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

2. 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

3. 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

4. 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

5. 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

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

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

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

9. 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

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

11. 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

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

13. 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.

14. 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.

15. 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

16. 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

17. 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.