Nonlinear time-varying system,such as a spacecraft formation flying system with chief spacecraft in elliptical orbit and under the effect of perturbation forces,is difficult to analyze,design,and control based on the ...Nonlinear time-varying system,such as a spacecraft formation flying system with chief spacecraft in elliptical orbit and under the effect of perturbation forces,is difficult to analyze,design,and control based on the presence of time-varying parameters.The proper functioning of aerospace systems and their ability to be able to achieve the designed mission objectives depend largely on proper understanding of their nonlinear time-varying nature,dynamics,and ability to keep them in the required mission operation configurations through high-fidelity optimal control strategy.This paper presents nonlinear dynamics and optimal control of J_(2)perturbed spacecraft formation flying.Via Euler–Lagrange approach,the nonlinear J_(2)perturbed motion dynamics was approximated into a time-varying nonlinear form,having periodic coefficients and time-varying parameters,suitable for designing fuel efficient control strategies,spacecraft formation flying,relative motion,and rendezvous mission analysis.Through the application of State-Dependent Riccati Equation(SDRE)approach,the approximated model was converted into a non-unique,pseudo-linear state-dependent coefficient(SDC)form.The numerical simulations confirmed that the SDRE controllers,developed using SDC parameterized systems,are maximally robust and able to return the system to the desired radial,along-track,and cross-track positions.展开更多
As interest in the use and launching of spacecraft for communications,earth observation,scientific experiment and navigation purposes increases and manned missions to the Moon and Mars intensify,there is need for the ...As interest in the use and launching of spacecraft for communications,earth observation,scientific experiment and navigation purposes increases and manned missions to the Moon and Mars intensify,there is need for the design of efficient and highfidelity relative motion dynamics to reduce spacecraft collisions and increase return on investment.The main aim of this work is to develop new approximate solution of spacecraft relative motion in elliptical orbit via power series method.Advantage of this method is that it does not involve evaluating complex integral I as employed for developing approximate solutions of linearized Tschauner–Hempel equations.Cauchy product,used for the discrete convolution of power series,is employed for the development of power series solutions of the approximated nonlinear spacecraft relative motion.Application of Cauchy criterion shows that the new solutions are convergent making them useful for spacecraft formation flying,proximity and rendezvous mission analysis.展开更多
The ultimate need to design and develop high-fidelity dynamical models for future space missions is necessitated by thecontinuous and enormous interest in spacecraft formation flying, rendezvous and spacecraft proximi...The ultimate need to design and develop high-fidelity dynamical models for future space missions is necessitated by thecontinuous and enormous interest in spacecraft formation flying, rendezvous and spacecraft proximity operations. In thispaper, to obtain high-fidelity dynamics, higher-order relative motion model is developed via nonlinear mapping of orbitelement differences and Hill coordinates. First, second-order variation of parameter technique of calculus of variations isapplied to the direction cosine matrix (DCM), which maps vector components in inertial frame to vector components inDeputy Hill frame, and deputy spacecraft inertial position and velocity vectors in Deputy Hill frame. Second, after series oftransformations and elimination of higher-order terms greater than quadratic terms, new, nonlinearly mapped radial, alongtrackand cross-track relative motion position and velocity equations are obtained. Using the newequation ofmotion, nonlinearstate space model is developed. The new equations, validated via numerical simulations, are amenable for the analysis ofspacecraft relative motion, formation flying, rendezvous and proximity operations in both circular and elliptical orbits.展开更多
文摘Nonlinear time-varying system,such as a spacecraft formation flying system with chief spacecraft in elliptical orbit and under the effect of perturbation forces,is difficult to analyze,design,and control based on the presence of time-varying parameters.The proper functioning of aerospace systems and their ability to be able to achieve the designed mission objectives depend largely on proper understanding of their nonlinear time-varying nature,dynamics,and ability to keep them in the required mission operation configurations through high-fidelity optimal control strategy.This paper presents nonlinear dynamics and optimal control of J_(2)perturbed spacecraft formation flying.Via Euler–Lagrange approach,the nonlinear J_(2)perturbed motion dynamics was approximated into a time-varying nonlinear form,having periodic coefficients and time-varying parameters,suitable for designing fuel efficient control strategies,spacecraft formation flying,relative motion,and rendezvous mission analysis.Through the application of State-Dependent Riccati Equation(SDRE)approach,the approximated model was converted into a non-unique,pseudo-linear state-dependent coefficient(SDC)form.The numerical simulations confirmed that the SDRE controllers,developed using SDC parameterized systems,are maximally robust and able to return the system to the desired radial,along-track,and cross-track positions.
文摘As interest in the use and launching of spacecraft for communications,earth observation,scientific experiment and navigation purposes increases and manned missions to the Moon and Mars intensify,there is need for the design of efficient and highfidelity relative motion dynamics to reduce spacecraft collisions and increase return on investment.The main aim of this work is to develop new approximate solution of spacecraft relative motion in elliptical orbit via power series method.Advantage of this method is that it does not involve evaluating complex integral I as employed for developing approximate solutions of linearized Tschauner–Hempel equations.Cauchy product,used for the discrete convolution of power series,is employed for the development of power series solutions of the approximated nonlinear spacecraft relative motion.Application of Cauchy criterion shows that the new solutions are convergent making them useful for spacecraft formation flying,proximity and rendezvous mission analysis.
文摘The ultimate need to design and develop high-fidelity dynamical models for future space missions is necessitated by thecontinuous and enormous interest in spacecraft formation flying, rendezvous and spacecraft proximity operations. In thispaper, to obtain high-fidelity dynamics, higher-order relative motion model is developed via nonlinear mapping of orbitelement differences and Hill coordinates. First, second-order variation of parameter technique of calculus of variations isapplied to the direction cosine matrix (DCM), which maps vector components in inertial frame to vector components inDeputy Hill frame, and deputy spacecraft inertial position and velocity vectors in Deputy Hill frame. Second, after series oftransformations and elimination of higher-order terms greater than quadratic terms, new, nonlinearly mapped radial, alongtrackand cross-track relative motion position and velocity equations are obtained. Using the newequation ofmotion, nonlinearstate space model is developed. The new equations, validated via numerical simulations, are amenable for the analysis ofspacecraft relative motion, formation flying, rendezvous and proximity operations in both circular and elliptical orbits.
