time-synchronized attitude tracking during rendezvous and docking maneuvers

Paper number

IAC-21,C1,IP,13,x62167

Author

Dr. Yufeng Gao, China, Harbin Institute of Technology

Coauthor

Dr. Dongyu Li, China, Beihang University (BUAA)

Coauthor

Prof. Chuanjiang Li, China, Harbin Institute of Technology

Coauthor

Prof. Guangfu Ma, China

Year

2021

Abstract

Previous research on attitude tracking control for rendezvous and docking maneuvers focuses on forcing the attitude vector to ultimately converge to the equilibrium, ignoring any consideration of when each attitude element converges relative to the others. However, during rendezvous and docking maneuvers, it is desirable if all the attitude elements reach the target values \textit{at the same time}, namely \textit{time-synchronized attitude tracking}. This convergence property would significantly avoid the chattering and improve the pointing accuracy during rendezvous and docking maneuvers, resulting in a higher mission success rate. To achieve time-synchronized attitude tracking, we first define time-synchronized stability and propose its sufficient Lyapunov-like conditions. 

To be more specific, we consider the following general system, 
\begin{align}\label{eq:systeml}
\dot x = f\left( x \right),\;f\left( 0 \right) = 0,\;x(0) = {x_0},
\end{align}
where $x = {\left[ {{x_1}, \ldots ,{x_n}} \right]^T} \in {\mathbb R^n}$, and with respect to an open neighborhood $\mathcal D_0 \subseteq {\mathbb R^n}$ of the origin, $f: \mathcal D_0 \to {\mathbb R^n}$ is continuous. We assume that   the system (1)  has a unique solution  for all initial conditions in forward time. Next, the following well-established results are introduced.
	
The time-synchronized stability is proposed as follows\\
Definition:  
The  equilibrium of the system (1) is   \textit{time-synchronized stable} if
\begin{itemize}
\item[i.] it is finite-time stable; 
\item[ii.]  for an open neighborhood $\mathcal N_0 \subseteq \mathcal D_0$ of the origin, there exists a function $T:{\mathcal N_0}\backslash \{ 0\}  \to \left( {0,\infty } \right)$, called the \textit{synchronized settling-time function}, such that for $\forall {x_0} \in \mathcal N_0  \backslash  \{ 0\}$ and $i \in \left\{ {1,2, \ldots ,n} \right\}$, we have $x\left( t \right) \in \mathcal N_0$, $\forall t\in [0,\infty)$, and for $x_i(0)\ne 0$, 
\begin{align} 
    x_i\left( t \right) \ne 0, \;{\lim\limits_{t \uparrow T\left( x_0 \right)}}x_i\left( t \right) = 0,  \; \forall t\in [0,T(x_0)), 
\end{align}
where $T\left( x_0 \right)$ is the \textit{synchronized settling time}. 
\end{itemize}
 The equilibrium is globally time-synchronized stable if it is time-synchronized stable with $\mathcal N_0 = \mathcal D_0 =\mathbb R^n$. 
 

Based on the time-synchronized stability formulations, we further suitably design a time-synchronized attitude tracking control strategy. In addition, the analytical solution of a time-synchronized stable attitude tracking system is obtained and discussed, explicitly offering a quantitative method to preview and predesign the control system performance during rendezvous and docking maneuvers \textit{in prior}. Finally, numerical simulations are conducted to present the time-synchronized attitude tracking features attained, compared with traditional control strategies; and further explorations of the merits of the time-synchronized convergence are described.

Abstract document

IAC-21,C1,IP,13,x62167.brief.pdf

Manuscript document

IAC-21,C1,IP,13,x62167.pdf (🔒 authorized access only).

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