Minimum Energy Trajectories for Techsat 21 Earth Orbiting Clusters Edmund M C Kong SSL Graduate Research Assistant Prof david w. miller Director, MIT Space Systems Lab Space 2001 Conference& Exposition Albuquerque August28-30,2001
Minimum Energy Trajectories for Minimum Energy Trajectories for Techsat Techsat 21 Earth Orbiting Clusters Earth Orbiting Clusters Edmund M. C. Kong SSL Graduate Research Assistant Prof David W. Miller Director, MIT Space Systems Lab Space 2001 Conference & Expositi o n Albuquerque August 28-30, 2001
Objective and outline Objective To determine the optimal trajectories to re orient a cluster of spacecraft Motivation To maximize the full potential of a cluster of spacecraft with minimal resources Presentation Outline · Techsat21 Overview Results Optimal control Formulation Tolerance setting Equations of Motions Cluster Initialization Dynamics) Cluster Re-sizing Propulsion System(Cost) (Geolocation) LQ Formulation Future Work Terminal Constraints Conclusions Space Systems Laboratory Massachusetts Institute of Technology
Space Systems Laboratory Massachusetts Institute of Technology Objective and Outline Objective and Outline Objective : To determine the optimal trajectories to reorient a cluster of spacecraft Motivation : To maximize the full potential of a cluster of spacecraft with minimal resources Presentation Outline • Techsat 21 Overview • Optimal Control Formulation – Equations of Motions (Dynamics) – Propulsion System (Cost) – LQ Formulation – Terminal Constraints • Results – Tolerance setting – Cluster Initialization – Cluster Re-sizing (Geolocation) • Future Work • Conclusions
Techsat 21 To explore the technologies required to enable a distributed satellite System Sparse Aperture Space Based Radar Full operational system of 35 clusters of 8 satellites to provide global coverage 2003 Flight experiment with 3 spacecraft Techsat 21 Flight Experiment Spacecraft will be equipped with Hall Thrusters Number of Spacecraft 3 Spacecraft Mass :1294kg 2 large thrusters for orbit raising and de-orbit Cluster Size :500m 10 micro-thrusters for full three. Orbital Altitude :600km axis control Orbital Period 84 mins Figure courtesy of AFOSR Techsat21 Geo-ocation size Research Review(29 Feb-1 Mar 2000 5000m Space Systems Laboratory Massachusetts Institute of Technology
Space Systems Laboratory Massachusetts Institute of Technology Techsat Techsat 21 • To explore the technologies required to enable a Distributed Satellite System • Sparse Aperture Space Based Radar • Full operational system of 35 clusters of 8 satellites to provide global coverage • 2003 Flight experiment with 3 spacecraft • Spacecraft will be equipped with Hall Thrusters Techsat 21 Flight Experiment Number of Spacecraft : 3 Spacecraft Mass : 129.4 kg Cluster Size : 500 m Orbital Altitude : 600 km Orbital Period : 84 mins – 2 large thrusters for orbit raising and de-orbit – 10 micro-thrusters for full threeaxis control * Figure courtesy of AFOSR Techsat21 Geo-location size : 5000 m Research Review (29 Feb - 1 Mar 2000)
Equations of Motions First order perturbation about natural circular Keplerian orbit Modified Hill's Equations 0r=-152-2)nx-2(nc)y (velocity vector) a,=j+2(nc)i a =z+k where 3E[1+3cs(2 √1+s re 3nJR- k=nv1+s+ Possible trajectory for Techsat 21: 200+-----i----i-Zx1 Ellipse i cOS Eliptical Trajectory x=A cos(ntv1-s) 0 2√1+s R-200 A sin(nt S 400 ------ Projected Ci 400 2√1+s A coS(kt -200 S Cross axis 400400 Velocity Vector Space Systems Laboratory Massachusetts Institute of Technology
Space Systems Laboratory Massachusetts Institute of Technology Equations of Motions Equations of Motions • First order perturbation about natural circular Keplerian orbit • Modified Hill’s Equations: ( ) ( ) ( ) 2 2 2 5 2 2 2 x y z a x c n x nc y a y nc x a z k z = − − − = + = + && & && & && cos( 1 ) 2 1 sin( 1 ) 1 2 1 cos( ) 1 o o o x A nt s s y A nt s s s z A kt s = − + = − − − + = − − • Possible trajectory for Techsat 21: -400 -200 0 200 -400 400 -200 0 200 400 -400 -200 0 200 400 Velocity Vector Elliptical Trajectory Projected Circle 2x1 Ellipse Cross Axis Z eni t h-Nad i r ( ) 2 2 2 3 1 3cos 2 8 e ref ref J R s i r = + ⎡ ⎤ ⎣ ⎦ where c s = 1+ ( ) 2 2 2 2 3 1 cos 2 e ref ref nJ R k n s i r = + + ⎡ ⎤ ⎣ ⎦
Propulsion Subsystem (Hall Thrusters)// High specific impulse low propellant expenditure Electrical power required e 2mn where 200 W Hall 100-200W m-mass of spacecraft (129. 4 kg) Thruster Hall thruster u -spacecraft acceleration(m/s) BHT-200-X2B Hal Thruster m -mass flow rate of propellant (kg/s)Specific Impulse :1530s n- thruster efficiency (% Thrust :10.5mN Mass flow rate 0.74mg/s Objective is to minimize electrical Typical Efficiency :42% energy required: Power Input :200W Pdt Figures courtesy of AFoSR Techsat21 Research Review(29 Feb-1 Mar 2000) Space Systems Laboratory Massachusetts Institute of Technology
Space Systems Laboratory Massachusetts Institute of Technology Propulsion Subsystem (Hall Thrusters) Propulsion Subsystem (Hall Thrusters) • High specific impulse – low propellant expenditure mη m u Pe 2 & 2 2 = where m - mass of spacecraft (129.4 kg) u - spacecraft acceleration (m/s) - mass flow rate of propellant (kg/s) - thruster efficiency (%) m & η BHT-200-X2B Hall Thruster Specific Impulse : 1530 s Thrust : 10.5 mN Mass flow rate : 0.74 mg/s Typical Efficiency : 42% Power Input : 200 W 200 W Hall Thruster * * Figures courtesy of AFOSR Techsat21 Research Review (29 Feb - 1 Mar 2000) • Objective is to minimize electrical energy required: ∫ = f ott J Pedt • Electrical power required: 100 - 200 W Hall Thruster *