Decentralized Consensus Control of a Rigid-Body Spacecraft Formation with Communication Delay

Abstract

The decentralized consensus control of a formation of rigid body spacecraft is studied in the framework of geometric mechanics while accounting for a constant communication time delay between spacecraft. The relative position and attitude (relative pose) are represented on the Lie group SE(3) while the communication topology is modeled as a digraph. The consensus problem is converted into a local stabilization problem of the error dynamics associated with the Lie algebra se(3) in the form of linear time-invariant delay differential equations (DDEs) with a single discrete delay in the case of a circular orbit while it is in the form of linear time-periodic DDEs in the case of an elliptic orbit, in which the stability may be assessed using infinite-dimensional Floquet

Extended state observer–based finite-time controller design for coupled spacecraft formation with actuator saturation

“…The 6-DOF relative-coupled dynamics for SFF system described by the exponential coordinates on the Lie group SE(3), which is the set of positions and orientations of the spacecraft moving in three-dimensional (3D) Euclidean space, as a useful mathematical tool has received increasing attention as in Lee and colleagues 7,9 and Nazari et al 10 However, structured and unstructured uncertainties haven't been considered in these papers, which can't be ignored due to external environment disturbances or fuel consuming or components/payloads releasing. That is to say, the controllers designed in these papers have poor robustness.…”

“…That is to say, the controllers designed in these papers have poor robustness. Meanwhile, the controllers designed in Lee and colleagues 7,9 could only guarantee asymptotical convergence of the system states, which means that the control objectives will realize when time tends to infinity, and the consensus problem was solved by a local stability controller in Nazari et al 10 Terminal sliding mode control (TSMC) proposed in Yu et al 11 for rigid robotic manipulators could provide finite-time stability in both the reaching phase and the sliding phase, which has been widely studied and explored in the spacecraft control field due to its ability to deal with the external disturbances and model uncertainties, such as finite-time attitude tracking control problem for rigid spacecraft solved in Jin and Sun,12 finite-time SFF orbit reconfiguration control in Hui and Li, 13 and a terminal sliding mode (TSM)-based observer developed in Xiao et al 14 to reconstruct all the states of the attitude system in the presence of actuator failures in finite time. However, TSM has two disadvantages of slower convergence than the sliding mode control (SMC) when the system states far away from the equilibrium and the singularity problem.…”

Adaptive fuzzy finite-time control for spacecraft formation with communication delays and changing topologies

“…In order to describe the 6-DOF relative-motion in a united framework and facilitate the controller synthesis work, constructing coupled dynamics by the relative position and attitude described on the Lie group SE (3) has been an effective tool and received increasing attention in [2], [10][11][12][13][14][15]. In [2], a sliding mode control scheme on the coupled dynamics on SE(3) was presented to achieve the desired formation with respect to the virtual leader whose trajectory was computed offline.…”

Neural network–based reconfiguration control for spacecraft formation in obstacle environments

“…The requirements for the accurate control on relative positions and synchronization between spacecraft are the major challenges. Attitude synchronization , as one of the most critical issue of SFF, has been widely investigated in recent years (eg, see other works()). In these literature works, several algorithms on attitude synchronization have been proposed to achieve asymptotic/exponential stability in infinite convergence time.…”

“…However, the algorithms are infeasible for the formation reconfiguration especially in obstacle environments. The position tracking control is essential and significant for SFF in deep‐space explorations, and a growing number of solutions have been presented (eg, see other works()); however, the existing solutions can only achieve the asymptotic/exponential stability in infinite convergence time, and therefore, they cannot meet the high‐precision control requirement in finite time. In addition, the aforementioned results neglect the adverse effect of obstacle/collision avoidances, which may cause the failure of tasks or even lead to disastrous consequences.…”