A model of relative translation and rotation in leader-follower spacecraft formations

Abstract

In this paper, a model of a leader-follower spacecraft formation in six degrees of freedom is derived and presented. The nonlinear model describes the relative translational and rotational motion of the spacecraft, and extends previous work by providing a more complete factorization, together with detailed information about the matrices in the model. The resulting model shows many similarities with models for systems such as robot manipulators and marine vehicles. In addition, mathematical models of orbital perturbations due to gravitational variations, atmospheric drag, solar radiation and third-body effects are presented for completeness. Results from simulations are presented to visualize the properties of the model and to show the impact of the different orbital perturbations on the flight path.

Finite-time formation control for linear multi-agent systems: A motion planning approach

“…For the relative position dynamics without any assumption, please refer to [1]. Further, let u = U/m, and assume that the relative orbit radius between the ith spacecraft and the reference orbit is very small compared to the radius of the reference orbit.…”

“…In the past two decades, the coordination problem of multiagent systems has been considerably studied due to its broad applications in such areas as spacecraft formation flying and sampling, distributed sensor networks, and automated highway systems, to name just a few [1][2][3]. One critical issue arising from multi-agent systems is to develop control laws that enable all agents to reach a desired formation, which is known as the formation problem.…”

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“…Using the true anomaly ν of the leader spacecraft, and denoting relative velocity as v =ṗ, the nonlinear position dynamics can be represented in the F l frame on the form (cf. Yan et al (2000), Kristiansen et al (2007))…”

Adaptive backstepping control for optimal descent with embedded autonomy

“…(22) is of the form of Eq. (5) with [16], the error attitude dynamics and kinematics can be expressed as,…”