Minimum-Fuel Orbit Design/Transfer in Earth Orbiting Missions

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

Minimum-Fuel Orbit Design/Transfer in Earth Orbiting Missions 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.

Minimum-Fuel Orbit Design/Transfer in Earth Orbiting Missions • Low altitude orbits = lack of coverage. • Electric propulsion to increase coverage in selected regions.

Minimum-Fuel Orbit Design/Transfer in Earth Orbiting Missions Typical example is to have a set of 20 sites on the terrestrial surface to be visited within 50 days.

Minimum-Fuel Orbit Design/Transfer in Earth Orbiting Missions Objective of Research • Find orbits that enable remote sensing missions with minimum usage for propulsion systems

Minimum-Fuel Orbit Design/Transfer in Earth Orbiting Missions 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

Minimum-Fuel Orbit Design/Transfer in Earth Orbiting Missions • 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

Minimum-Fuel Orbit Design/Transfer in Earth Orbiting Missions

Minimum-Fuel Orbit Design/Transfer in Earth Orbiting Missions Golman and Kogan: Active Solution for this case implements thrusters continuously all time, fuel consumption 5g/day, thrust level of 1mm/s2

Minimum-Fuel Orbit Design/Transfer in Earth Orbiting Missions • In case the solution is not satisfactory, the set of sites, S, is split into two subsets, S1 and S2.

Minimum-Fuel Orbit Design/Transfer in Earth Orbiting Missions • 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

Minimum-Fuel Orbit Design/Transfer in Earth Orbiting Missions • Given S={1,2,3,… N} find the optimal split subsets S1 and S2

Minimum-Fuel Orbit Design/Transfer in Earth Orbiting Missions • Using GA to find minimum-fuel orbit transfer solutions • GA is successfully implemented for impulsive orbit transfers

Minimum-Fuel Orbit Design/Transfer in Earth Orbiting Missions N-Impulse Orbit Transfer Cost function: J = ΣΔv New Formulation proposed using GA

Minimum-Fuel Orbit Design/Transfer in Earth Orbiting Missions Hohman Transfer

Minimum-Fuel Orbit Design/Transfer in Earth Orbiting Missions • Hohman Transfer

Minimum-Fuel Orbit Design/Transfer in Earth Orbiting Missions Single Impulse Maneuver

Minimum-Fuel Orbit Design/Transfer in Earth Orbiting Missions 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 Minimum-Fuel Orbit Design/Transfer in Earth Orbiting Missions Parking to GEO Transfer

Minimum-Fuel Orbit Design/Transfer in Earth Orbiting Missions 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 Minimum-Fuel Orbit Design/Transfer in Earth Orbiting Missions To be developed: • Develop minimum-fuel solutions for dynamic targets

Minimum-Fuel Orbit Design/Transfer in Earth Orbiting Missions Anticipated Results Proposed solution Guelman and Kogan solution

Minimum-Fuel Orbit Design/Transfer in Earth Orbiting Missions