Navigation support for the RadioAstron mission

A developed method of determination of orbital parameters allows one to estimate, along with orbit elements, some additional parameters that characterize solar radiation pressure and perturbing accelerations due to unloadings of reactiion wheels. A parameterized model of perturbing action of solar radiation pressure on the spacecraft motion is described (this model takes into account the shape, reflecting properties of surfaces, and spacecraft attitude). Some orbit determination results are presented obtained by the joint processing of radio measurements of slant range and Doppler, laser range measurements used to calibrate the radio measurements, optical observations of right ascension and declination, and telemetry data on spacecraft thrusters’ firings during an unloading of reaction wheels.     

Orbital and angular motion construction for low thrust interplanetary flight

Low thrust interplanetary flight is considered. Firstly, the fuel-optimal control is found. Then the angular motion is synthesized. This motion provides the thruster tracking of the required by optimal control direction. And, finally, reaction wheel control law for tracking this angular motion is proposed and implemented. The numerical example is given and total operation time for thrusters is found. Disturbances from solar pressure, thrust eccentricity, inaccuracy of reaction wheels installation and errors of inertia tensor are taken into account.     

Hybrid thrusters and reaction wheels strategy for large angle rapid reorientation with high precision

The quaternion-based, high precision, large angle rapid reorientation of rigid spacecraft is the main problem investigated in this study. The operation is accomplished via a hybrid thrusters and reaction wheels strategy where thrusters are engaged in providing a primary maneuver torque in open loop, while reaction wheels provide fine control torque to achieve high precision in closed-loop control. The inaccuracy of thrusters is handled by a variable structure control (VSC). In addition, a signum function is mixed in the switching surface in VSC to produce a maneuver to the reference attitude trajectory in a shortest distance. Detailed proofs and numerical simulation examples are presented to illustrate all the technical aspects of this work.     

High-precision single-input control of relative motion in spacecraft formation

A Newton-type method is proposed to improve the accuracy of control for relative motion of two satellites in close formation. We assume that the deputy satellite is equipped with a passive attitude control system that provides one-axis stabilization, and one or two orbit control thrusters are installed along the stabilized axis. Previous studies show that it is possible to construct periodic relative trajectories both in case of passive magnetic and spin stabilization. However, the accuracy of the numerically obtained control is quite low due to modeling errors caused by linearization of the equations of relative motion. Therefore, a correction procedure is required to compensate for nonlinear effects. To this end we suggest a recently developed algorithm based on the Newton method for solving nonlinear systems with geometric constraints. Being implemented, this algorithm allows decreasing the modeling error by up to ten times. The previously found control and trajectory of the linearized system are used as initial approximations.     

挠性空间飞行器姿态控制系统的时间域鲁棒稳定性分析

本文研究挠性空间飞行器姿态控制系统的时间域鲁棒稳定性分析,由于太阳帆板的转动和动量轮的转速变化,使飞行器的数学模型具有不确定性。这些不确定性可以归结为对动力学系统运动方程式的摄动。文中导出了鲁棒稳定性判据,并用算例说明其应用。     

Asymptotic study of a complete magnetic attitude control cycle providing a single-axis orientation

The angular motion of an axisymmetrical satellite equipped with the active magnetic attitude control system is examined. Attitude control system has to ensure necessary orientation of the axis of symmetry in the inertial space. It implements the following strategy: coarse reorientation of the axis of symmetry with nutation damping or “-Bdot” without initial detumbling; spinning-up about the axis of symmetry to achieve the property of a gyro; fine reorientation of the axis in the inertial space. Dynamics of the satellite is analytically studied using averaging technique on the complete control loop consisting of five algorithms. Solutions of the equations of motion are obtained in terms of quadratures for most cases or even in closed-form. The latter allowed to study the dependence of motion parameters including time-response with respect to the orbit inclination and other parameters for all algorithms.     

Rosetta enters hibernation

The International Rosetta Mission was launched on 2nd March 2004 on its 10 years journey to comet 67P/Churyumov–Gerasimenko. Rosetta will reach the comet in 2014, orbit it for about 1.5 years down to distances of a few kilometres and deliver the Lander Philae onto its surface.Following the fly-by of Asteroid (21-)Lutetia in 2010, Rosetta continued its travel towards the planned comet encounter in 2014. In this phase Rosetta became the solar-powered spacecraft that reached the largest Sun distances in history of spaceflight, up to an aphelion at 5.3 AU in October 2012. At distances above 4.5 AU the spacecraft's solar generator power is not sufficient to keep all spacecraft systems active. Therefore in June 2011 the spacecraft was spun up to provide gyroscopic stabilisation, and most of its on-board units, including those used for attitude control and communications, were switched off. Over this “hibernation” phase of about 2.5 years the spacecraft will keep a minimum of autonomy active to ensure maintenance of safe thermal conditions.After Lutetia fly-by, flight controllers had to tackle two anomalies that had significant impacts on the mission operations. A leak in the reaction control subsystem was confirmed and led to the re-definition of the operational strategy to perform the comet rendezvous manoeuvres planned for 2011 and 2014. Anomalous jumps detected in the estimated friction torque of two of the four reaction wheels used for attitude control forced the rapid adoption of measures to slow down the wheels degradation. This included in-flight re-lubrication activities and changes in the wheels operational speed regime.Once the troubleshooting of the two anomalies was completed, and the related operational scenarios were implemented, the first large (790 m/s) comet rendezvous manoeuvre was executed, split into several long burns in January and February 2011. The second burn was unexpectedly interrupted due to the anomalous behaviour of two thrusters, causing attitude off-pointing. Flight controllers modified the thrusters operation parameters in the on-board software and managed to re-start the sequence of burns and successfully complete the manoeuvre. After the manoeuvre, preparation for the critical spin-up and hibernation entry activities, planned for June 2011, began.This paper presents the activities carried out on Rosetta in the final year before hibernation entry. The major anomalies and the related troubleshooting and workaround solutions are detailed. Lessons learned from the operation of the first spacecraft operating with solar power at Jupiter-like distances from the Sun are presented and discussed.     

Optimal control of the deployment process of solar wings on spacecraft

The optimal attitude control problem of spacecraft during the stretching process of solar wings is investigated in this paper. The dynamical equations of the nonholonomic system are derived from the conservation principle of the angular momentum of the multibody system. Attitude control of the spacecraft with internal motion is reduced to a nonholonomic motion planning problem. The spacecraft attitude control is transformed into the steering problem for a drift free control system. The optimal solution for steering a spacecraft with solar wings is presented. The controlled motion of spacecraft is simulated for two cases. The numerical results demonstrate the effectiveness of the optimal control approach.     

间接Legendre伪谱法的欠驱动航天器姿态运动轨迹跟踪

针对仅带有两组喷气推力器的非轴对称欠驱动刚性航天器,提出一种基于间接Legendre伪谱法的姿态运动轨迹跟踪控制算法。首先采用Legendre伪谱法(LPM)离线规划出系统的最短时间姿态机动参考轨迹。接着将实际运行轨迹与参考轨迹之间的偏差作为变量,根据Pontryagin极小值原理必要条件把系统姿态运动跟踪问题转化为一个两点边值问题(TPBVP)。最后采用 Legendre-Gauss-Lobatto(LGL)点将此两点边值问题离散转化为一个线性方程组来求解,避免了对传统Riccati微分方程的积分运算。数值仿真校验了本文基于间接Legendre伪谱法的姿态运动轨迹跟踪控制算法的有效性。     

Application of recursive Gibbs–Appell formulation in deriving the equations of motion of N-viscoelastic robotic manipulators in 3D space using Timoshenko Beam Theory

The goal of this paper is to describe the application of Gibbs–Appell (G–A) formulation and the assumed modes method to the mathematical modeling of N-viscoelastic link manipulators. The paper’s focus is on obtaining accurate and complete equations of motion which encompass the most related structural properties of lightweight elastic manipulators. In this study, two important damping mechanisms, namely, the structural viscoelasticity (Kelvin–Voigt) effect (as internal damping) and the viscous air effect (as external damping) have been considered. To include the effects of shear and rotational inertia, the assumption of Timoshenko beam (TB) theory (TBT) has been applied. Gravity, torsion, and longitudinal elongation effects have also been included in the formulations. To systematically derive the equations of motion and improve the computational efficiency, a recursive algorithm has been used in the modeling of the system. In this algorithm, all the mathematical operations are carried out by only 3×3 and 3×1 matrices. Finally, a computational simulation for a manipulator with two elastic links is performed in order to verify the proposed method.     

Modal control of the planar motion of a long flexible beam in orbit

Attitude control techniques for the pointing and stabilization of very large, inherently flexible spacecraft systems are investigated. The attitude dynamics and control of a long, homogeneous flexible beam whose center of mass is assumed to follow a circular orbit is analyzed. In this study, first order effects of gravity-gradient are included, whereas external perturbations and related orbital station keeping maneuvers are neglected. A mathematical model which describes the system deflections within the orbital plane has been developed by treating the beam as having a maximum of three discretized mass particles connected by massless, elastic structural elements. The uncontrolled dynamics of this system are simulated and, in addition, the effects of the control devices are considered. The concept of distributed modal control, which provides a means for controlling a system mode independently of all other modes, is examined. The effect of varying the number of modes in the model as well as the number and location of the control devices are also considered.     

Nonlinear attitude control of flexible spacecraft under disturbance torque

We present a control law for large-angle single-axis rotational maneuvers of a spacecraft-beamtip body (an antenna or a reflector) configuration. It is assumed that an unknown but bounded disturbance torque is acting on the spacecraft. A model reference adaptive torque control law is derived for the slewing of the space vehicle. This controller includes a dynamic system in the feedback path and requires only attitude angle and rate of the space vehicle for feedback. For damping out the elastic motion excited by the slewing maneuver, a stabilizer is designed assuming that a torquer and a force actuator are available at the tip body. The stabilizer uses only the flexible modes for the synthesis of the control law. Simulation results are presented to show that fast, large-angle rotational maneuvers can be performed using the adaptive controller and the stabilizer in spite of the presence of continuously acting unknown torque on the spacecraft.     

基于固体微推力器阵列的卫星控制一体化算法

为了使固体微推力器阵列更具实用性,提出了一种适用于一体化控制的推力器布局方法;对基于固体微推力器阵列的推力器姿轨控分配算法问题分别进行了建模,引入了成本概念,保证推力器使用个数最少;将动态规划及贪心策略思想引入到了推力器分配问题求解中,建立了求解数学模型,进行了算法实现;对用于一体化控制中的推力器分配问题以及信息共享问题进行了分析。经过算法分析及仿真验证,该方法能有效快速求解该问题,有利于实现实时控制,能满足一体化控制的要求。     

Analysis and experiments for delay compensation in attitude control of flexible spacecraft

Space vehicles are often characterized by highly flexible appendages, with low natural frequencies which can generate coupling phenomena during orbital maneuvering. The stability and delay margins of the controlled system are deeply affected by the presence of bodies with different elastic properties, assembled to form a complex multibody system. As a consequence, unstable behavior can arise. In this paper the problem is first faced from a numerical point of view, developing accurate multibody mathematical models, as well as relevant navigation and control algorithms. One of the main causes of instability is identified with the unavoidable presence of time delays in the GNC loop. A strategy to compensate for these delays is elaborated and tested using the simulation tool, and finally validated by means of a free floating platform, replicating the flexible spacecraft attitude dynamics (single axis rotation). The platform is equipped with thrusters commanded according to the on–off modulation of the Linear Quadratic Regulator (LQR) control law. The LQR is based on the estimate of the full state vector, i.e. including both rigid – attitude – and elastic variables, that is possible thanks to the on line measurement of the flexible displacements, realized by processing the images acquired by a dedicated camera. The accurate mathematical model of the system and the rigid and elastic measurements enable a prediction of the state, so that the control is evaluated taking the predicted state relevant to a delayed time into account. Both the simulations and the experimental campaign demonstrate that by compensating in this way the time delay, the instability is eliminated, and the maneuver is performed accurately.     

Rotational motion of <Emphasis Type="Italic">Foton M-4</Emphasis>

The actual controlled rotational motion of the Foton M-4 satellite is reconstructed for the mode of single-axis solar orientation. The reconstruction was carried out using data of onboard measurements of vectors of angular velocity and the strength of the Earth’s magnetic field. The reconstruction method is based on the reconstruction of the kinematic equations of the rotational motion of a solid body. According to the method, measurement data of both types collected at a certain time interval are processed together. Measurements of the angular velocity are interpolated by piecewise-linear functions, which are substituted in kinematic differential equations for a quaternion that defines the transition from the satellite instrument coordinate system to the inertial coordinate system. The obtained equations represent the kinematic model of the satellite rotational motion. A solution of these equations that approximates the actual motion is derived from the condition of the best (in the sense of the least squares method) match between the measurement data of the strength vector of the Earth’s magnetic field and its calculated values. The described method makes it possible to reconstruct the actual rotational satellite motion using one solution of kinematic equations over time intervals longer than 10 h. The found reconstructions have been used to calculate the residual microaccelerations.     

Application of SDRE technique to orbital and attitude control of spacecraft formation flying

This paper proposes the application of a nonlinear control technique for coupled orbital and attitude relative motion of formation flying. Recently, mission concepts based on the formations of spacecraft that require an increased performance level for in-space maneuvers and operations, have been proposed. In order to guarantee the required performance level, those missions will be characterized by very low inter-satellite distance and demanding relative pointing requirements. Therefore, an autonomous control with high accuracy will be required, both for the control of relative distance and relative attitude. The control system proposed in this work is based on the solution of the State-Dependent Riccati Equation (SDRE), which is one of the more promising nonlinear techniques for regulating nonlinear systems in all the major branches of engineering. The coupling of the relative orbital and attitude motion is obtained considering the same set of thrusters for the control of both orbital and attitude relative dynamics. In addition, the SDRE algorithm is implemented with a timing update strategy both for the controller and the proposed nonlinear filter. The proposed control system approach has been applied to the design of a nonlinear controller for an up-to-date formation mission, which is ESA Proba-3. Numerical simulations considering a tracking signal for both orbital and attitude relative maneuver during an operative orbit of the mission are presented.     

The results of flight tests of an attitude control system for the Chibis-M microsatellite

The attitude control system of the Chibis-M microsatellite is described. Results of flight experiments on damping the initial angular velocity (made using magnetorquers) are considered, as well as stabilization in the orbital referece frame, and orientation of solar arrays toward the Sun using reaction wheels. The operation of algorithms of satellite attitude determination on sunlit and shadow segments of the orbit is also under study. The general logic of operation of the attitude control system in automatic mode is presented and discussed.     

小型固体运载器起飞段姿态控制方法研究

针对控制系统,采用侧喷流发动机和栅格舵的新型小型多级固体运载火箭开展了起飞段姿态控制方法研究。给出了在低马赫数条件下侧喷流发动机的力放大因子和栅格舵的控制力矩,建立了运载器姿态控制模型。根据侧喷流和栅格舵的特点,设计了PID控制器与智能开关控制器相结合的新型控制器,运用神经网络算法实现了开关控制器参数的在线选择。仿真结果表明,所设计的控制器满足控制精度、稳定度和鲁棒性的要求,算法简便,具有工程可实现性,以侧喷流发动机和栅格舵为执行机构的控制系统能满足运载火箭起飞段姿态控制要求,为陆基或空射小型固体运载火箭姿态控制方法提供了一种新思路。     

大气层外自旋稳定微型拦截器点火算法研究

对大气层外自旋稳定微型拦截器的脉冲点火算法进行了研究。在考虑变质量后质心位置变化所产生的扰动力矩对拦截器姿态的干扰以及弹体自旋运动对直接力分量影响的基础上,建立了自旋稳定微型拦截器六自由度数学模型,结合比例导引律设计出拦截器脉冲发动机的点火算法。该点火算法可以在满足脱靶量要求的前提下减少脉冲发动机的消耗并降低对拦截器姿态运动的影响。仿真结果表明,该方法能有效实现微型拦截器在末制导段的精确制导控制。