Eigenmotion control for near rectilinear halo orbits

Patent metadata

Field	Value
Publication number	US-12286241-B2
Application number	US-202217873078-A
Country	US
Kind code	B2
Filing date	Jul 25, 2022
Priority date	Jun 3, 2022
Publication date	Apr 29, 2025
Grant date	Apr 29, 2025

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.

First claim

What is claimed is:

1. A controller for maintaining a spacecraft near an orbit, the controller comprising:
a memory configured to store executable instructions; and
a processor configured to execute the executable instructions to cause the controller to:
detect 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:
linearize 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;
determine 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
generate 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.

2. The controller of claim 1 , wherein to detect that the distance is greater than the spacecraft threshold, the processor is configured to:
determine a current state of the spacecraft within a specified time period; and
determine a distance between a location governed by the current state of the spacecraft and the orbit; and
compare the determined distance between the location governed by the current state of the spacecraft and the orbit with the spacecraft threshold.

3. The controller of claim 2 ,
wherein the specified time period is outside the time horizon, and
wherein to determine the current state of the spacecraft, the processor is further configured to obtain measurements corresponding to one or a combination of positions and translational velocities of the spacecraft, and perturbations acting on a multi-object celestial system defined by the spacecraft and at least one celestial object.

4. The controller of claim 1 , wherein, to determine the state transition matrix, the processor is further configured to
obtain a linear model of a dynamical system defined by the spacecraft and at least one celestial object;
compute discrete time update of perturbations of the high fidelity reference trajectory; and
propagate a numerical expression defined by the high fidelity reference trajectory and elementary basis vectors for the STM over a defined time period.

5. The controller of claim 1 , wherein the processor is further configured to obtain a different spacecraft threshold for a visitor spacecraft to perform eigenvector-based control of motion of the visitor spacecraft using the high fidelity reference trajectory.

6. The controller of claim 1 , wherein to determine the control action the processor is further configured to determine the direction of the correction of the upcoming state by linear combination of a direction of each non-expanding eigenvector of the STM to achieve a mixed state with natural motion that is a combination of corresponding eigenmotion of each non-expanding eigenvector of the STM.

7. The controller of claim 1 , wherein, to generate the control command, the processor is further configured to solve a nonlinear optimization problem to find a fuel-efficient maneuver that transfers the spacecraft to a set of desirable states that yield desirable natural motion.

8. The controller of claim 7 , wherein the nonlinear optimization problem is directed towards a finite horizon optimization of a model of the spacecraft, a set of objectives of motion of the spacecraft, and constraints on a propulsion system of the spacecraft and the motion of the spacecraft.

9. The controller of claim 8 , wherein the constraints on the propulsion system of the spacecraft and the motion of the spacecraft include one or more physical limitations of the spacecraft, one or more safety limitations on operation of the spacecraft, and one or more performance limitations on a trajectory of the spacecraft.

10. The controller of claim 1 , wherein the spacecraft is configured to execute a task of docking to a space station that maintains its position near the orbit at a distance smaller than a station threshold, wherein the controller is further configured to select the spacecraft threshold greater than the station threshold.

11. The controller of claim 1 , wherein the upcoming state of the spacecraft includes one or combination of positions, orientations, and translational and angular velocities of one or more of the spacecraft and a payload of the spacecraft, and perturbations acting on a multi-object celestial system defined by the spacecraft, the payload, and one or more celestial objects.

12. The controller of claim 11 , wherein the perturbations acting on the multi-object celestial system are natural orbital forces that include solar and lunar gravitational perturbations, anisotropic gravitational perturbations due to a central body's nonsphericity, solar radiation pressure, and air drag.

13. The controller of claim 1 , wherein the high-fidelity reference trajectory is an uncontrolled, natural motion trajectory which lies near a near-rectilinear halo orbit (NRHO) in an Earth-Moon circular-restricted three-body problem, and is estimated using multiple shooting approach.

14. The controller of claim 13 , wherein the high-fidelity reference trajectory comprises a finite number of aperiodic revolutions around Moon over a finite number of days.

15. The controller of claim 1 , wherein the orbit is one of a circular orbit, an elliptic orbit, a halo orbit, a near rectilinear halo orbit, or a quasi-satellite orbit.

16. The controller of claim 1 , wherein the control command is generated as a solution to a model predictive control policy that produces the control command by optimizing a cost function over a receding horizon.

17. The controller of claim 16 , wherein the cost function includes a stabilization component for directing a movement of the spacecraft to the upcoming state, a component for an objective of an operation of the spacecraft, and a performance component for optimizing the movement of the spacecraft until the upcoming state is achieved.

18. The controller of claim 1 , wherein the control command is generated for each specified time period of multiple specified time periods in the time horizon, or generated iteratively over a receding time-horizon.

19. 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 a

Assignees

• Mitsubishi Electric Res Laboratories Inc

Inventors

• Weiss Avishai
• Elango Purnanand
• Di Cairano Stefano
• Kalabic Uros

Classifications

• B64G1/2422

  using Lagrange points, e.g. halo orbits · CPC title

• B64G1/244

  Spacecraft control systems · CPC title

• B64G1/242 Primary

  Orbits and trajectories · CPC title

• B64G1/646 Primary

  Docking or rendezvous systems (refuelling in space B64G1/4024) · CPC title