Spacecraft Close-range Relative Motion: Reachability Analysis And Optimal Control

With the continuous development and utilization of the space environment,the number of space vehicles continues to increase,and the demand for on-orbit services of space vehicles is increasingly urgent.In order to achieve on-orbit service,maneuvering spacecraft need to work near the target spacecraft.One of the key technologies that need to be solved urgently is the relative motion guidance and control of spacecraft in close range,which covers many aspects such as spacecraft orbit prediction,position maneuver and attitude adjustment.Based on reachability theory,this paper studies the feasibility of terminal approaching for failure spacecraft and early warning for space safety flight.Meanwhile,based on optimal control theory,the optimal control proble m with path constraints in various mission scenarios is studied by using model predictive control and state-dependent Riccati equation,and a three-degree-of-freedom air-bearing platform is built.The experimental system verifies the proposed algorithms.The main contents of this paper include:Firstly,based on reachability theory,the feasibility of terminal proximity and collision risk in spacecraft close relative motion are analyzed.On the one hand,zonotope-based backward reachable set method is used to analyze the six-degree-of-freedom approaching problem for space rotating target,and the approaching feasible initial state set is visually displayed by optimization method,which provides a basis for the reasonable design of approaching task.On the other hand,based on the propagation characteristics of uncertainties predicted by the zonotope-based forward reachable set and the unified use of the zonotope to characterize the geometric shape of the spacecraft,the concept of the dangerous domain considering the geometric shape of the spacecraft,navigation uncertainty and system disturbance is proposed to test flight safety,and a method for estimating the distance between the dangerous domains of different spacecraft is proposed.The collision risk of spacecraft in close relative motion is predicted.Secondly,the model predictive control(MPC)is used to study the relative motion of spacecraft in close range with various constraints.On the one hand,a robust control strategy is proposed based on the zonotope forward reachable set method,which guarantees that the field of view angle constraints and obstacle avoidance constraints can always be satisfied in the rendezvous process even under the disturbance of the system.The effects of the geometric shape and relative attitude of spacecraft and obstacles on collision avoidance are analyzed.On the other hand,considering the effect of the line of sight constraint and the attitude of the spacecraft on collision avoidance,the non-linear constraints of position-attitude coupling are proposed and solved in the framework of model predictive control by direct linearization method.Thirdly,based on the state-dependent Riccati equation,the optimal control of spacecraft relative motion in close range is studied.On the one hand,an approximate optimal tracking controller is designed based on the state-dependent Riccati equation for the optimal approximation problem of space tumbling targets,and compared with the existing methods.On the other hand,aiming at the shortcomings of traditional state constraints processing methods in dealing with path constraints,the logarithmic obstacle function is introduced to characterize and process path constraints,and the controller is designed by relaxing its first derivative.Several typical orbit and attitude path constraints are successfully solved,which verifies the effectiveness of the proposed method.Finally,a three-degree-of-freedom air-bearing platform system is built to verify the proposed method.Aiming at the approaching task scenario of uniformly rotating target,the proposed approximate optimal tracking control algorithm is used to verify the simulation results.The results show that the proposed method can achieve excellent tracking,and the theoretical results are basically consistent with the experimental results.The validity and practicability of the approximate optimal tracking control algorithm are tested,and the control accuracy of the system is reflected,which provides a basis for experimental verification based on numerical simulation results.Aiming at the mission scenario where the position and attitude of a planar elliptical spacecraft pass through a narrow gap formed by two obstacles,the proposed model predictive control algorithm and the state-dependent Riccati equation optimal control method are used to verify the simulation results.The experimental results show that both methods can successfully avoid obstacles and achieve the desired position and attitude.The effectiveness and practicability of the proposed methods are verified.Based on the optimal control theory,the analysis and control of spacecraft close-range relative motion are deeply studied in this paper.A relative motion analysis method based on the reachable set of zonotope is proposed,which can play an important role in the approach of failure targets and collision risk assessment,and a solution to the problem of position and attitude path constraints under various working conditions is proposed.The experiment validation provides a useful reference for the design of autonomous approach control system of spacecraft.Relevant research results can be extended to the engineering practice of spacecraft close-range relative motion,and have broad application prospects.