Continuous finite-time control for spacecraft formation flying on elliptical orbits

Revisiting the general periodic relative motion in elliptic reference orbits

This paper investigates the problem of relative motion control for spacecraft rendezvous on an arbitrary elliptical orbit. The simplified dynamic model describing the relative motion between the chaser spacecraft and the target spacecraft is established via using transformed variables. Due to the presence of time variant parameters in this novel model, robust control scheme and adaptive control scheme are designed to solve the rendezvous problem. Theoretical analyses and simulation results demonstrate the effectiveness of the proposed methods.

In this paper we present a solution for real-time reference generation for a leader-follower spacecraft formation. The solution is assuming a nadir pointing leader spacecraft and a follower spacecraft which is complimenting the measurement of the leader by tracking the point located at the intersection on the Earth surface between Earth center and leader spacecraft. Desired relative attitude, angular velocity and angular acceleration are generated in real-time based on the relative position, velocity and acceleration between the leader and follower spacecraft. A passivity based PD+ controller is derived and the equilibrium points of the closed-loop system are shown uniformly asymptotically stable, and simulation results are presented to show the performance of both the reference generation method and the control law during a formation reconfiguration.

This paper investigates the spacecraft rendezvous problem with the target spacecraft on an arbitrary elliptical orbit. The relative motion of two spacecrafts is established based on the Lawden equations. In order to take the model parameter uncertainty into consideration, an adaptive backstepping controller is designed by a Lyapunov approach. The proposed control laws can guarantee the asymptotic stability of the closed-loop system and can estimate the uncertain model parameters at the same time. Finally, simulation results are presented to illustrate the effectiveness of the proposed approach.

In this paper, the problem of anti-disturbance, anti-saturation and fixed-time control for a class of telescopic wing morphing aircraft is studied. The telescopic wing morphing aircraft treats the variable wingspan as an extra control input to construct the dynamic model of the morphing-aided maneuver. According to the model characteristics, the controller design is divided into two loops: the speed loop and the attitude loop. Through a fixed-time continuous feedback control scheme, fixed time of the tracking reference trajectory is ensured. By combining the integral sliding mode control (ISMC) method with super-twisting control (STC), the uncertainties of aerodynamic coefficients and external disturbances are overcome. In addition, the anti-saturation problem of the aircraft actuator is solved by the initial solution correction method based on Null-space augmented solutions. The simulation result shows that the designed algorithm has great tracking performance, while the robustness and anti-saturation performance are guaranteed.

Extended state observer-based continuous finite time control for a fixed-wing vertical take-off and landing unmanned aerial vehicle

Adaptive neural network based quadrotor UAV formation control under external disturbances

This paper investigates the leader-follower formation control problem for autonomous underwater vehicles (AUVs) in the presence of intermittent communications and external disturbances. For intermittent communication control, the time intervals of communication are made up of two parts: the normal time interval and the break time interval. During the normal communication period, the AUV will transmit its own states to its neighbors, while in the break time, there is no information interaction in the communication network. Hence, it is unknown whether the stability of the formation could be guaranteed in the presence of intermittent communication. Moreover, the existence of external disturbance will further affect the performance of the formation in a negative way. Considering these problems, a sliding mode surface constructed by a segment auxiliary variable is developed to relieve the system instability caused by the sudden change in control effectiveness during the intermittent interruption period. The first controller realized the formation mission by combining the adaptive algorithm and the proposed auxiliary system. However, the leader in the above discussion is static which is limited in practical application. Considering a dynamic leader whose velocity is not available to every follower, a distributed dynamic compensator is developed to deliver the leader’s velocity information among the followers. Finally, theoretical analysis and simulation results demonstrate the effectiveness of the designed formation control scheme.

This paper studies the relative orbit geometry of a leader–follower spacecraft formation flying in unperturbed elliptical reference orbits. The first-order relative position equations, derived using the reference orbital element approach under the condition that the follower and leader spacecraft have equal semimajor axes, are transformed fromtrigonometricformstoparametricandalgebraicforms.Theconditionsforandthenumberofself-intersections oftherelativeorbitprojectedontothethreecoordinateplanesoftheleaderlocal-vertical–local-horizontal frameare obtained. The relative orbit proves to be three-dimensional instead of planar in most cases, and may self-intersect spatially at most once. The collision between the follower and leader spacecraft corresponds to the case where the solution curve to the first-order relative motion equations passes through the origin. The conditions for collision are subsequently determined. For anondegenerate case(in which none of the relative motion in the radial, in-track, and cross-trackdirectionsvanish),threetypesofrelativeorbitarepossible.Mostfrequently,therelativeorbitisonaonesheet hyperboloid. Otherwise, when the relative orbit has a real or finite imaginary self-intersection, it rests on an elliptic cone. In the rest of the cases, including that with an imaginary self-intersection at infinity, the relative orbit is on an elliptic cylinder. The criteria for these three types are given, respectively, followed by examples.

Considering the existence of disturbance in the induction machine (IM) drive system, this paper develops a composite control scheme based on linear extended state observer (LESO) and continuous finite time control (FTC) to improve the disturbance rejection property of system. First, a LESO is introduced to estimate the disturbances of system. The estimated value is used in the feed-forward compensation design. Second, a continuous finite-time feedback control technique is applied in the feedback design. Then the stability of the controller is analyzed. Simulation and experimental comparisons with two other control methods, traditional Proportional Integral (PI) and Proportional feedback plus feedforward compensation based on LESO(P+LESO), are provided to verify the effectiveness of the proposed method.

This paper deals with the maneuver method for the spacecraft formation reconfiguration in the elliptic reference orbit considering two control input types. During the satellite operation, the formation size and/or geometry should be modified according to the mission requirements and space environment. The follower spacecraft can change the formation radius and/or geometry with respect to the leader spacecraft, while minimizing the control effort during the maneuver. For the continuous control input, the optimal control problem in the relative motion is solved based on the nonlinear programming method, where the initial and final relative positions and velocities are specified in the local frame. For the impulsive control input, on the other hand, the Lambert’s problem is modified to construct the transfer problem in the relative motion, given two position vectors at the initial and final time and the flight time. Furthermore, the minimum velocity change is investigated through the grid search for transferring orbit using the impulsive control input. As a result, the transfer trajectories to resize the formation radius and change the formation geometry are presented by performing the numerical simulation.

Quasioptimal interorbit transfers of a low-thrust spacecraft in strong central Newtonian gravity field

The complete error equations are derived for an inertial navigator operating in a vehicle flying in an arbitrary elliptical orbit. The derivation incorporates a new notation that makes it easy to obtain the basic results in a correct manner. It is shown that the error equations of any inertial navigator (either on earth or in orbit) are identical to the equations for the perturbations of the coordinates of a satellite. When the normalized orbital error equations are coordinatized in a locally level reference frame, they become the Tschauner-Hempel equations. The structure of the solutions of the Tschauner-Hempel equations is discussed in detail, and a partially closed form (sampled data solution) for the case of periodic error sources is presented. A number of typical solutions for various error sources are given, and the problem of reducing these errors by various modes of operation is discussed.

The extended nonholonomic double integrator (ENDI) cannot be asymptotically stabilized by a continuous and time-invariant feedback controller since it violates the Brockett’s condition. In this paper, a new continuous control scheme is proposed to stabilize the ENDI system without drift. The dynamics of an ENDI system is enlarged to a higher dimensional space where a continuous but time-varying control law is designed for its stabilization. Besides the theoretical proofs, simulations conducted on the dynamics of a mobile robot are also presented to demonstrate the validity and performance of the proposed method.

<abstract><p>The prescribed-time spacecraft formation flying problem with uncertainties and unknown disturbances is investigated. First, based on Lie group SE(3), the coupled 6-degrees-of-freedom kinematics and dynamics for spacecraft with uncertainties and unknown disturbances are introduced. Second, with the aid of some key properties of a class of parametric Lyapunov equations, novel prescribed-time control laws are designed. It is proved that the proposed control laws can drive the relative motion between the leader spacecraft and follower spacecraft to zero in any prescribed time and are bounded. Finally, numerical simulations verify the effectiveness of the proposed control scheme.</p></abstract>