System and method of substantially autonomous geosynchronous time-optimal orbit transfer

The invention relates generally to orbiting spacecraft, and particularly to an on-board, substantially autonomous propulsion control system for efficiently carrying out orbit transfer, and a method for practicing the same.

To increase the payload mass delivered to orbit, large geosynchronous spacecraft may perform an orbit transfer using high-efficiency ion propulsion. During the orbit transfer, either Hall Current Thrusters (HCTs) or Xenon Ion Thrusters (XITs) are fired nearly continuously for a period of several weeks to months. While the thrusters are fired, the spacecraft attitude is controlled so the thrust vector tracks a specified inertial trajectory vector and the solar arrays remain pointed at the sun. The orbit transfer trajectory vector may be determined by solving the well-known minimum-time continuous firing orbit transfer problem. The trajectory is determined using a computationally intensive numerical iteration procedure that is not practical to implement on-board the spacecraft. The results of the optimization are a set of parameters, known as co-states, that can be used to generate the thrust trajectory on board the spacecraft.

During actual mission operations, the spacecraft generates the orbit transfer trajectory vector using ground-supplied co-states, and follows the trajectory while firing ion thrusters to execute the orbit transfer. However, over time, the actual orbit trajectory will deviate from the ideal orbit trajectory due to the effects of thrust and mass uncertainties, attitude determination and control errors, and perturbations due to the sun, moon, and earth gravity non-uniformities. To mitigate these effects, the ground routinely performs orbit determination using ranging data collected at times when ground contact with the spacecraft is possible. Using the estimated orbit, the ground generates updated co-states that are sent to the spacecraft to compute the updated thrust trajectory that corrects the orbit. This trajectory correction procedure is repeated every several days until the orbit transfer is complete.

There are several significant drawbacks to this approach. The first is that it requires a potentially large and highly skilled ground support staff to generate the orbit determination and trajectory replans for upload to the spacecraft. This staff must support the entire orbit transfer, which can be 100 days or greater. Also, because of the need for ground contact for ranging and commanding, generally at least three ground stations widely spaced in longitude must be available. Ground stations and their support staffs are a significant mission support cost, and it is desirable to reduce the number of stations needed. Additionally, there is a practical limit to the frequency that the firing plan can be updated due to the time required to collect and process orbit determination data and perform the numerical optimization. Larger update intervals reduce the orbit transfer efficiency, because the actual trajectory will deviate to a greater extent from the ideal trajectory. This deviation results in a longer orbit transfer requiring more fuel to complete.

Finally, the upload plans and parameters must be carefully checked and verified by the ground support staff before transmission to the spacecraft. As is true with all operations involving frequent ground commanding, mistakes are possible that can have negative consequences for the mission.

The subject matter disclosed herein solves these problems by providing an on-board, substantially autonomous capability for transferring a spacecraft from an initial orbit to a final geosynchronous orbit. At any time during the orbit transfer, the planned trajectory to complete the transfer is one that minimizes the remaining transfer time and the orbit transfer fuel. The spacecraft determines its orbit using a GPS-based system, or other means, to determine spacecraft orbital elements. Based on a measured orbit error, corrected co-state parameters are calculated and used to generate an updated thrust trajectory. The corrections are calculated using an innovative numerical procedure that is computationally simple and easy to implement in flight software. The procedure is carried out repetitively at a fixed interval until the target geosynchronous orbit is achieved.

Because the system is substantially autonomous, only a small ground support staff is needed that functions primarily in a monitoring role. Also, reduced ground station coverage is possible, because of the reduced requirements for range data collection and ground commanding. Finally, the frequent updates improve fuel efficiency because the closed loop corrections reduce the deviation of the actual orbit from an ideal minimum-time orbit trajectory.

Additional advantages and aspects of the disclosure will become readily apparent to those skilled in the art from the following detailed description, wherein embodiments of the present disclosure are shown and described, simply by way of illustration of the best mode contemplated for practicing the present disclosure. As will be described, the disclosure is capable of other and different embodiments, and its several details are susceptible of modification in various obvious respects, all without departing from the spirit of the disclosure. Accordingly, the drawings and description are to be regarded as illustrative in nature, and not as limitative.

The following detailed description of the embodiments of the present disclosure can best be understood when read in conjunction with the following drawings, in which the features are not necessarily drawn to scale but rather are drawn as to best illustrate the pertinent features, wherein

FIG. 1 is a block diagram showing an embodiment of a substantially autonomous orbit transfer control system, as taught herein.

FIG. 2 is a diagram showing detail of the Thrust Trajectory Generation Logic, implemented in the system of FIG. 1 .

FIG. 3 is a series of graphs showing low-thrust orbit transfer, of the prior art.

FIG. 4 is a series of graphs showing the same, in accord with the system disclosed herein.

FIG. 1 is a block diagram of a system 100 according to the invention. The system 100 is applicable to different types of spacecraft including geosynchronous spacecraft or any spacecraft that executes a time-optimal orbit transfer by continuous or near-continuous firing of thrusters.

To determine the spacecraft inertial attitude, the system 100 processes data from sensors 102 , that may include earth sensors, sun sensors, star trackers, and an inertial measurement unit (IMU), all being conventional. The earth sensors, sun sensors, and star trackers provide direct attitude measurements, and the IMU provides angular rate information. This processing is carried out in an Attitude Determination Logic 104 , implemented in the flight software in a preferred embodiment.

An Orbit Determination Logic 106 processes measurements from a conventional GPS receiver 108 and provides estimates of the spacecraft orbit elements based on an orbit dynamics model and knowledge of the applied thruster thrust. The GPS receiver 108 is connected to antennas that are arranged in such a way that signals from GPS spacecraft are received for a wide range of spacecraft attitudes.

The orbit elements produced by Orbit Determination Logic 106 are input to a novel Thrust Trajectory Generation Logic 110 , implemented in the flight software, which computes the inertial thrust trajectory vector for orbit transfer. This logic, which is described in detail below, computes the thrust trajectory vector based on the measured orbit elements and the target GEO orbit.

The thrust trajectory vector is then input to a Target Frame Generator 112 . This logic, which is also conventional, computes a target inertial reference frame, such that when the spacecraft body axes are aligned with this frame, the nominal thruster thrust direction is parallel to the thrust trajectory vector.

To ensure that target and spacecraft body frames remain aligned, an Attitude and Rate Error Generator 114 computes spacecraft attitude and rate errors with respect to the target reference frame. The attitude and rate errors, along with the reaction wheel (RWA) momentum error, are input to an Attitude and Momentum Controller 116 that computes torque commands for attitude and momentum control that are input to Torque Distribution Logic 118 . This logic in turn distributes torque commands to the RWAs and the thruster gimbals 103 .

FIG. 2 is a more detailed diagram of the Thrust Trajectory Generation Logic 110 comprising Orbit and Thrust Trajectory Generator 120 and Trajectory Update Logic 122 . Orbit and Thrust Trajectory Generator 120 propagates the orbit and co-state equations and determines the 3-element thrust trajectory unit vector u that is supplied to the Target Frame Generator 112 according to:

z . = M ⁡ ( z ) ⁢ us + [ 0 0 0 0 0 na γ ] T = f ⁡ ( z , u , s ) ( 1 ) λ . = - [ ∂ f ∂ z ] T ⁢ λ u ∥ M T ⁢ λ

where z is the 6-element orbit state vector, λ is the 6-element co-state vector, and s is the nominal acceleration due to thruster firing. Additionally, n is the orbit mean motion, a is the orbit semi-major axis, and γ is the distance from the spacecraft to the center of the earth. These expressions assume two-body orbit dynamics and a uniform spherical Earth. As known to those with skill in the art, these equations may be modified to include the effects of orbit perturbations due to the Sun, Moon, or earth gravity asymmetries.

At the beginning of the orbit transfer, the initial orbit elements and co-states are uploaded from the ground. The initial co-states and orbit transfer time are determined by ground-based numerical optimization. This starting orbit transfer trajectory is then modified as described below based on the actual orbit transfer performance.

The GPS receiver 108 provides data that is processed by the Orbit Determination Logic 106 within the flight software to obtain the measured orbit elements, z m . Periodically, the measured orbit elements are used to update the co-state vector λ to correct the trajectory such that the target orbit is achieved. Trajectory Update Logic 122 carries out the update steps, as follows, at some regular time interval, for example every 1, 2 or 12 hours.

Consider some time T during the orbit transfer where the update is to be carried out, and where z(T) and λ(T) are the corresponding propagated orbit elements and co-states, z m (T) are the measured orbit elements, and T f is the orbit transfer time remaining. The first step is to propagate Eq. (1) forward for the remaining transfer time T f starting from the initial conditions z(T)=z m (T) and λ(T). This is done to determine the expected final orbit elements and their time derivatives, denoted as z f and ż f . The error between the target orbit elements z target and the expected final orbit is then computed as

Δ z f =z target −z f   (2)

The next step is to solve for the perturbations to the co-states Δλ(T) and the remaining transfer time ΔT f that eliminates the error

[ Δ ⁢ ⁢ λ ⁢ Δ ⁢ ⁢ T f ] = A T ⁡ ( AA T ) - 1 ⁢ Δ ⁢ ⁢ z f ( 3 )

where A is a 6×7 matrix that relates the perturbations to the orbit error, and that is formed as a composite of the 6×6 matrix Z and the orbit element derivative at the final time

The matrix Q, which may be computed numerically or analytically, relates a co-state perturbation δλ(T) to changes in the final orbit δz f

δz f =Qδλ ( T )   (5)

The final step is to update the co-states and time remaining for the orbit transfer:

λ( T )=λ( T )+Δλ( T )

T f =T f +ΔT f   (6)

Starting from these initial conditions, Eq. (1) is then propagated to generate the thrust trajectory until the time of the next update, at which point the steps described above are repeated.

Other embodiments of the present invention will be obvious to those skilled in the art. For example, rather than using a GPS, the orbit may be determined by some other means. For example, the orbit elements may be determined on the ground using range and angle data and periodically uploaded to the spacecraft. The orbit and co-state propagation may consider continuous firing, or constraints may be imposed such that the thruster may be turned off and on at specific times.

FIG. 3 is a series of graphs showing a prior-art low-thrust orbit transfer using Hall Current Thrusters (HCTs). Table 1 gives the spacecraft starting orbit, final orbit, and other spacecraft parameters.

The Figure shows how the actual orbit trajectory deviates from and ideal orbit trajectory because the HCT thrust is 5% lower than expected (the solid line is the ideal trajectory and the dashed line is the actual trajectory). The trajectory deviation would be observed by ground-based orbit determination, and periodically a new orbit transfer plan would be developed and uploaded to the spacecraft to correct the trajectory. Because the actual orbit trajectory deviates from an ideal trajectory, the orbit transfer will take longer at the expense of increased fuel.

FIG. 4 shows the same orbit transfer, but this time using a system according to the invention. As a result of the continuous on-board corrections, the actual trajectory closely tracks the optimal trajectory, resulting in only a small increase in the orbit transfer time (0.14 day).

Those skilled in the art will understand that the method and system of the present invention need not be limited to orbit transfer. For instance, the method and system of the present invention can be employed to optimally move a spacecraft from one position to another in the same orbit—e.g., from an East Coast position to a West Coast position—without departing from the scope of the present invention. Furthermore, the present invention may be utilized to maintain orbital positions once a spacecraft has reached its desired orbit.

The foregoing description of the invention illustrates and describes the present invention. Additionally, the disclosure shows and describes only the preferred embodiments of the invention, but as aforementioned, it is to be understood that the invention is capable of use in various other combinations, modifications, and environments and is capable of changes or modifications within the scope of the inventive concept as expressed herein, commensurate with the above teachings, and/or the skill or knowledge of the relevant art. The embodiments described hereinabove are further intended to explain best modes known of practicing the invention and to enable others skilled in the art to utilize the invention in such, or other, embodiments and with the various modifications required by the particular applications or uses of the invention. Accordingly, the description is not intended to limit the invention to the form disclosed herein. Also, it is intended that the appended claims be construed to include alternative embodiments.