Equal-collision-probability-curve method for safe spacecraft close-range proximity maneuvers

Abstract An equal-collision-probability-curve (ECPC) method is developed in this paper to address the problem of safe spacecraft proximity maneuvers. Considering the uncertainties’ influence, the ECPC, which represents the curve of equal-collision-probability-points in the space around the target spacecraft, is firstly established. It is optimal to maneuver along the gradient direction of the ECPC, which is the fastest change in the ECPC. To calculate this direction, a novel auxiliary function, which has the same gradient direction as the collision probability function, is proposed. Compared to traditional collision probability functions, the proposed function does not contain transcendental elements and hence the computational burden can be greatly decreased while maintaining the necessary accuracy. Then, the safe close-range proximity maneuver generated by ECPC method can be implemented along the estimated gradient direction. Analytical validation is performed to assess the use of such collision avoidance scheme for safety critical operations. Furthermore, an improved Linear Quadratic Regulator (LQR) is designed to track the reference trajectory and a Lyapunov-based analysis verifies the stability of the overall closed-loop system. Numerical simulations show that the novel ECPC method is more computationally efficient than traditional methods while maintaining the same accuracy. Moreover, the novel scheme can be easily validated to guarantee the safety of the mission.

[1]  Deok-Jin Lee,et al.  Probability of Collision Error Analysis , 1999 .

[2]  C. Bussy‐Virat.  Spacecraft Collision Avoidance , 2017 .

[3]  Thierry Peynot,et al.  Learned Stochastic Mobility Prediction for Planning with Control Uncertainty on Unstructured Terrain , 2014, J. Field Robotics.

[4]  Gianmarco Radice,et al.  Close proximity formation flying via linear quadratic tracking controller and artificial potential function , 2015 .

[5]  Xiangyu Wang,et al.  Hybrid Consensus-Based Cubature Kalman Filtering for Distributed State Estimation in Sensor Networks , 2018, IEEE Sensors Journal.

[6]  Feng-Yi Lin.  Robust Control Design: An Optimal Control Approach , 2007 .

[7]  Guo-Jin Tang,et al.  Uncertainty Quantification for Short Rendezvous Missions Using a Nonlinear Covariance Propagation Method , 2016 .

[8]  Ye Yan,et al.  Output Feedback Control of Underactuated Spacecraft Hovering in Circular Orbit With Radial or In-Track Controller Failure , 2016, IEEE Transactions on Industrial Electronics.

[9]  Vincent Agi Coppola,et al.  Evaluating the Short Encounter Assumption of the Probability of Collision Formula , 2012 .

[10]  Ye Yan,et al.  Nonlinear Control of Underactuated Spacecraft Hovering , 2016 .

[11]  Maruthi R. Akella,et al.  Probability of Collision Between Space Objects , 2000 .

[12]  Wigbert Fehse,et al.  Automated Rendezvous and Docking of Spacecraft , 2003 .

[13]  David A. Spencer,et al.  Prox-1 University-Class Mission to Demonstrate Automated Proximity Operations , 2016 .

[14]  Gary Slater,et al.  Collision Avoidance for Satellites in Formation Flight , 2004 .

[15]  Martin Sweeting,et al.  Very-Small-Satellite Design for Distributed Space Missions , 2007 .

[16]  Ou Ma,et al.  A review of space robotics technologies for on-orbit servicing , 2014 .

[17]  Mark L. Psiaki,et al.  Absolute Orbit and Gravity Determination using Relative Position Measurements Between Two Satellites , 2007 .

[18]  Dong Qiao,et al.  Suboptimal artificial potential function sliding mode control for spacecraft rendezvous with obstacle avoidance , 2018 .

[19]  Arun K. Misra,et al.  Minimum sliding mode error feedback control for fault tolerant reconfigurable satellite formations with J2 perturbations , 2014 .

[20]  Sreeja Nag,et al.  Behaviour based, autonomous and distributed scatter manoeuvres for satellite swarms , 2013 .

[21]  Guo-Jin Tang,et al.  Maximum collision probability considering variable size, shape, and orientation of covariance ellipse , 2016 .

[22]  Shuzhi Sam Ge,et al.  Dynamic Motion Planning for Mobile Robots Using Potential Field Method , 2002, Auton. Robots.

[23]  Richard Linares,et al.  Spacecraft Uncertainty Propagation Using Gaussian Mixture Models and Polynomial Chaos Expansions , 2016 .

[24]  Atri Dutta,et al.  Peer-to-Peer Refueling Strategy Using Low-Thrust Propulsion , 2010 .

[25]  Hua Wang,et al.  Quantitative Performance for Spacecraft Rendezvous Trajectory Safety , 2011 .

[26]  Kyle J. DeMars,et al.  Collision Probability with Gaussian Mixture Orbit Uncertainty , 2014 .

[27]  Russell P. Patera,et al.  Satellite Collision Probability for Nonlinear Relative Motion , 2002 .

[28]  G. Tang,et al.  Explicit expression of collision probability in terms of RSW and NTW components of relative position , 2013 .

[29]  R. Patera.  General Method for Calculating Satellite Collision Probability , 2001 .

[30]  Aude Rondepierre,et al.  Fast and Accurate Computation of Orbital Collision Probability for Short-Term Encounters , 2016 .

[31]  Russell P. Patera,et al.  Collision Probability for Larger Bodies Having Nonlinear Relative Motion , 2006 .

[32]  Martin Sweeting,et al.  A low-cost femtosatellite to enable distributed space missions , 2006 .

[33]  Guo-Jin Tang,et al.  Satellite formation design and optimal stationkeeping considering nonlinearity and eccentricity , 2007 .

[34]  Xiao-Qian Chen,et al.  Nonlinear control of spacecraft formation flying with disturbance rejection and collision avoidance , 2017 .

[35]  Riccardo Bevilacqua,et al.  Development and experimentation of LQR/APF guidance and control for autonomous proximity maneuvers of multiple spacecraft , 2011 .

[36]  Feng Han,et al.  Attitude control for on-orbit servicing spacecraft using hybrid actuator , 2018 .

[37]  Ye Yan,et al.  Underactuated spacecraft formation reconfiguration with collision avoidance , 2017 .

[38]  Ya-Zhong Luo,et al.  Spacecraft rendezvous trajectory safety quantitative performance index eliminating probability dilution , 2014 .