This study is mainly focusing on the problem of spacecraft close-range proximity with obstacle avoidance in the presence of complex shape. A novel Gaussian mixture model–based nonsingular terminal sliding mode control (GMM-NTSMC) is proposed. This is achieved by developing GMM-based potential function with a switching surface of NTSMC. It is theoretically proved that the closed-loop system is globally stable. The main contribution of this study is that the GMM-based avoiding strategies, which include the GMM-based terminal sliding mode control (GMM-TSMC) and GMM-NTSMC, can solve the collision avoidance problem considering complex shape while the artificial potential function–based terminal sliding model control (APF-TSMC) fails. Moreover, the GMM-NTSMC and the GMM-TSMC require less energy with respect to the APF-TSMC. Furthermore, the GMM-NTSMC retains the advantage of the NTSMC and can avoid singularity problem while GMM-TSMC cannot. Finally, numerical simulations are performed to verify the effectiveness and superiority of the proposed GMM-NTSMC.
JiX-YLiY-ZLiuG-Q, et al.A brief review of ground and flight failures of Chinese spacecraft. Prog Aerospace Sci2019; 107: 19–29.
2.
ElleryAKreiselJSommerB. The case for robotic on-orbit servicing of spacecraft: spacecraft reliability is a myth. Acta Astronautica2008; 63(5): 632–648.
3.
RumfordRE. Demonstration of autonomous rendezvous technology (DART) project summary. Proc SPIE-The Int Soc Opt Eng2003; 5088: 10–19.
4.
Flores-AbadAMaOPhamK, et al.A review of space robotics technologies for on-orbit servicing. Prog Aerospace Sci2014; 68(1): 1–26.
5.
LiW-JChengD-YLiuX-G, et al.On-orbit service (OOS) of spacecraft: a review of engineering developments. Prog Aerospace Sci2019; 108: 32–120.
6.
ZhangJChuXZhangY, et al.Safe-trajectory optimization and tracking control in ultra-close proximity to a failed satellite. Acta Astronautica2018; 144: 339–352.
7.
HuaBHuangYWuYH, et al.Spacecraft formation reconfiguration trajectory planning with avoidance constraints using adaptive pigeon-inspired optimization. Sci China Inf Sci2019; 62: 070209.
8.
FreyGRPetersenCDLeveFA, et al.Constrained spacecraft relative motion planning exploiting periodic natural motion trajectories and invariance. J Guidance, Control Dyn2017; 40(12): 3100–3115.
9.
LuoY-ZSunZ-J. Safe rendezvous scenario design for geostationary satellites with collocation constraints. Astrodynamics2017; 1(1): 71–83.
10.
LuoY-ZSunZ-JZhangJ. Proximity scenario design for geostationary rendezvous with collocated satellite avoidance. Acta Astronautica2019; 154: 153–168.
11.
NiQHuangYYChenXQ. Nonlinear control of spacecraft formation flying with disturbance rejection and collision avoidance. Chin Phys B2017; 26(1): 014502.
12.
CaoLQiaoDXuJ. Suboptimal artificial potential function sliding mode control for spacecraft rendezvous with obstacle avoidance. Acta Astronautica2018; 143: 133–146.
13.
WangYBaiYXingJ, et al.Equal-collision-probability-curve method for safe spacecraft close-range proximity maneuvers. Adv Space Res2018; 62(9): 2599–2619.
14.
WangYChenXQBaiYZ, et al.Motion planning of spacecraft with obstacle avoidance under low uncertainty using the improved equal-collision-probability-curve and improved linear quadratic regulator strategy. Proc Inst Mech Eng G: J Aerospace Eng2019; 233(14): 5456–5467.
15.
WangYChenXRanD, et al.Spacecraft formation reconfiguration with multi-obstacle avoidance under navigation and control uncertainties using adaptive artificial potential function method. Astrodynamics2020; 4(1): 41–56.
16.
WenGXChenCLDouH, et al.Formation control with obstacle avoidance of second-order multi-agent systems under directed communication topology. Sci China Inf Sci2019; 62(9): 192205.
17.
BaiX-ZMaC-WChenL, et al.Maximum collision probability considering variable size, shape, and orientation of covariance ellipse. Adv Space Res2016; 58(6): 950–966.
18.
WangYChenXQRanDC, et al.Multi-equal-collision-probability-curve method for convex polygon shape spacecraft safe proximity maneuvers. J Navigation2019; 72(2): 405–429.
19.
WangYBaiYRanD, et al.Dual-equal-collision-probability-curve method for spacecraft safe proximity maneuvers in presence of complex shape. Acta Astronautica2019; 159: 65–76.
20.
LauDEdenJOetomoD. Fluid motion planner for nonholonomic 3-D mobile robots with kinematic constraints. IEEE Trans Robotics2015; 31(6): 1537–1547.
21.
EckartB. Compact Generative Models of Point Cloud Data for 3D Perception. PhD dissertation. Pittsburgh, Pennsylvania: The Robotics Institute, Carnegie Mellon University, 2016.
22.
ZhuXZ. Research on Vision Based Close-Range Sensing of Uncooperative Targets. PhD dissertation. Changsha, Hunan Province, China: College of Aeronautics and Astronautics, National University of Defense Technology, 2017. (in Chinese)
23.
VittaldevVRussellRPLinaresR. Spacecraft uncertainty propagation using gaussian mixture models and polynomial chaos expansions. J Guidance, Control Dyn2016; 39(12): 2615–2626.
24.
LuoY-zYangZ. A review of uncertainty propagation in orbital mechanics. Prog Aerospace Sci2017; 89: 23–39.
25.
YuJ. A nonlinear kernel Gaussian Mixture Model based inferential monitoring approach for fault detection and diagnosis of chemical processes. Chem Eng Sci2012; 68(1): 506–519.
26.
VanMGeSSRenH. Finite time fault tolerant control for robot manipulators using time delay estimation and continuous nonsingular fast terminal sliding mode control. IEEE Trans Cybernetics2017; 47(7): 1681–1693.
27.
LiB. An experiment of K-Means initialization strategies on handwritten digits dataset. Intell Inf Manage2018; 10(2): 43–48.
28.
DempsterAPLairdNMRubinDB. Maximum likelihood from incomplete data via the EMAlgorithm. J R Stat Soc Ser B (Methodological)1977; 39(1): 1–22.
29.
FengLCBaiYZChenXQ. Finite-time sliding mode control for spacecraft rendezvous with collision avoidance. J Astronautics2016; 37(11): 1342–1348. (in Chinese)
30.
CaoLChenXMisraAK. Minimum sliding mode error feedback control for fault tolerant reconfigurable satellite formations with J2 perturbations. Acta Astronautica2014; 96: 201–216.
31.
CaoLChenYZhangZ, et al.Predictive smooth variable structure filter for attitude synchronization estimation during satellite formation flying. IEEE Trans Aerospace Electron Syst2017; 53(3): 1375–1383.
32.
YamanakaKAnkersenF. New state transition matrix for relative motion on an arbitrary elliptical orbit. J Guidance, Control Dyn2002; 25(1): 60–66.
33.
FuYMLiWDuanGR. Satellite trajectory model reference output tracking control based on T-H equation. J Astronautics2013; 34(4): 496–502. (in Chinese)
