods used to solve the problem Ocampo, Cesar, “An Architecture for a Generalized Spacecraft Trajectory Design and Optimization System,” The University of Texas at Austin, Austin, TX, 2003.

What it can do… 2-body transfer/rendezvous Return trajectories Libration point considerations Low thrust trajectories Gravity assists Ballistic/low energy captures using third-body effects

Conclusions General system is necessary Saves mission design time, and man hours Reliable for any conceivable problem Copernicus is the most general trajectory design and optimization system available combines features of other programs without their weaknesses Copernicus is still a prototype, hence there is still a lot to be done – i.e. graphical user interface, OpenGL graphics

References For more information about the trajectory systems discussed, see: Ocampo, Cesar, “An Architecture for a Generalized Spacecraft Trajectory Design and Optimization System,” The University of Texas at Austin, Austin, TX, 2003. http://trajectory.grc.nasa.gov/Tools http://www.astos.de