A Formation Flying Control Algorithm for the CanX-4/5 Low Earth Orbit Nanosatellite Mission
- Paper number
IAC-07-B4.6.04
- Author
Mr. Jesse Eyer, University of Toronto Institute for Aerospace Studies, Canada
- Coauthor
Dr. Chris Damaren, University of Toronto Institute for Aerospace Studies, Canada
- Coauthor
Dr. Robert E. Zee, University of Toronto, Canada
- Coauthor
Mrs. Elisabeth Cannon, University of Calgary, Canada
- Year
2007
- Abstract
The latest Canadian Advanced Nanospace eXperiment, CanX-4/5, is a dual-satellite formation flying demonstration mission. The mission objective is to demonstrate that satellite formation flying can be accomplished with sub-meter tracking error accuracy for low delta V requirements. The formation flying maneuvers for this mission require the development of control algorithms for autonomous formation maintenance and reconfiguration in the presence of orbital perturbations. In this paper, the development of a linear quadratic regulator state-feedback solution for the control problem is described. A discrete thrusting scheme, using pulse width modulation, is applied to account for the fixed impulse limitation of the real spacecraft. Attitude target vectors are generated from the propagation of the nonlinear orbital dynamics of the system and are used in conjunction with real-time GPS position and velocity data. The relative position and velocity data is determined using GPS carrier phase and Doppler data to achieve an accuracy of 2-5cm and 1-3cm/s respectively. An estimated state of the spacecraft is formed by combining noisy GPS measurements with a simulated state via an extended Kalman filter (EKF). During normal operation, the EKF filters the noise from the sensor measurements and ensures that the simulated state remains up-to-date. During a GPS blackout scenario, formation flying continues using the simulated data alone. Four formations will be flown on the CanX-4/5 mission: 2 along-track orbit (ATO) formations with spacecraft separation distances of 1000m and 500m, and 2 projected circular orbit (PCO) formations with separation distances of 100m and 50m. In each formation, the primary concern is the development of suitable, bounded relative reference trajectories to closely match the natural perturbed motion of the controlled (or deputy) satellite. Given the worst case eccentricity of the CanX-4/5 orbit, 0.025, it is found that minimum delta V requirements and tracking errors are obtained by using a) circular reference trajectories based on solutions to Hill’s equations for the PCO formations and b) elliptical reference trajectories based on Lawden’s equations for the ATO formations. The transition between each formation is accomplished through a series of impulsive maneuvers performed by the deputy satellite. Current simulations of the overall mission—75 orbits in each formation—demonstrate sub-meter tracking errors during formation maintenance and a total required delta V of 10.45m/s. These results have been verified with Satellite Tool Kit and signify that low Earth orbit formation flying can be accomplished with a high degree of accuracy for modest delta V requirements. With the successful completion of the CanX-4/5 mission in 2008, this study will establish formation flying as a cost effective and versatile alternative to expensive single-satellite missions.
- Abstract document
- Manuscript document
IAC-07-B4.6.04.pdf (🔒 authorized access only).
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