Global Distributed Attitude Tracking Control of Multiple Rigid Bodies via Quaternion-Based Hybrid Feedback

Finite‐time attitude consensus control for multiple rigid spacecraft based on distributed observers

“…It can be found in Figure 9 that by the proposed finite‐time attitude consensus protocol, the overall attitude tracking errors and overall attitude tracking errors of four followers are almost zeros. Moreover, the convergence rate of the tracking errors under the proposed protocol is faster than those under the protocols in [5] and [8]. In view of Figure 10, it is found that the control effort and fuel consumption of the closed‐loop system under the proposed protocol are less than those under the protocols in [5] and [8].…”

“…To further demonstrate the merit of the proposed solution, a comparative experiment with the recent attitude consensus results in [5] and [8] is carried out. For comparison, some index functions are defined as $$$$\begin{eqnarray} \text{ATE}&=&\sqrt {\sum _{i=1}^{4}{\left\Vert \bm{q}_{{\rm e}i,\mathrm{v}}\right\Vert} _{2}^2},\quad \text{AVTE}=\sqrt {\sum _{i=1}^{4}{\left\Vert \bm{\omega }_{{\rm e}i}\right\Vert} _{2}^2},\nonumber\\ \text{CE}&=&\sqrt {\sum _{i=1}^{4}{\left\Vert {\bm{u}}_i\right\Vert} _{2}^2},\quad F_{\rm index}=\sum _{i=1}^{4}\int _{0}^{t}{{\left\Vert \bm{u}_{i}(\tau )\right\Vert} _{1}}d\tau .\qquad \end{eqnarray}$$$$From the aforementioned definitions, ATE and AVTE describe the overall attitude tracking errors of four followers and overall angular velocity tracking errors of four followers, respectively.…”

“…For leader-follower attitude consensus problem, many researchers focus on the scenario where only a subset of fol-lowers have access to the leader's information. To achieve attitude consensus under such a scenario, distributed continuous observers were constructed in [5,6] to estimate the leader's attitude and angular velocity when the interaction network among followers is bidirectional, and an attitude consensus protocol based on distributed observers was proposed for multiple rigid spacecraft systems. An advantage of the distributed observer-based consensus protocol in [5,6] is that once the distributed observers are properly constructed, the attitude consensus control for multi-spacecraft systems can be transformed to the attitude tracking control for a single spacecraft.…”

“…To achieve attitude consensus under such a scenario, distributed continuous observers were constructed in [5,6] to estimate the leader's attitude and angular velocity when the interaction network among followers is bidirectional, and an attitude consensus protocol based on distributed observers was proposed for multiple rigid spacecraft systems. An advantage of the distributed observer-based consensus protocol in [5,6] is that once the distributed observers are properly constructed, the attitude consensus control for multi-spacecraft systems can be transformed to the attitude tracking control for a single spacecraft. The distributed continuous observers in [6] were generalised in [7,8] to the case where the interaction network among followers is directed, and further generalised in [9,10] to the case where the interaction network is switching network.…”

“…2) Based on such distributed observers, an FNTSM attitude consensus protocol is constructed. Compared with the distributed consensus protocol in [5][6][7][8][9], the finite-time attitude consensus performance is achieved for the closed-loop system by the proposed distributed observer-based FNTSM consensus protocol. 3) Unlike the works in [17][18][19]21], the complete convergence analysis of the system states and an explicit expression of the settling time on the proposed sliding surface are provided in this paper.…”