Modified Rodriguez Parameters Research Articles

A moving platform photometric observation based attitude and angular velocity estimation method for space target

Based on the photometric information, a method is proposed for estimating space target attitude and angular velocity under the condition of moving observation platform. Firstly, according to the dynamically changing relative pose relationship among the target, the observation platform and the sun, photometric measurement model is established. Then, in the framework of Unscented Kalman Filter, the joint estimation of target attitude and angular velocity is realized by combining use of quaternion and Modified Rodriguez Parameters. Finally, the feasibility and estimation accuracy of the method are verified by numerical simulation experiments. The results show that the proposed method achieves high accuracy and has certain value in practical application.

Health Checking Autonomous Attitude Control System of Earth-Observing Miniature Satellite in Initial Orientation Modes

The problems of autonomous digital control of a spacecraft (SC) orientation and checking the operability of its attitude control system (ACS) in the initial orientation modes are considered. The developed methods, algorithms, and simulation results for a miniature Earth-surveying satellite in a Sun-synchronous orbit are presented. Autonomous angular guidance and modularly limited vector digital control using a vector of the modified Rodriguez parameters are applied to bring the SC's orientation from completely arbitrary to the required one. We briefly discuss the health check of the mini-satellite's ACS, as well as our discrete algorithms for onboard diagnostics of faults based on computer processing of available measurements and explicit relations.

Spacecraft formation and orbit control using differential attitude-dependent solar radiation pressure

This paper introduces a linear model for spacecraft formation dynamics subject to attitude-dependent solar radiation pressure (SRP) disturbance, with the SRP model accounting for both absorption and specular/diffuse reflection. Spacecraft attitude is represented in modified Rodriguez parameters (MRPs), which also parameterize the orientation of individual facets for a spacecraft with fixed geometry. Compared to earlier work, this model incorporates analytic approximation of the SRP-perturbed chief orbit behavior in a manner enabling its use in applications with infrequent guidance updates. Control examples are shown for single-plate representations of hypothetical spacecraft with generally realistic optical parameters. The results demonstrate the validity of the model and the feasibility of SRP-based formation and rendezvous control in orbits around small bodies and in high orbits around the Earth such as the GEO belt.

Fixed-time attitude stabilization for a rigid spacecraft

This paper mainly investigates the problem of the attitude stabilization for a rigid spacecraft based on the model of Modified Rodriguez Parameters. A fixed-time attitude stabilization controller is designed to guarantee that the attitude of the rigid spacecraft will be stabilized to the equilibrium in a fixed time which is independent of any initial condition. The design of fixed-time attitude controller is mainly based on improved backstepping method. The proposed fixed-time attitude control scheme can deal with not only the parameters’ uncertainties but also the external disturbances. Reliability and effectiveness of the proposed approach are proved by simulations.

Integrated robust adaptive tracking control of non-cooperative fly-around mission subject to input saturation and full state constraints

This paper investigates the relative position and attitude tracking control of non-cooperative fly-around mission in the presence of parameter uncertainties, external disturbances, input saturation and full state constraints. Firstly, an integrated and coupled 6 DOF relative motion dynamic model is established, which is consisted of relative position model depicted in the line-of-sight (LOS) frame and relative attitude model described by Modified Rodriguez parameters (MRPs). Subsequently, by using the backstepping control method, an integrated robust adaptive anti-windup control scheme is proposed, in which uncertain parameters and unknown upper bound of the disturbances are estimated by adaptive technique, and the adverse effects caused by input saturation are reduced by the designed anti-windup compensator. To guarantee the full state constraints satisfied all the time, the barrier Lyapunov function method is incorporated into the backstepping control design. Rigorous stability proofs show that the designed robust adaptive controller guarantees that the relative motion states not only can be restricted in the prescribed constraint regions, but also can converge into the small regions with good robustness. Finally, numerical simulation results demonstrate the effectiveness and performance of the designed control scheme.

Adaptive fixed-time relative position tracking and attitude synchronization control for non-cooperative target spacecraft fly-around mission

In this paper, the problem of adaptive fixed-time tracking control for non-cooperative target spacecraft fly-around mission in the presence of the parameter uncertainties and external disturbances is investigated. Firstly, a novel and effective 6 DOF relative motion dynamic model constructed by relative position motion model expressed in the LOS frame and attitude dynamic model described by Modified Rodriguez parameters (MRPs) is firstly established. Subsequently, a new modified nonsingular fast terminal sliding mode (MNFTSM) with bounded convergence time in regardless of the initial states is designed, which not only can circumvent the singularity problem effectively, but also has the advantages of FTSM. By employing MNFTSM and adaptive techniques, two continuous adaptive fixed-time nonsingular fast terminal sliding mode (AFNFTSM) control laws are proposed, which can eliminate the chattering phenomenon and do not require precise knowledge of the mass, inertia matrix. Rigorous proofs show that both of two AFNFTSM control laws can guarantee that the relative position and attitude errors can converge to the small regions containing the origin in fixed time. Finally, numerical simulations are performed to demonstrate the effectiveness of the proposed control schemes.

Finite-time distributed cooperative attitude tracking control for multiple rigid spacecraft

We investigate the finite-time cooperative attitude synchronization and tracking control for multiple rigid spacecrafts with a time-varying leader, whose attitude is represented by modified rodriguez parameters. In particular, the studied systems are composed of one dynamic leader with bounded unknown acceleration inputs and some followers with bounded disturbances. A novel nonlinear tracking control protocol is constructed via nonsingular terminal sliding mode scheme. It is shown that the proposed protocol can effectively drive the states of the followers to track the leader within the finite-time. Finally, an example is illustrated to verify the proposed protocol.

Attitude Stabilization of Spacecrafts Under Actuator Saturation and Partial Loss of Control Effectiveness

A practical solution is presented to the problem of fault tolerant attitude stabilization for a rigid spacecraft by using feedback from attitude orientation only. The attitude system, represented by modified Rodriguez parameters, is considered in the presence of external disturbances, uncertain inertia parameters, and actuator saturation. A low-cost control scheme is developed to compensate for the partial loss of actuator effectiveness fault. The derived controller not only has the capability to protect the control effort from actuator saturation but also guarantees all the signals in the closed-loop system to be uniformly ultimately bounded. Another feature of the approach is that the implementation of the controller does not require any rate sensor to measure angular velocity. An example is included to verify those highly desirable features in comparison with the conventional velocity-free control strategy.

Distributed attitude consensus of spacecraft formation flying

The consensus problem of the distributed attitude synchronization in the spacecraft formation flying is considered. Firstly, the attitude dynamics of a rigid body spacecraft is described by modified Rodriguez parameters (MRPs). Then global stable distributed cooperative attitude control laws are proposed for different cases. In the first case, the control law guarantees the state consensus during the attitude synchronization. In the second case, the control law ensures both the attitudes synchronizing to a desired constant attitude and the angular velocities converging at zero. In the third case, an attitude consensus control law with bounded control input is proposed. Finally, the effectiveness and validity of the control laws are demonstrated by simulations of six rigid bodies formation flying.

Spacecraft Adaptive Sliding Mode Attitude Tracking Control Using DGCMG

This investigation is concerned with the non-linear multi-in-multi-out tracking control of a spacecraft with Double-gimbaled control moment gyros as actuators. An attitude dynamic model of rigid spacecraft with DGCMG and a kinematics model in terms of Modified Rodriguez parameters are given for the controller development. Then the control objective and system uncertainties in tracking problem are analyzed considering the major elements which work on the control performance such as moment of inertia change, wheel speed drift and external torque. A adaptive sliding mode controller is designed and is proved stable later in which the sliding mode control are used to compensate external torque and un-modeled dynamics while the adaptive parameters are used to estimate inertia and wheel speed on line. And a steering law of parallel mounted DGCMG is illuminated. Finally Monte Carlo simulation is carried out to prove the effectiveness of the controller.

Decentralized Robust Adaptive Control for Attitude Synchronization Under Directed Communication Topology

T HE need to maintain accurate relative orientation between spacecraft is critical in many satellite formation missions. For instance, in interferometry application, the relative orientation between spacecraft in a formation is required to be maintained precisely during formation maneuvers. In interspacecraft laser communication operation, the participating spacecraft are also required to maintain accurate relative attitude throughout the communication process. This control problem, commonly referred to as attitude synchronization in the literature, has attracted much research attention. Various solutions have been proposed and these can be broadly classified according to the advocated techniques: leader– follower [1–4], virtual structure [5,6], behavior-based [7–11], and graph-theoretical approach [12–15]. In particular, the graph-theoretical approach has been actively studied for cooperative control of multi-agent system using limited local interaction [16,17] and was adopted for attitude synchronization problem in [12–15]. In the above-cited decentralized attitude synchronization results, except [14,15], it is assumed that the interspacecraft communication links are undirected (i.e. bidirectional). However, in practice, the interspacecraft communication topology may be restricted to be directed, such as in unidirectional satellite laser communication system. The control problem of attitude synchronization under directed communication topology is more challenging as compared with the case with undirected communication topology. This issue was studied in [14] but the proposed control law requires derivative of the angular velocity, which may introduce additional noise into the system. Furthermore, the attitude-tracking performance analysis in [14] is applicable only to the casewhere the directed graph can be simplified to a graph with only one node. This constraint on communication topology is relaxed in [15], which uses modified Rodriguez parameters and Euler– Lagrange system to describe the satellite attitude dynamics. However,modifiedRodriguez parameters contain singularity and are thus not suitable for the development of globally stabilizing control algorithms. This Note proposes a decentralized adaptive sliding-mode control lawwhich regulates attitude and angular velocity errors of individual spacecraft with respect to reference commands and minimizes relative attitude and angular velocity errors between spacecraft. Thus, the proposed control law ensures that each spacecraft attains desired time-varying attitude and angular velocity while maintaining attitude synchronization with other spacecraft in the formation even in the presence of model uncertainties and external disturbances. Moreover, the design is applicable to general communication topology and is not restricted to ring topology or undirected communication topology. In the following section, unit quaternion representation will be introduced into the satellite attitude control problem and algebraic graph theory will be applied to describe general directed communication topology.

Decentralised cooperative attitude tracking using modified Rodriguez parameters based on relative attitude information

In this article, the problem of decentralised cooperative attitude tracking based on relative attitude information is considered in the context of deep space spacecraft formation flying. We use modified Rodriguez parameters for attitude representation due to its nonreduction. We first present a distributed sliding-mode estimator and a cooperative attitude tracking control law such that the attitudes and angular velocities of all spacecraft track their references. Then we extend the result to three different cases. In the first case, we use a passivity approach to derive a control law without angular velocity measurements, which is of significance for applications with low-cost configurations of spacecraft. In the second case, to relax the special connectivity condition given in the original control design, we obtain a locally asymptotical stability condition for any undirected connected communication topology. In the third case, we consider cooperative attitude tracking in the presence of a dynamic communication topology. Simulation results are presented to validate the effectiveness of these control laws.

Distributed Cooperative Attitude Synchronization and Tracking for Multiple Rigid Bodies

In this paper, distributed cooperative attitude synchronization and tracking problems are considered for multiple rigid bodies with attitudes represented by modified rodriguez parameters. Two distributed control laws are proposed and analyzed. The first control law applies a passivity approach for distributed attitude synchronization. The control law guarantees attitude synchronization without the requirement for absolute angular velocity measurements and relative angular velocity measurements between neighboring rigid bodies. The second control law incorporates a time-varying reference attitude, where the reference attitude is allowed to be available to only a subset of the group members under general directed information exchange. The control law guarantees that all rigid bodies track the time-varying reference attitude as long as a virtual leader whose attitude is the time-varying reference attitude has a directed path to all other rigid bodies in the group. Simulation results are presented to demonstrate the effectiveness of the two control laws.

Linearization‐based attitude error regulation: multiplicative error case

PurposeThe purpose of this paper is to design and simulate a linearized attitude stabilizer based on linear quadratic regulator theory (LQR) using the multiplicative definition of the attitude.Design/methodology/approachThe attitude is modeled by the modified Rodriguez parameters that provide a minimal representation of attitude and always invertible kinematics. The nonlinear model of the satellite attitude dynamics is linearized around the origin and an LQR is proposed for the linearized design. They are also simulated using the original nonlinear satellite dynamics in order to verify that the controller is operating properly. Simulations include randomly selected initial conditions to justify the stability against various initial conditions.FindingsTheoretically, the resultant controllers are locally stable around the origin. However, the simulation results show that the attitude is well regulated in the presence of both inertia uncertainties and random initial conditions.Originality/valueThe originality of this work is due to its demonstration that complicated attitude regulators are not the solution for proper satellite or spacecraft attitude stabilization.

Linearization in satellite attitude control with modified Rodriguez parameters

PurposeThe purpose of this paper is to analyze the results of the Jacobian matrix linearization of the satellite attitude dynamics with modified Rodriguez parameters (MRP) as attitude representation.Design/methodology/approachThe satellite dynamics is linearized using Jacobian differentiation around origin and reference values of the MRP. The controller is designed through linear quadratic regulation approach.FindingsIt is found that, for both cases the overall system converges but there exists a tracking error. The error can be reduced by increasing the controller coefficients in both cases however cannot be eliminated. In the case of linearization around zero, the torque requirements are quite higher than the case of linearization around the reference attitude trajectory.Originality/valueThe attempt of Jacobian linearization of a satellite dynamics with the MRP as the attitude representation constitutes the value of this paper. In addition, the results obtained in the derivations may be used in future research.

An almost disturbance decoupling solution of the attitude control problem

PurposeThe purpose of this paper is to derive a robust nonlinear attitude control law intended for practical application.Design/methodology/approachThe method of input/output feedback linearization is utilized for having a linear model and a recently developed almost disturbance decoupling (ADD) approach is adopted for designing a robust satellite attitude control (SAC) system. The kinematics of the satellite is modeled by modified Rodriguez parameters because of their continuous invertibility. The design is simulated on the model of a realistic satellite project (BILSAT‐I), which is developed by the Turkish Scientific and Technological Research Council.FindingsThe torque requirement of the operation does not exceed the maximum limit provided by the actuator. The square error levels are staying under the boundary of final global attractor, which is one of the important proofs for the successful operation of the generated ADD control law.Originality/valueThe ADD concept is investigated on SAC problem. By that way, simple control structures with known disturbance attenuation capability can be designed.

Satellite attitude control by integrator back‐stepping with internal stabilization

PurposeThis paper aims to focus on the implementation of the integral back‐stepping control on the model of BILSAT – 1 satellite of the Turkish Scientific and Technological Research Council (TUBITAK).Design/methodology/approachThe nonlinear model of the satellite is divided into three groups and the control Lyapunov function is constructed systematically. The formed closed loop system is analyzed for stability according to a recently developed stability analysis procedure and multi‐run simulations.FindingsSince the studied model includes the dynamics of a practical reaction wheel (SSTL Type: Microwheel), the simulation results showed that the designed controllers are suitable for practical application. The torque requirement is far below the maximum torque supplied by the wheel. In addition, the system seems to be quite fast and robust against the parametric uncertainties.Research limitations/implicationsSince the control system is nonlinear, the computational complexity will be an issue in practical application. The stability analysis should be improved to have more reliable information concerning the disturbance torques. Currently this analysis is performed by multi‐run simulations. An observer or estimator may also be designed in order to compute the attitudes from the gyroscope readings.Practical implicationsThe controller designed here can be implemented on the proceeding satellite projects (foregoing BILSAT projects) by TUBITAK.Originality/valueThe paper provides a satellite control application of back‐stepping using a model involving modified Rodriguez parameters and reaction wheel dynamics that is not studied in the literature.