Benchmark Problems for Spacecraft Formation Flying Missions

Abstract

To provide high-level focus to distributed space system flight dynamics and control research, several Ijenchmark problems are suggested. These problems are not specific to any current or proposed mission, but instead are intended to capture high-level features that would be generic to many similar missions.

Deployment procedure for the Tetrahedron Constellation

“…The solution of the TPBVP can be preferred for the formation of the tetrahedron constellation at the apogee point, but there are some other considerations related to the solution of this problem. For these reasons, the correction of the separation distance constraints for the proposed tetrahedron constellation [Carpenter et al 2003] will be based on the DLQR control scheme [Capó-Lugo and Bainum 2006a]. With this DLQR control scheme, the tetrahedron constellation can be formed with the required separation distance at the following apogee point.…”

“…Equation (12) will not require a transformation with (6c) because ψ(k) is defined in terms of the mean orbital elements of the satellites in the proposed constellation [Carpenter et al 2003], as shown in Table 2. In [Capó-Lugo and Bainum 2006a], the solution of the DLQR problem is obtained but is rewritten here for the y j system as…”

“…These techniques were based on the orbital elements of the constellation and did not contain an active control scheme to satisfy the separation distance conditions of the NASA Benchmark Tetrahedron Constellation. For the first specific size (phase I) of the proposed constellation [Carpenter et al 2003], the initial positions and velocities for the four satellites are expressed in Table 1. These initial coordinates and velocities are the required conditions such that the final tetrahedron constellation can be obtained at the apogee point.…”

“…According to the NASA Benchmark problem [Carpenter et al 2003] definition for the tetrahedron constellations, the nominal separation distance between any two of the satellites at apogee is 10 km, and the separation error at subsequent apogees should be within 10%, giving an acceptable range between 9 and 11 km. At other points in the orbit, the minimum separation distance between any pair of satellites should be 1 km.…”

“…One concern in the NASA Benchmark Tetrahedron Constellation problem [Carpenter et al 2003] is the deployment and reconfiguration procedures. Some papers solved these procedures using different numerical schemes based on pseudospectral methods [Williams and Trivailo 2006;.…”