Integrated Orbit and Attitude Control for a Nanosatellite with Power Constraints Bo Naasz Matthew Berry Hye-Young Kim Chris Hall 13th Annual AAS/AIAA Space Flight Mechanics Meeting February 9-13, 2003, Ponce, Puerto Rico Virginia Tech Department of Aerospace & Ocean Engineering AAS

Overview ION-F and HokieSat Orbit & Attitude Coupling Dynamics Control Simulation/Software Results

Ionospheric Observation Nanosatellite Formation (ION-F) Three of 10 student-built spacecraft in AFOSR/DARPA University Nanosatellite Program, also sponsored by NASA Goddard Space Flight Center Three-satellite stack will launch from Shuttle Hitchhiker Experiment Launcher System Mission goals –Formation flying demonstration –Distributed ionospheric measurements HokieSat inch major diameter Hexagonal footprint 12 inches tall 39 lbs (~18 kg) ION-F USUSat Dawgstar

HokieSat DCS Hardware Orbit control –UW/Primex Pulsed Plasma Thrusters (PPT) Impulse bit per thruster: 56  N No radial thrust Paired thrusters cannot fire simultaneously Attitude control –Magnetic torque coils Interact with Earth’s magnetic field Provide < 5 x N-m Torque –PPTs for limited yaw steering Pulsed Plasma Thruster PPT layout

Maneuver Modes “Normal” mode –Slew as required to point thrusters –Negligible thrust torque –180 degree slews required “Sideways” mode –Allow thrust torque –Frequent control interruption –No slews required V V

Sources of Orbit-Attitude Coupling Natural dynamics: Attitude dependent orbit perturbations –Atmospheric drag –Solar radiation pressure Orbit dependent attitude perturbations –Magnetic field variation –Gravity gradient torque Dynamical coupling (very weak) Guidance Navigation & Control (GNC) System: Actuator induced disturbances –Non-coupled thrusters –Thruster disturbance torques Shared resources –Actuators –Sensors –Others Subsystem inter-dependencies –Drag/SRP control –Thruster pointing

Dynamics Orbit –Two body motion –Control forces from thrusters –Perfect state knowledge Attitude –External torques from gravity gradient, thrusters –Control torques from magnetic torque coils –Perfect state knowledge

Orbit Control * * * * * * Gains vary with trig functions of true anomaly to minimize error growth Mean motion control: Elemental Lyapunov Control:

Thrust On/Off Logic Normal mode Fire PPT 2&3 55 b2b2 b1b1 If Then Else

Thrust On/Off Logic (cont’d) Sideways mode Fire PPT 1 Fire PPT 2&3 Fire PPT 4 b2b2 b1b Pointing requirement independent of desired thrust direction

Attitude Control LQR Torque perpendicular to magnetic field direction only Desired attitude set by maneuvering mode and desired thrust direction Assume torque is throttleable, with a maximum of ~ 5 x N-m Torque

Simulation Reference orbit: –Semi-major axis: 6770 km –Circular (e  0) –Inclination: 52  Spacecraft initial conditions: –700m leader follower –700m same ground track Propagation: –1 second time step –Runge-Kutta integration for Orbit and Attitude Software –written in C ++ –Prototype of flight code –4 processes Orbit determination Orbit control Attitude determination Attitude control Leader Follower Formation Same Ground Track Formation

Results – Leader Follower, Normal Mode

Results – Same Ground Track, Normal Mode

Results – Same Ground Track, Sideways Mode

Summary Future Work Orbit-attitude coupling issues are real for HokieSat –Induced disturbances –Subsystem independences “Normal” maneuvering mode –May be sufficient for simple maneuvers –Fails for more complex maneuvers (insufficient torque, power) “Sideways” maneuvering mode –Successful for all attempted maneuvers –Thrust in +/- velocity direction, one out of plane direction (no slews) Estimation (GPS) Orbit perturbations (mean element feedback) Nanosat Cross Link Transceiver (NCLT) issues

Normal mode clip Sideways mode clip Questions? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

Choosing the control we get: Use LaSalle’s Invariance Principle to prove global asymptotic stability under this control law Control orbital 6DOF as two systems –First System: First five elements (size, shape, orientation of orbit) Orbital Control

We want: Combing these equations (with  =1) And solving for a For uncontrolled spacecraft, And the relative dynamics are: Orbit Control –Second system (a feedback phasing maneuver): Sixth element (angular position within the orbit)

Orbit Dynamics f and G given by Gauss’ Form of LPE u includes external forces from control, perturbations Attitude Dynamics g e includes external torques from magnetic control, gravity gradient, thrusters

Results – Leader Follower, Sideways Mode, Eclipse

Spacecraft Formation Flying Very Large Array – New Mexico 27 dishes, 25-m diameter = resolution of a 36km antenna TechSat21 – Air Force radar formation. Increase geolocation accuracy from 5-10 km to ~10m Multiple spacecraft in formation provide Unlimited effective aperture Improved reliability Reduced life cycle cost Inherent adaptability

Problem Statement Control the motion of formation-flying spacecraft using integrated nonlinear orbit and attitude feedback control laws to achieve a predefined target orbit. Sample formations: Leader follower Same ground track Constraints: No radial thrust Magnetic torque No simultaneous orbit & attitude control Eclipse constraints − maneuvering spacecraft − target orbit − leader spacecraft