The present status and prospects in the research of orbital dynamics and control near small celestial bodies

Small celestial body exploration is of great significance to deep space activities. The dynamics and control of orbits around small celestial bodies is of top priority in the exploration research. It includes the modeling of dynamics environment and the orbital dynamics mechanism. This paper introduced state-ofthe-art researches, major challenges, and future trends in this field. Three topics are mainly discussed： the gravitational field modeling of irregular-shaped small celestial bodies, natural orbital dynamics and control, and controlled orbital dynamics. Finally, constructive suggestions are made for China’s future space exploration missions.

Adaptive Quasi Fixed-Time Orbit Control Around Asteroid with Performance Guarantees

This paper investigates a novel quasi fixed-time orbit tracking control method for spacecraft around an asteroid in the presence of uncertain dynamics and unknown uncertainties.To quantitatively characterize the transient and steady-state responses of orbit tracking error system,a continuous performance function is devised via using a quartic polynomial.Then,integrating backstepping control technique and barrier Lyapunov function leads to a quasi fixed-time convergent orbit tracking controller without using any fractional state information and symbolic functions.Finally,two groups of illustrative examples are employed to test the effectiveness of the proposed orbit control method.

Key Role of Some Specific Occupied Molecular Orbitals of Short Chain n-Alkanes in Their Surface Tension and Reaction Rate Constants with Hydroxyl Radicals: DFT Study

Basing on the DFT calculations we propose the new theoretical model which describes both the surface tension σ of the short chain n-alkanes at their normal boiling points and their reaction rate constants with hydroxyl radicals OH• (at 297 ± 2 K) on the basis of their molecular orbital electronic characteristics. It has been shown that intermolecular dispersion attraction within the surface liquid monolayer of these compounds, as well as their reaction rate constants k with OH• radicals are determined by the energies Eorb of the specific occupied molecular orbitals which are the same in the determination of both the above physico-chemical characteristics of the studied n-alkanes. The received regression equations confirm the theoretically found dependences between the quantities of σ and k and the module |Eorb|. For the compounds under study this fact indicates the key role of their electronic structure particularities in determination of both the physical (surface tension) and the chemical (reaction rate constants) properties.

Molecular Orbital Nature of Solubility of Shot Chain n-Alkanes in Water and Their Reaction Rate Constants with Nitronium Cations: A DFT Study

The new theoretical models describe both the solubility S of the shot chain n-alkanes in water at 298.15 K, and their reaction rate constants k with nitronium cation NO2+ at 293.15 K on the basis of their molecular orbital characteristics. It is shown that both the quantities S and k are determined by the energies Eorb of the specific virtual (for S) and occupied (for k) molecular orbitals of these n-alkanes. The obtained regression equations confirm the theoretically found dependences of S and k on the absolute value of Eorb. This fact demonstrates that the electronic structure particularities of the studied n-alkanes play a crucial role in both their above-mentioned physicochemical properties.

Design and simulation of fault diagnosis based on NUIO/LMI for satellite attitude control systems

This paper presents a scheme of fault diagnosis for flexible satellites during orbit maneuver. The main contribution of the paper is related to the design of the nonlinear input observer which can avoid false alarm arising from the disturbance from orbit control force. The effects of orbit control force on the fault diagnosis system for satellite attitude control systems, including the disturbing torque caused by the misalignments and the model uncertainty caused by the fuel consumed, are discussed, where standard Lu- enberger observer cannot work well. Then the nonlinear unknown input observer is proposed to decouple faults from disturbance, Besides, a linear matrix inequality approach is adopted to reduce the effect of nonlinear part and model uncertainties on the observer. The numerical and semi-physical simulation demonstrates the effectiveness of the proposed observer for the fault diagnosis system of the satellite during orbit maneuver.

Multi-spacecraft Intelligent Orbit Phasing Control Considering Collision Avoidance

This paper proposes an intelligent low-thrust orbit phasing control method for multiple spacecraft by simultaneously considering fuel optimization and collision avoidance. Firstly,the minimum-fuel orbit phasing control database is generated by the indirect method associated with the homotopy technique. Then,a deep network representing the minimum-fuel solution is trained. To avoid collision for multiple spacecraft,an artificial potential function is introduced in the collision-avoidance controller. Finally,an intelligent orbit phasing control method by combining the minimum-fuel neural network controller and the collision-avoidance controller is proposed. Numerical results show that the proposed intelligent orbit phasing control is valid for the multi-satellite constellation initialization without collision.

Controlof Orbitand Controlof Chaosina Class of Dynamic System

The problem of control of orbit for the dynamic system x ¨+x(1-x)(x-a)=0 is discussed. Any unbounded orbit of the dynamic system can be controlled to become a bounded periodic orbit by adding a periodic step excitation to the system. By using a nonlinear feedback control law presented in this paper the chaos of the dynamic system with excitation and damping is stabilized. This method is more effectual than the linear feedback control.

An improved nonlinear control strategy for deep space formation flying spacecraft

This paper aims to provide further study on the nonlinear modeling and controller design of formation flying spacecraft in deep space missions. First, in the Sun-Earth system, the nonlinear formation dynamics for the circular restricted three-body problem （CRTBP） and elliptic restricted three-body problem （ERTBP） are presented. Then, with the Floquet mode method, an impulsive controller is developed to keep the Chief on the desired Halo orbit. Finally, a nonlinear adaptive control scheme based on Nonzero set- point LQR and neural network is proposed to achieve high precision formation maneuver and keeping. The simulation results indicate that the proposed nonlinear control strategy is reasonable as it considers not only the orbit keeping of the Chief, but also the formation modeling inaccuracy. Moreover, the nonlinear adaptive control scheme is effective to improve the control accuracy of the formation keeping.

Modeling and simulations of orbital capture with space tether-net system

A new flexible tether-net space robotic system used to capture space debris is presented in this paper. With a mass point assumption, a dynamic model of the tether-net system was established in orbital frame by applying Lagrange Equations. In order to investigate the net in-plane trajectories after being cast, the non-controlled R-bar and V-bar captures were simulated with ignoring the out-of-plane libration, and the effect of in-plane libration on the trajectories of the capture net was demonstrated by simulation results. With an effort to damp the in-plane libration, the control scheme based on tether tension was investigated, then an integrated control scheme was proposed by introducing thrusters into the system, and the nonlinear close-loop dynamics was linearised by feedforward strategy. Simulation results show that the feedforward controller is effective for in-plane libration damping and enables the capture net to track an expected trajectory.

Analytic optimal pose tracking control in close-range proximity operations with a non-cooperative target

This paper investigates an analytical optimal pose tracking control problem for chaser spacecraft during the close-range proximity operations with a non-cooperative space target subject to attitude tumbling and unknown orbital maneuvering.Firstly,the relative translational motion between the orbital target and the chaser spacecraft is described in the Line-of-Sight(LOS)coordinate frame along with attitude quaternion dynamics.Then,based on the coupled 6-Degree of Freedom(DOF)pose dynamic model,an analytical optimal control action consisting of constrained optimal control value,application time and its duration are proposed via exploring the iterative sequential action control algorithm.Meanwhile,the global closed-loop asymptotic stability of the proposed predictive control action is presented and discussed.Compared with traditional proximity control schemes,the highlighting advantages are that the application time and duration of the devised controller is applied discretely in light of the influence of the instantaneous pose configuration on the pose tracking performance with less energy consumptions rather than at each sample time.Finally,three groups of illustrative examples are organized to validate the effectiveness of the proposed analytical optimal pose tracking control scheme.

Distributed adaptive prescribed-time orbit containment control for satellite cluster flight

The distributed prescribed-time orbit containment control for the satellite cluster flight with multiple dynamic leaders is investigated.The directed information communication topology between followers is taken into account in the overall paper.When the satellite mass is assumed to be constant,a distributed prescribed-time orbit containment controller is,firstly,presented to drive the followers into the dynamic convex hull produced by multiple leaders.Then,the parameter uncertainty is considered,and a prescribed-time sliding mode estimator is introduced to estimate the desired velocity of each follower.Based on the estimated state,a novel distributed adaptive prescribed-time orbit containment control scheme is proposed.The Lyapunov stability theory is utilized to prove the prescribed-time stability of the closed-loop system.Finally,several numerical simulations and comparison of different control methods are provided to verify the effectiveness and superiority of the proposed control method.

Guidance strategy of motion camouflage for spacecraft pursuit-evasion game

This work is inspired by a stealth pursuit behavior called motion camouflage whereby a pursuer approaches an evader while the pursuer camouflages itself against a predetermined background.We formulate the spacecraft pursuit-evasion problem as a stealth pursuit strategy of motion camouflage,in which the pursuer tries to minimize a motion camouflage index defined in this paper.The Euler-Hill reference frame whose origin is set on the circular reference orbit is used to describe the dynamics.Based on the rule of motion camouflage,a guidance strategy in open-loop form to achieve motion camouflage index is derived in which the pursuer lies on the camouflage constraint line connecting the central spacecraft and evader.In order to dispose of the dependence on the evader acceleration in the open-loop guidance strategy,we further consider the motion camouflage pursuit problem within an infinite-horizon nonlinear quadratic differential game.The saddle point solution to the game is derived by using the state-dependent Riccati equation method,and the resulting closed-loop guidance strategy is effective in achieving motion camouflage.Simulations are performed to demonstrate the capabilities of the proposed guidance strategies for the pursuit–evasion game scenario.

Attitude and Orbit Optimal Control of Combined Spacecraft via a Fully-Actuated System Approach

This paper investigates the attitude and orbit control for the combined spacecraft formed after a target spacecraft without the autonomous control ability is captured by a service spacecraft.The optimal controller of fully-actuated system is proposed to realize the attitude and orbit stabilization control of combined spacecraft.The stability of the system is proved by introducing Lyapunov function.Numerical simulation of the combined spacecraft and physical experiment based on the combined spacecraft simulator(CSS)are completed.Both simulation and experiment results demonstrate the effectiveness and practicability of the optimal controller of fully-actuated system.

Chang’E-2 satellite asymmetric-descent orbit control technology

To accomplish high-resolution imaging of the preselected landing area, it was necessary for the Chang＇E-2 mission to perform orbital maneuvering on the far side of the moon to meet the conditional height requirement of the imaging area. Engine shutdown would be executed invisibly on the back side of the moon if the descent maneuver mode opposite to the target perilune or the fuel optimal maneuver mode was used. To ensure the satellite safety, the project collectivety required that the engine shutdown should be designed to be executed in the domestic segmental arcs and meet the requirement of satellite emergency treatment simultaneously. Accordingly, the asymmetric-descent orbit control technology was adopted by offsetting the ma- neuver point, which obtained the orbit control parameters of finite-thrust mode with an iteration algorithm and modified the results with target perilune drift estimation. The Chang＇E-2 satellite declined to the target of 100 km×l5 km orbit successfully on 26 October 2010, and has been flying for 32 circles in the experimental orbit to accomplish the preselected landing area imaging. This paper describes the mechanism and realization method of the asymmetric-descent orbit control technology and evaluates the maneuver effect with the actual mission data.

On all-propulsion design of integrated orbit and attitude control for inner-formation gravity field measurement satellite

The inner-formation gravity field measurement satellite （IFS） is a novel pure gravitational orbiter. It aims to measure the Earth＇s gravity field with unprecedented accuracy and spatial resolution by means of precise orbit determination （POD） and relative state measurement. One of the key factors determining the measurement level is the outer-satellite control used for keeping the inner-satellite flying in a pure gravitational orbit stably. In this paper the integrated orbit and attitude control of IFS during steady-state phase was investigated using only thrusters. A six degree-of-freedom translational and rotational dynamics model was constructed considering nonlinearity resulted from quaternion expression and coupling induced by community thrusters. A feasible quadratic optimization model was established for the integrated orbit and attitude control using con- strained nonlinear model predictive control （CNMPC） techniques. Simulation experiment demonstrated that the presented CNMPC aigorithm can achieve rapid calculation and overcome the non-convexity of partial constraints. The thruster layout is rational with low thrust consumption, and the mission requirements of IFS are fully satisfied.

Elliptical formation control based on relative orbit elements

A new set of relative orbit elements（ROEs）is used to derive a new elliptical formation flying model.In-plane and out-of-plane motions can be completely decoupled,which benefts elliptical formation design.The inverse transformation of the state transition matrix is derived to study the relative orbit control strategy.Impulsive feedback control laws are developed for both in-plane and out-of-plane relative motions.Control of in-plane and out-of-plane relative motions can be completely decoupled using the ROE-based feedback control law.A tangential impulsive control method is proposed to study the relationship of fuel consumption and maneuvering positions.An optimal analytical along-track impulsive control strategy is then derived.Different typical orbit maneuvers,including formation establishment,reconfguration,long-distance maneuvers,and formation keeping,are taken as examples to demonstrate the performance of the proposed control laws.The effects of relative measurement errors are also considered to validate the high accuracy of the proposed control method.

Design, development, and performance of an ammonia self-managed vaporization propulsion system for micro-nano satellites

An ammonia self-managed vaporization propulsion (ASVP) system for micro-nano satellites is presented. Compared with a normal cold gas or liquefied gas propulsion system, a multiplex parallel sieve type vaporizer and related vaporization control methods are put forward to achieve self-managed vaporization of liquefied propellant. The problems of high vaporization latent heat and incomplete vaporization of liquefied ammonia are solved, so that the ASVP system takes great advantage of high theoretical specific impulse and high propellant storage density. Furthermore, the ASVP operation procedure and its physical chemistry theories and mathematical models are thoroughly analyzed. An optimal strategy of thrust control is proposed with consideration of thrust performance and energy efficiency. The ground tests indicate that the ASVP system weighs 1.8 kg (with 0.34-kg liquefied ammonia propellant) and reaches a specific impulse of more than 100 s, while the power consumption is less than 10 W. The ASVP system meets multiple requirements including high specific impulse, low power consumption, easy fabrication, and uniform adjustable thrust output, and thus is suitable for micro-nano satellites.

A simplex method for the orbit determination of maneuvering satellites

A simplex method of orbit determination （SMOD） is presented to solve the problem of orbit determination for maneuvering satellites subject to small and continuous thrust. The objective function is established as the sum of the nth powers of the observation errors based on global positioning satellite （GPS） data. The convergence behavior of the proposed method is analyzed using a range of initial orbital parameter errors and n values to ensure the rapid and accurate convergence of the SMOD. For an uncontrolled satellite, the orbit obtained by the SMOD provides a position error compared with GPS data that is commensurate with that obtained by the least squares technique. For low Earth orbit satellite control, the precision of the acceleration produced by a small pulse thrust is less than 0.1% compared with the calibrated value. The orbit obtained by the SMOD is also compared with weak GPS data for a geostationary Earth orbit satellite over several days. The results show that the position accuracy is within 12.0 m. The working efficiency of the electric propulsion is about 67% compared with the designed value. The analyses provide the guidance for subsequent satellite control. The method is suitable for orbit determination of maneuvering satellites subject to small and continuous thrust.

Invariant submanifolds for systems of vector fields of constant rank

Given a system of vector fields on a smooth manifold that spans a plane field of constant rank, we present a systematic method and an algorithm to find submanifolds that are invariant under the flows of the vector fields. We present examples of partition into invariant submanifolds, which further gives partition into orbits. We use the method of generalized Frobenius theorem by means of exterior differential systems.