Dynamics and control of underactuated spacecraft formation reconfiguration in elliptic orbits

Abstract

Feasibility of underactuated formation reconfiguration in elliptic orbits without radial or in-track thrust is investigated in this paper. For either underactuated case, by using a linear time-varying dynamical model of spacecraft formation, controllability and feasibility analyses are conducted, based on which the preconditions on reconfigurable formations are then derived. With the inherent coupling of system dynamics, the reduced-order sliding mode control technique is employed to design a closed-loop underactuated controller for either case. To ensure the stability of the closed-loop system, the conditions imposed on the controller parameters are derived, and the parameter adaptation laws are then solved analytically. Meanwhile, the explicit relationships between the steady accuracies of system states and the controller parameters are obtained via a Lyapunov-based approach. Numerical examples are simulated in a J 2-perturbed environment to validate the theoretical analyses. The results indicate that by using the proposed control schemes, underactuated reconfiguration in elliptic orbits is still feasible even in the absence of radial or in-track thrust and in the presence of unmatched disturbances.

Feasibility analysis and saturation control for underactuated spacecraft formation reconfiguration in elliptic orbits

“…2) New underactuated control schemes that decouple the radial and along-track system states are presented for spacecraft formation reconfiguration without either the radial or the along-track control. Notably, the Lyapunov-based approach proves that the bounded convergence regions of system states in this work are less than those in Huang et al 27,28 3) To address the challenges posed by thrust loss, timevarying system coefficients, and input saturation, the underactuated saturation controllers are developed for either underactuated case. Especially for the case without along-track thrust, the timeinvariant and time-varying coefficients of the system in the controller satisfy the same linear transformation.…”

“…is nonsingular, where t 0 and t f are the initial and terminal times, respectively. By using Lemma 2, Huang et al 27 concluded the controllability analysis of underactuated formation flying in elliptic orbits: the system is controllable for the case without radial control but uncontrollable in the absence of along-track control. Note that the controllability decomposition approach is based on the rank criterion theory, which can only analyze the controllability of a linear time-invariant system.…”

“…As the linearized Tschauner-Hempel (TH) equation is a linear time-varying one, 24,25 the controllability analysis based on the rank criterion method can only give a sufficient condition rather than a necessary and sufficient one. 26 Huang et al 27 employed the Gramian matrix method to judge the controllability for both underactuated cases in elliptic orbits and stated that the minimum eigenvalue is considered to be zero if it is less than the order of 10 À10 . Hence, the same underactuated conclusions could be drawn in elliptic reference orbits as in circular ones, these are, the system is controllable without radial control but uncontrollable without along-track control.…”

“…Since it is unfeasible to decompose the uncontrollable linear time-varying system into controllable and uncontrollable subspaces, the controller can only be designed based on the fully actuated dynamics in the absence of along-track control. 27 A situation then occurs whereby the results of the controllability analysis do not match the order of the underactuated error dynamics. To solve this unmatched problem, Huang and Chen 28 analyzed the controllability of the angular domain system derived from the coordinate transformation by using the rank criterion method and presented the fifth-order underactuated error dynamics.…”

Optimal control of rapid cooperative spacecraft rendezvous with multiple specific-direction thrusts

“…There are some studies investigating non-radial thrust in the orbital-transfer problem. 13–15 More recently, Quarta and Mengali 16 proposed a new formulation to reassess the classical circumferential-thrust problem, assuming the propulsive acceleration modulus to be sufficiently small to reduce the mathematical complexity of the problem. In 2019, the same research group investigated the optimal-transfer trajectories from a circular parking orbit toward the apocenter of a rectilinear ellipse, for a spacecraft equipped with a burning system that provides a circumferential continuous propulsive acceleration.…”