Minimum-Fuel Orbit Design/Transfer in Earth Orbiting Missions

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Minimum-Fuel Orbit Design/Transfer in Earth Orbiting Missions Ossama Abdelkhalik Assistant Professor Michigan Technological University Department of Mechanical Engineering. Minimum-Fuel Orbit Design/Transfer in Earth Orbiting Missions. Background and Motivation.

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Minimum-Fuel Orbit Design/Transfer in Earth Orbiting MissionsOssama AbdelkhalikAssistant ProfessorMichigan Technological UniversityDepartment of Mechanical Engineering

Background and Motivation

• Considering a remote sensing mission:
• The orbit selection dictates:
• Ground resolution,
• Area coverage, and
• Frequency of coverage parameters.
• Electric propulsion systems are used at low altitudes for drag compensation.
• Low altitude orbits = lack of coverage.
• Electric propulsion to increase coverage in selected regions.

Typical example is to have a set of 20 sites on the terrestrial surface to be visited within 50 days.

Objective of Research

• Find orbits that enable remote sensing missions with minimum usage for propulsion systems

Technical Approach

• Natural orbit: Ground track of a natural orbit passes through the sites without propulsion
• Propulsion compensates perturbations
• For a given set of sites:

search for the natural orbit

• Optimization problem
• Penalty function: how far is
• the orbit from being an exact natural solution.
• Penalty function depends on mission objectives.
• Maximum Resolution Mission
• Maximum Observation Time Mission

Golman and Kogan: Active Solution for this case implements thrusters continuously all time, fuel consumption 5g/day, thrust level of 1mm/s2

• In case the solution is not satisfactory, the set of sites, S, is split into two subsets, S1 and S2.
• Find the optimal split to minimize the mission cost:
• The cost of orbit transfer between the orbits of the different subsets of sites
• The cost of each subset orbit
• Given S={1,2,3,… N}

find the optimal split subsets S1 and S2

• Using GA to find minimum-fuel orbit transfer solutions
• GA is successfully implemented for impulsive orbit transfers

N-Impulse Orbit

Transfer

Cost function:

J = ΣΔv

New Formulation

proposed using GA

Hohman Transfer

• Hohman Transfer

Single

Impulse

Maneuver

Parking to GEO Transfer

Parking to GEO Transfer

Solution

ΔiI

ΔiF

ΔvKm/sec

Optimal

3.305

25.195

4.05897

Final

3.244

25.256

4.0590

GA

3.300

25.257

4.0610

Parking to GEO Transfer

To be developed:

• Optimal splitting algorithm
• Optimal orbit transfer using GA for continuous thrust systems
• Develop minimum-fuel solutions for dynamic targets

Updated Orbit

Current Orbit

Dynamic Target at its previous location

2

1

After moving

To be developed:

• Develop minimum-fuel solutions for dynamic targets

Anticipated Results

Proposed solution

Guelman and Kogan solution

Anticipated Results

Proposed solution

Guelman and Kogan solution