Abstract: A computer-implemented method for maintaining a spacecraft near an orbit comprises steps of detecting that a distance from the spacecraft to the orbit is greater than a spacecraft threshold and in response, linearizing dynamics of the spacecraft from a current time over a time horizon with respect to a high-fidelity reference trajectory to produce a state transition matrix (STM) for an uncontrolled motion of the spacecraft within the time horizon. The STM includes non-expanding eigenvectors with magnitudes less than or equal to one and expanding eigenvectors with magnitudes greater than one. The method further comprises determining a control action that changes an upcoming state of the spacecraft to a linear combination of the non-expanding eigenvectors of the STM and generating a control command to an actuator of the spacecraft.

Abstract: A computer-implemented method for maintaining a spacecraft near an orbit comprises steps of detecting that a distance from the spacecraft to the orbit is greater than a spacecraft threshold and in response, linearizing dynamics of the spacecraft from a current time over a time horizon with respect to a high-fidelity reference trajectory to produce a state transition matrix (STM) for an uncontrolled motion of the spacecraft within the time horizon. The STM includes non-expanding eigenvectors with magnitudes less than or equal to one and expanding eigenvectors with magnitudes greater than one. The method further comprises determining a control action that changes an upcoming state of the spacecraft to a linear combination of the non-expanding eigenvectors of the STM and generating a control command to an actuator of the spacecraft.