For autonomous spacecraft close proximity under environments containing multiple obstacles and complicated constraints, incrementally rapid planning approaches stemming from sampling-based methods are investigated in this paper. Exploring planners are separately developed for the impulsive maneuvered translation and the piecewise constant controlled rotation, which, however, is constrained by the pointing limits coupling with relative positions during the proximity. Using a cost-informed parent-connecting strategy originating from dynamic programming as well as a sweeping growth fashion balanced between tree-based and graph-based methods, an asymptotically optimal unidirectional exploration method is proposed to search energy-efficient translational trajectory without collision. As for the rotation planning, the pointing constraints are taken as virtual obstacles in the state-space augmented with time horizon planned by the translation and, accordingly, a bidirectional exploration method is developed to generate constraint-satisfied slew paths with fast convergence rate. Numerical experiments indicate that the proposed sampling-based methods can rapidly return asymptotic optimal translation trajectory and rotation path satisfying collision avoidance and sensor field-of-view constraints.
WenCGurfilP. Guidance, navigation and control for autonomous R-bar proximity operations for geostationary satellites. Proc IMechE, Part G: J Aerospace Engineering2017; 231: 452–473.
2.
GeJZhaoJYuanJ. A novel guidance strategy for autonomously approaching a tumbling target. Proc IMechE, Part G: J Aerospace Engineering2018; 232: 861–871.
3.
SeongJDKimHDChoiHY. A study of a target identification method for an active debris removal system. Proc IMechE, Part G: J Aerospace Engineering2017; 231: 180–189.
4.
StarekJAAcikmeseBNesnasIAet al.Spacecraft autonomy challenges for next-generation space missions. Lecture Notes in Control and Information Sciences, New York: Springer, 2016, pp. 1–48.
5.
BoyarkoGYakimenkoORomanoM. Optimal rendezvous trajectories of a controlled spacecraft and a tumbling object. J Guid Control Dyn2011; 34: 1239–1252.
6.
WangYXuS. Stabilizing the coupled orbit-attitude dynamics of a rigid body in a J2 gravity field using Hamiltonian structure. Acta Astronaut2015; 128: 180–203.
7.
WangYXuS. Stabilization of coupled orbit-attitude dynamics about an asteroid utilizing Hamiltonian structure. Astrodynamics2018; 2: 53–67.
8.
LuoYZTangGJLiYJet al.Optimization of multiple-impulse, multiple-revolution, rendezvous-phasing maneuvers. J Guid Control Dyn2007; 30: 946–952.
9.
LuPLiuX. Autonomous trajectory planning for rendezvous and proximity operations by conic optimization. J Guid Control Dyn2013; 36: 375–389.
10.
MorganDChungSJHadaeghFY. Model predictive control of swarms of spacecraft using sequential convex programming. J Guid Control Dyn2014; 37: 1725–1740.
11.
Baldini F, Bandyopadhyay S, Foust R, et al. Fast motion planning for agile space systems with multiple obstacles. In: AIAA/AAS astrodynamics specialist conference, Long Beach, CA, USA, 12–15 September 2016, pp.1–16.
12.
GrantMBoydS. CVX: Matlab software for disciplined convex programming. Global Optimization2008, pp. 155–210.
13.
HuntingtonGTRaoAV. Optimal reconfiguration of spacecraft formations using the Gauss pseudospectral method. J Guid Control Dyn2008; 31: 689–698.
14.
JiangXLiS. Mars atmospheric entry trajectory optimization via particle swarm optimization and Gauss pseudo-spectral method. Proc IMechE, Part G: J Aerospace Engineering2016; 230: 2320–2329.
15.
ZhangLYuCZhangSet al.Optimal attitude trajectory planning method for CMG actuated spacecraft. Proc IMechE, Part G: J Aerospace Engineering2018; 232: 131–142.
16.
PattersonMARaoAV. GPOPS-II: A MATLAB software for solving multiple-phase optimal control problems using hp-adaptive Gaussian quadrature collocation methods and sparse nonlinear programming. ACM Trans Math Softw2014; 41: 1–37.
17.
ChuXZhangJLuSet al.Optimised collision avoidance for an ultra-close rendezvous with a failed satellite based on the Gauss pseudospectral method. Acta Astronaut2016; 128: 363–376.
18.
WuYHHuYBHuaBet al.A time suboptimal method for real-time spacecraft attitude agile maneuvering with angular velocity constraint. Proc IMechE, Part G: J Aerospace Engineering2017.
19.
GuiHde RuiterAHJ. Adaptive fault-tolerant spacecraft pose tracking with control allocation. IEEE Trans Control Syst Technol2018; 99: 1–16.
20.
GuiHVukovichG. Finite-time output-feedback position and attitude tracking of a rigid body. Automatica2016; 74: 270–278.
21.
GuiHVukovichG. Dual-quaternion-based adaptive motion tracking of spacecraft with reduced control effort. Nonlinear Dyn2016; 83: 597–614.
22.
FrazzoliE. Quasi-random algorithms for real-time spacecraft motion planning and coordination. Acta Astronaut2003; 53: 485–495.
23.
Garcia I and How JP. Trajectory optimization for satellite reconfiguration maneuvers with position and attitude constraints. In: American control conference, Portland, USA, 8–10 June 2005, pp.889–894.
24.
Frazzoli E, Dahleh MA, Feron E, et al. A randomized attitude slew planning algorithm for autonomous spacecraft. In: AIAA guidance, navigation, and control conference and exhibit, Montreal, Canada, 6 August 2001, pp.4155–4162.
25.
FrazzoliEDahlehMAFeronE. Real-time motion planning for agile autonomous vehicles. J Guid Control Dyn2002; 25: 116–129.
26.
ChenYHeZZhouDet al.Integrated guidance and control for microsatellite real-time automated proximity operations. Acta Astronaut2018; 148: 175–185.
27.
KavrakiLESvestkaPLatombeJCet al.Probabilistic roadmaps for path planning in high-dimensional configuration spaces. IEEE Trans Robot Autom1996; 12: 566–580.
28.
LaValle SM. Resolution complete rapidly-exploring random trees. In: Proceedings of the 2002 IEEE International Conference on Robotics and Automation, ICRA 2002, Washington, DC, USA, 11–15 May 2002, pp.267–272.
LavalleSM. Planning algorithms, Cambridge: Cambridge University Press, 2006.
31.
KaramanSFrazzoliE. Sampling-based algorithms for optimal motion planning. Int J Robot Res2011; 30: 846–894.
32.
DiGirolamo LJ, Hoskins AH, Hacker KA, et al. A hybrid motion planning algorithm for safe and efficient close proximity, autonomous spacecraft missions. In: AIAA/AAS astrodynamics specialist conference, San Diego, CA, USA, 4–7 August 2014, pp.4130–4148.
33.
JansonLSchmerlingEClarkAet al.Fast marching tree: a fast marching sampling-based method for optimal motion planning in many dimensions. Int J Robot Res2015; 34: 883–921.
34.
StarekJASchmerlingEMaherGDet al.Fast, safe, propellant-efficient spacecraft motion planning under Clohessy-Wiltshire-Hill dynamics. J Guid Control Dyn2017; 40: 418–438.
35.
KobilarovM. Cross-entropy motion planning. Int J Robot Res2012; 31: 855–871.
36.
KobilarovMPellegrinoS. Trajectory planning for CubeSat short-time-scale proximity operations. J Guid Control Dyn2014; 37: 566–579.
37.
Francis GD, Collins Jr EG, Chuy O, et al. Sampling-based trajectory generation for autonomous spacecraft rendezvous and docking. In: AIAA guidance, navigation, and control conference and exhibit, Boston, MA, USA, 19–22 August 2013, pp.4549–4556.
Goretkin G, Perez A, Platt Jr R, et al. Sampling-based planning for linear-quadratic kinodynamic systems. In: IEEE international conference on robotics and automation (ICRA), Karlsruhe, Germany, 6–10 May 2013, pp.2429–2436.
40.
Karaman S and Frazzoli E. Optimal kinodynamic motion planning using incremental sampling-based methods. In: 49th IEEE conference on decision and control (CDC), Atlanta, GA, USA, 2 April 2010, pp.7681–7687.
41.
HaltonJH. On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numer Math1960; 2: 84–90.
42.
ChiHMascagniMWarnockTet al.On the optimal Halton sequence. Math Comput Simul2005; 70: 9–21.
43.
LuP. Introducing computational guidance and control. J Guid Control Dyn2017; 40: 193–193.
44.
TsiotrasPMehranM. Toward an algorithmic control theory. J Guid Control Dyn2017; 40: 194–196.
