Henderson, David M. | Search NASA

NASA NTRS1992

Reference equations of motion for automatic rendezvous and capture

The analysis presented in this paper defines the reference coordinate frames, equations of motion, and control parameters necessary to model the relative motion and attitude of spacecraft in close proximity with another space system during the Automatic Rendezvous and Capture phase of an on-orbit operation. The relative docking port target position vector and the attitude control matrix are defined based upon an arbitrary spacecraft design. These translation and rotation control parameters could be used to drive the error signal input to the vehicle flight control system. Measurements for these control parameters would become the bases for an autopilot or feedback control system (FCS) design for a specific spacecraft.

Henderson, David M.↗

NASA NTRS1991

Use of non-spherical gravity harmonics for relative motion GN/C (category 2)

Detailed analysis of the Automatic Rendezvous and Capture problem indicate a need for three different regions of mathematical description for the GN&C algorithms: (1) multi-vehicle orbital mechanics to the rendezvous interface point, i.e., within 100 nm; (2) relative motion solutions (such as Clohessy-Wiltshire type) from the far-field to the near-field interface, i.e., within 1 nm and; (3) close proximity motion - the near-field motion where the relative differences in the gravitational and orbit inertial accelerations can be neglected from the equations of motion. Limit boundaries to these regions can be precisely defined by further analysis and will be functions of the tracking measurement accuracies and the computer resources available for the solution of the algorithms. This paper analyzes the relative motion in Regions 2 and 3 above and present the derivation and discussion of the general case of non-spherical gravitational perturbed relative motion. Mathematical deviations from the numerically integrated spherical gravity case and solutions from the Clohessy-Wiltshire equations are presented in the analysis. Based upon this preliminary analysis, it is recommended that further efforts be used to assess the relative position and velocity differences in Region 2 due to non-spherical gravity harmonics and that viable GN&C algorithms be developed to include these gravity perturbations (especially the effects of the first gravity harmonic, J2).

Henderson, David M.↗

NASA NTRS1991

GN/C translation and rotation control parameters for AR/C (category 2)

Detailed analysis of the Automatic Rendezvous and Capture problem indicate a need for three different regions of mathematical description for the GN&C algorithms: (1) multi-vehicle orbital mechanics to the rendezvous interface point, i.e., within 100 n.; (2) relative motion solutions (such as Clohessy-Wiltshire type) from the far-field to the near-field interface, i.e., within 1 nm; and (3) close proximity motion, the nearfield motion where the relative differences in the gravitational and orbit inertial accelerations can be neglected from the equations of motion. This paper defines the reference coordinate frames and control parameters necessary to model the relative motion and attitude of spacecraft in the close proximity of another space system (Region 2 and 3) during the Automatic Rendezvous and Capture phase of an orbit operation.

Henderson, David M.↗