Eigenmotion control for near rectilinear halo orbits

A computer-implemented method for maintaining a spacecraft near an orbit, comprising:

• detecting that a distance from the spacecraft to the orbit is greater than a spacecraft threshold;
• in response to detecting that the distance from the spacecraft to the orbit is greater than the spacecraft threshold:
• 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, wherein the state transition matrix includes non-expanding eigenvectors with magnitudes less than or equal to one and expanding eigenvectors with magnitudes greater than one;
• determining a control action that changes an upcoming state of the spacecraft to a linear combination of the non-expanding eigenvectors of the state transition matrix;
• and
• generating a control command to an actuator of the spacecraft causing correction of the upcoming state of the spacecraft along a direction corresponding to at least one of the non-expanding eigenvectors of the state transition matrix.

A non-transitory computer readable storage medium having embodied thereon a program executable by a processor for performing a method for maintaining a spacecraft near an orbit, the method comprising:

• detecting that a distance from the spacecraft to the orbit is greater than a spacecraft threshold;
• in response to detecting that the distance from the spacecraft to the orbit is greater than the spacecraft threshold:
• 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, wherein the state transition matrix includes non-expanding eigenvectors with magnitudes less than or equal to one and expanding eigenvectors with magnitudes greater than one;
• determining a control action that changes an upcoming state of the spacecraft to a linear combination of the non-expanding eigenvectors of the state transition matrix;
• and
• generating a control command to an actuator of the spacecraft causing correction of the upcoming state of the spacecraft along a direction corresponding to at least one of the non-expanding eigenvectors of the state transition matrix.