A Hybrid Control Framework for Impulsive Control of Satellite Rendezvous

Abstract

We focus on the problem of satellite rendezvous between two spacecraft in elliptic orbits. Using a linearized model of the relative dynamics, we first propose a periodic similarity transformation based on Floquet-Lyapunov theory, leading to a set of coordinates under which the free motion is linear timeinvariant. Then we address the problem of impulsive control of satellite rendezvous as a hybrid dynamical system, and we show that the arising elegant representation enables designing impulsive control laws with different trade-offs between computational complexity and fuel consumption. The adopted hybrid formalism allows us to prove suitable stability properties induced by the proposed controllers. The results are comparatively illustrated on simulation examples.

Impulsive zone model predictive control for rendezvous hovering phases

“…In order to assess the performance of the proposed controller, four hovering scenarios extracted from [20] are simulated. They are described by the spacecraft parameters, the thrusters limits, the hovering zone and the initial states, and are given in Table I.…”

“…One can observe, also, that for every scenario the consumption decreases as the control horizon grows. [20] proposes several hybrid controllers that stabilize a given relative orbit (selected for satisfying the the hovering box limits). By comparison with the results from [20], the convergence is faster and consume less fuel in most of case (especially for ∆ν = 120 • ).…”

“…[20] proposes several hybrid controllers that stabilize a given relative orbit (selected for satisfying the the hovering box limits). By comparison with the results from [20], the convergence is faster and consume less fuel in most of case (especially for ∆ν = 120 • ). These facts are expected since the controller developed in this paper is optimization-based contrary to the hybrid controllers from [20].…”

“…To this ends, some interesting periodicity properties -coming from the formal description of the periodic relative orbits included in a given polytope (developed in several recent works, [17], [18], [19]) -are exploited. The benefits of these properties in the context of IzMPC can be described three fold: it ensures recursive feasibility and closed-loop stability, it has an enlarged domain of attraction (in a rather natural form, without using additional optimization variables) and it shows a good performance (in terms of the objective function, convergence rate and fuel consumption) in comparison with other recent strategies [20], [19].…”

On the Impulsive Formation Control of Spacecraft Under Path Constraints

“…For sufficiency, a proof by contradiction is used. Suppose τ 1 = τ 2 and R 1,2 (τ 1 ) ∩ R 1,2 (τ 2 ) = ∅, then there exists a position r t and two time intervals ∆t 21 and ∆t 21 such that r t (∆t 21 , τ ) = r t (∆t 21 , τ ). Thus, from Lemma 1 if ∆t 21 = ∆t 21 , then no equality exists and if ∆t 21 = ∆t 21 , then τ 1 = τ 2 which demonstrates a contradiction.…”