Orbit and attitude control of spacecraft formation flying

Formation flying is a novel concept of distributing the functionality of large spacecraft among several smaller, less expensive, cooperative satellites. Some applications require that a controllable satellite keeps relative position and attitude to observe a specific surface of another satellite among the cluster. Specially, the target space vehicle is malfunctioning. The present paper focuses on the problem that how to control a chaser satellite to fly around an out-of-work target satellite closely in earth orbit and to track a specific surface. Relative attitude and first approximate relative orbital dynamics equations are presented. Control strategy is derived based on feedback linearization and Lyapunov theory of stability. Further, considering the uncertainty of inertia, an adaptive control method is developed to obtain the correct inertial ratio. The numerical simulation is given to verify the validity of proposed control scheme.

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.

HAMILTON-JACOBI EQUATIONS FOR A REGULAR CONTROLLED HAMILTONIAN SYSTEM AND ITS REDUCED SYSTEMS

In this paper,we give the geometric constraint conditions of a canonical symplectic form and regular reduced symplectic forms for the dynamical vector fields of a regular controlled Hamiltonian(RCH)system and its regular reduced systems,which are called the Type I and Type II Hamilton-Jacobi equations.First,we prove two types of Hamilton-Jacobi theorems for an RCH system on the cotangent bundle of a configuration manifold by using the canonical symplectic form and its dynamical vector field.Second,we generalize the above results for a regular reducible RCH system with symmetry and a momentum map,and derive precisely two types of Hamilton-Jacobi equations for the regular point reduced RCH system and the regular orbit reduced RCH system.Third,we prove that the RCH-equivalence for the RCH system,and the RpCH-equivalence and RoCH-equivalence for the regular reducible RCH systems with symmetries,leave the solutions of corresponding Hamilton-Jacobi equations invariant.Finally,as an application of the theoretical results,we show the Type I and Type II Hamilton-Jacobi equations for the Rp-reduced controlled rigid body-rotor system and the Rp-reduced controlled heavy top-rotor system on the generalizations of the rotation group SO(3)and the Euclidean group SE(3),respectively.This work reveals the deeply internal relationships of the geometrical structures of phase spaces,the dynamical vector fields and the controls of the RCH system.

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.

Design and control of multiple spacecraft formation flying in elliptical orbits

Spacecraft formation flying is an attractive new concept in international aeronautic fields because of its powerful functions and low cost. In this paper, the formation design and PD closed-loop control of spacecraft formation flying in elliptical orbits are discussed. Based on two-body relative dynamics, the true anomaly is applied as independent variable instead of the variable of time. Since the apogee is considered as the starting point, the six integrating constants are calculated. Therefore, the algebraic solution is obtained for the relative motion in elliptical orbits. Moreover, the formation design is presented and both circular formation and line formation are provided in terms of an algebraic solution. This paper also discusses the PD-closed loop control for precise formation control in elliptical orbits. In this part, the error-type state equation is put forward and the linear quadratic regulator （LQR） method is used to calculate PD parameters. Though the gain matrix calculated from LQR is time-variable because the error-type state equation is time variable, the PD parameters are also considered as constants because of their small changes in simulation. Finally, taking circular formation as an example, the initial orbital elements are achieved for three secondary spacecraft. And the numerical simulation is analyzed under PD formation control with initial errors and J2 perturbation. The simulation results demonstrate the validity of PD closed-loop control scheme.

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.

Trajectory and Correction Maneuver During the Transfer from Earth to Halo Orbit

This article addresses the design of the trajectory transferring from Earth to Halo orbit, and proposes a timing closed-loop strategy of correction maneuver during the transfer in the frame of circular restricted three body problem （CR3BP）. The relation between the Floquet multipliers and the magnitudes of Halo orbit is established, so that the suitable magnitude for the aerospace mission is chosen in terms of the stability of Halo orbit. The stable manifold is investigated from the Poincar6 mapping defined which is different from the previous researches, and six types of single-impulse transfer trajectories are attained from the geometry of the invariant manifolds. Based on one of the trajectories of indirect transfer which are ignored in the most of literatures, the stochastic control theory for imperfect information of the discrete linear stochastic system is applied to design the trajectory correction maneuver. The statistical dispersion analysis is performed by Monte-Carlo simulation,

Shift control method for the local time at descendi ngnode based on sun-synchronous orbit satellite

This article analyzes the shift factors of the descending node local time for sun-synchronous satellites and proposes a shift control method to keep the local time shift within an allowance range. It is found that the satellite orbit design and the orbit injection deviation are the causes for the initial shift velocity, whereas the atmospheric drag and the sun gravitational perturbation produce the shift acceleration. To deal with these shift factors, a shift control method is put forward, through such methods as orbit variation design, orbit altitude, and inclination keeping control. The simulation experiment and practical application have proved the effectiveness of this control method.

Adaptive control for autonomous rendezvous of spacecraft on elliptical orbit

A strategy for spacecraft autonomous rendezvous on an elliptical orbit in situation of no orbit information is developed. Lawden equation is used to describe relative motion of two spacecraft. Then an adaptive gain factor is introduced, and an adaptive control law for auton- omous rendezvous on the elliptical orbit is designed using Lyapunov approach. The relative motion is proved to be ultimately bounded under this control law, and the final relative position error can achieve the expected magnitude. Simulation results indicate that the adaptive control law can realize autonomous rendezvous on the elliptical orbit with relative state information only.

Neuro-Optimal Guidance Control for Lunar Soft Landing

Returning to moon has become a top topic recently. Many studies have shown that soft landing is a challenging problem in lunar exploration. The lunar soft landing in this paper begins from a 100 km circular lunar parking orbit. Once the landing area has been selected and it is time to deorbit for landing, a ΔV burn of 19.4 m/s is performed to establish a 100×15 km elliptical orbit. At perilune, the landing jets are ignited, and a propulsive landing is performed. A guidance and control scheme for lunar soft landing is proposed in the paper, which combines optimal theory with nonlinear neuro-control. Basically, an optimal nonlinear control law based on artificial neural network is presented, on the basis of the optimum trajectory from perilune to lunar surface in terms of Pontryagin's maximum principle according to the terminal boundary conditions and performance index. Therefore some optimal control laws can be carried out in the soft landing system due to the nonlinear mapping function of the neural network. The feasibility and validity of the control laws are verified in a simulation experiment.

The design and artificial realization of a controller of pulse coupling feedback

In this paper a controller of pulse coupling feedback （PCF） is designed to control chaotic systems. Control principles and the technique to select the feedback coefficients are introduced. This controller is theoretically studied with a three dimensional （3D） chaotic system. The artificial simulation results show that the chaotic system can be stabilized to different periodic orbits by using the PCF method, and the number of the periodic orbits are 2^n×3^m p （n and m are integers）. Therefore, this control method is effective and practical.

A survey on orbital dynamics and navigation of asteroid missions

Asteroid exploration is currently one of the most concerned topics among international space agencies. Or- bital dynamics and navigation are obviously crucial for asteroid exploration. This paper aims to give a brief review on the dynamics, control and navigation of asteroid reconnaissance orbits, including the heliocentric transfer orbit and near as- teroid orbit. The developments in optimization techniques of the transfer segment are discussed in detail. We surveyed global researches in this field and made comments on several important progresses. The final section proposed a prospec- tive of future studies with emphasis on the key techniques of these issues in the asteroid 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.

Stability and control of dynamic walking for a five-link planar biped robot with feet

During dynamic walking of biped robots, the underactuated rotating degree of freedom （DOF） emerges between the support foot and the ground, which makes the biped model hybrid and dimension-variant. This paper addresses the asymptotic orbit stability for dimension-variant hybrid systems （DVHS）. Based on the generalized Poincare map, the stability criterion for DVHS is also presented, and the result is then used to study dynamic walking for a five-link planar biped robot with feet. Time-invariant gait planning and nonlinear control strategy for dynamic walking with fiat feet is also introduced. Simulation results indicate that an asymptotically stable limit cycle of dynamic walking is achieved by the proposed 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.

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.

Impulsive orbit control for spacecraft around asteroid

An impulse feedback control law to change the mean orbit elements of spacecraft around asteroid is presented. First, the mean orbit elements are transferred to the osculating orbit elements at the burning time. Then, the feedback control law based on Gauss’s perturbation equations of motion is given. And the impulse control for targeting from the higher circulation orbit to the specified periapsis is developed. Finally, the numerical simulation is performed and the simulation results show that the presented impulse control law is effective.

Spacecraft formation control strategy on Sun-Earth Lissajous orbit

To carry out the deep space exploration tasks near Sun-Earth Libration point L2, the CRTBP dynamic model was built up and the numerical conditional quasi-periodic orbit （Lissajons orbit） was computed near L2. Then, a formation controller was designed with linear matrix inequality to overcome the difficuhy of parameter tuning. To meet the demands of formation accuracy and present thruster＇s capability, a threshold scheme was adopted for formation control. Finally, some numerical simulations and analysis were completed to demonstrate the feasibility of the proposed control strategy.

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.

A Status Graph Based Control Allocation Algorithm of Digital Micro-Thruster Array for Micro/Nano-Satellites Orbit Control Application

Digital micro-thruster arrays can be used for special missions of micro/nano-satellites with the requirements of high precision and small impulse.This paper presents a novel control allocation algorithm for the digital micro-thruster array,namely status graph based control allocation(SGBCA)algorithm,which aims at finding the optimal micro thrusters combination scheme to realize the sequential control synthesis for micro/nano-satellite during real-time orbit control tasks.A mathematical model is set up for the control allocation of this multivariate over-actuated system.Through dividing thrusters into disjoint segments by offline calculation and combining segments dynamically online to provide a sequence of the required impulse for the micro/nano-satellite,the time complexity of the control allocation algorithm decreases significantly.All levels of impulse can be generated by the digital micro thruster arrays and the service life of the arrays can be extended using the segment converting strategy proposed in this paper.The simulation indicates that the algorithm can satisfy the requirements of real-time orbit control for micro/nano-satellites.