Optimization Samples

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These sample Mission Plans show examples of working with FreeFlyer's Optimizer object. After exploring these Mission Plans, continue to the Optimization guide for more information.

 

Jump to a Mission Plan Description:

 

Mission Plan

Engineer

Mission

Coverage Time Optimization

 

Hohmann Transfer Optimization

 

Minimize Analytic Function With Known Derivatives

 

Optimal Earth Mars Transfer

 

Optimal Lunar Gravity Assist

 

Optimal Orbit Raise

 

Optimizer Seeded From Targeter

 

 

Coverage Time Optimization

This Mission Plan illustrates the use of FreeFlyer's optimization capability to configure a constellation of 30 Spacecraft for coverage of a region. The constellation is divided into five planes with six Spacecraft per plane. The optimizer varies the inclination of the planes and the semi-major axis of the Spacecraft. A cost function is established based on the semi-major axis. This enables FreeFlyer to find the best coverage at the lowest altitude. Coverage is optimized over the period of 1/4th of a day. FreeFlyer first runs a propagation loop inside the optimization process to compute the optimal solution. It will then run a final pass of the propagation loop, using the best solution found by the Optimizer, to visualize the results.

 

View of optimal constellation configuration

View of optimal constellation configuration

 

Hohmann Transfer Optimization

This Mission Plan illustrates the use of FreeFlyer's optimization capability to model a transfer between two circular orbits. The Optimizer minimizes the necessary total delta-v across two maneuvers to achieve the desired orbit altitude. A Hohmann transfer uses the least delta-v to transfer a spacecraft between two circular orbits; therefore, a Hohmann transfer is the expected result.

 

View of final Hohmann transfer trajectory

View of final Hohmann transfer trajectory

 

Minimize Analytic Function With Known Derivatives

This Mission Plan demonstrates the use of FreeFlyer's optimization capabilities to minimize an analytic function with known derivatives. The user can choose to solve either the Rastrigin or Rosenbrock function and whether to use numeric or analytic derivatives. Once an optimization configuration is selected, FreeFlyer plots the function using a GraphicsOverlay and solves for the minimum point using the Optimizer.

 

Display of minimum point found in Rosenbrock function

Display of minimum point found in Rosenbrock function

 

Optimal Earth Mars Transfer

This Mission Plan illustrates the use of FreeFlyer's optimization capability to design an optimal Earth to Mars transfer using two impulsive burns. The user can choose the departure and arrival ranges for the analysis as well as whether to minimize delta-V or time of flight. During the optimization process FreeFlyer displays the scaled Jacobian color coded to show the relative correlation of the Constraints and State Variables. This Mission Plan uses the NLopt optimization system.

 

View of Earth to Mars transfer trajectory which minimizes total delta-V

View of Earth to Mars transfer trajectory which minimizes total delta-V

 

Optimal Lunar Gravity Assist

This Mission Plan illustrates the use of FreeFlyer's optimization capability to model an optimal lunar flyby for insertion into a highly elliptical Earth orbit. In order to break the difficult problem down into smaller, more easily solved problems, multiple segments are defined. The Optimizer then patches these segments together while satisfying mission constraints.

 

Views of preliminary and final results of optimization processes

Views of preliminary and final results of optimization processes

 

Optimal Orbit Raise

This Mission Plan illustrates the use of FreeFlyer's optimization capability to raise a spacecraft's orbit using one finite burn. FreeFlyer finds the optimal burn duration and true anomaly at which to begin the maneuver to minimize the required delta-v.

 

View of final orbit raising trajectory which minimizes delta-v

View of final orbit raising trajectory which minimizes delta-v

 

Optimizer Seeded From Targeter

This Mission Plan uses FreeFlyer's optimization capability to minimize the total required delta-V of a finite maneuver to adjust a Spacecraft's elliptical orbit to achieve a longitude of 265 degrees at apogee. A Targeting loop is run before the optimization process to generate initial guesses for the burn parameters, which are then passed in to the Optimizer as initial values.

 

View of final trajectory achieving desired longitude at apogee

View of final trajectory achieving desired longitude at apogee