Time-optimal reorientation for rigid satellite with reaction wheels

This article introduces a time-optimal reorientation manoeuvre controller with saturation constraints on both reaction wheels’ torques and angular momentum. The proposed control scheme consists of two parts. The first part is an open-loop time-minimum reorientation trajectory generated by the Legendre pseudospectral method. Actuator dynamics, saturations on control torques and angular momentums of reaction wheels are taken into account in generating the open-loop optimal trajectory. The second part is a closed-loop tracking control law to track the optimised reference trajectory based on attitude error dynamics with reaction wheel dynamics. Numerical simulations show that reaction wheel dynamics play an important role in attitude manoeuvres. The proposed controller performs better for rest-to-rest reorientation manoeuvre than other existing methods.     

A basic attitude instability of spacecraft with imperfect momentum wheels

On a few occasions, spacecraft with momentum wheels have exhibited an undesired, and at first unexplained, attitude wobble. The present paper suggests a possible cause and also suggests that with the present trend in momentum wheel design using magnetic wheel bearings, the problem may get worse.A momentum wheel in practice will run in bearings which comply to the loads placed on them, to a very tiny extent. The compliance will be reduced to zero by the bearing reaction forces precessing the wheel back to its undeflected position. However, in doing so the combination of the very small compliance angle with the angular velocity of the spacecraft will cause an energy flow which will enhance the nutation of the spacecraft which caused the deflection in the first place.     

带有两个动量飞轮刚体航天器的姿态非完整运动规划问题

航天器利用三个动量飞轮可以控制其姿态和任意定位.当其中一个动量飞轮失效,在某些特定的情况下,如何控制航天器的姿态问题还没有有效的方法.利用最优控制方法研究了带有两个动量飞轮的刚体航天器姿态优化控制问题.为此考虑系统角动量为零的情况下,将航天器姿态运动方程化为非完整形式约束方程,系统的控制问题可转化为无漂移系统的非完整运动规划问题.通过Ritz近似理论得到求解带有两个动量飞轮航天器姿态的运动规划控制算法.通过数值仿真,表明该方法对航天器姿态运动规划控制是有效的.     

Variable structure controller design for spacecraft nutation damping

Variable structure systems theory is used to design an automatic controller for active nutation damping in momentum biased stabilized spacecraft. Robust feedback stabilization of roll and yaw angular dynamics is achieved with prescribed qualitative characteristics which are totally independent of the spacecraft defining parameters.     

A special case of spacecraft optimal attitude control

The problem of optimal control of a spacecraft reorientation from an arbitrary initial attitude to a prescribed angular attitude is studied. The reorientation time is given. The case when the quadratic norm of the angular velocity vector of the spacecraft is minimized is studied. Using the necessary optimality conditions in the form of Pontryagin??s maximum principle and the quaternion method for spacecraft motion control, an analytical solution of this problem is obtained. Formal equations are derived and expressions for the optimal control program are obtained. For a dynamically symmetric spacecraft, the angular velocity is obtained in the analytical form. Results of the mathematical simulation of the spacecraft dynamics under the optimal control are presented that demonstrate the practical usefulness of the proposed algorithm for the spacecraft attitude control.     

Unloading angular momentum for inertial actuators of a spacecraft in the pitch channel

The problem of gravitational unloading of the angular momentum of inertial actuators of a spacecraft in the pitch channel for circular and elliptic orbits is considered using the band theory of modal control. Control laws for gravitational unloading and stabilization of a given spacecraft position unambiguously determined by the object parameters and given coefficients of characteristic equation are obtained.     

Dynamics of a rotating flexible and symmetric spacecraft using impedance matrix in terms of the flexible appendages cantilever modes

The subject of this work is the dynamics of a rotating spacecraft. The spacecraft is modeled as a main rigid body connected to two flexible solar panels. The orbital motion of the whole spacecraft with a constant angular velocity is considered, interacting with small rigid motions of the main body, and small elastic deformations and infinitesimal vibrations of the solar panels. A continuum approach based on the Rayleigh–Ritz discretization is used to describe the distributed flexibility in the spacecraft. Rayleigh–Ritz discretization functions used are the clamped modes of the solar panels. This method enables us to construct the impedance matrix of the whole system relating to the displacement of the main body and the external torque. A spectral expansion of this impedance matrix, in terms of these clamped modes is obtained in the frequency domain. The numerical results presented show that for small values of orbital angular velocity, the vibration motion frequencies of the flexible parts (solar panels) are not perturbed substantially. Moreover, when great values of orbital angular velocity are simulated, these frequencies change considerably. The present investigation based on the Rayleigh–Ritz discretization shows the effect of the interaction between the orbital motion of the whole spacecraft and the vibration motions of the flexible parts.     

基于飞轮的欠驱动航天器姿态控制器设计

在以飞轮作为姿态控制执行机构的航天器中,如果部分飞轮发生故障而使得航天器欠驱动时,姿态控制性能会急剧下降.本文对两个匕轮的刚性航天器,研究了姿态控制问题.在零动量的假设下,利用Backstepping方法,为欠驱动姿态控制系统设计了一个新型的姿态控制器.设计过程分两步进行:首先,根据姿态运动学模型,设计出可使航天器姿态全局渐近稳定的控制角速率;然后,根据姿态动力学模型,得到使航天器姿态全局渐近稳定的控制力矩.该控制器为非连续控制器,可使航天器姿态误差全局一致渐近收敛为零,并使系统具有良好的动态性能.计算机仿真表明,本文所设计出的控制器是可行的.     

欠驱动航天器双飞轮—单喷气姿态最优控制原理及方法

欠驱动航天器的姿态控制能够增强航天器的可靠性.本文针对欠驱动航天器姿态控制, 从喷气姿态阻尼的角动量等效原理出发, 推导脉宽调制公式, 得到燃料消耗最小时给定姿态、非给定姿态两种情况下的喷气最优组合方案.同时, 为了实现喷气全局最优, 提出欠驱动飞轮姿态控制策略, 实现了运动航天器机动至预期姿态.进一步分析欠驱动飞轮航天器的姿态控制原理及稳定性, 提出了共面双飞轮-单喷气的配置方案, 通过双飞轮组合稳定航天器的角速度, 使得航天器到达预期姿态机动时燃料全局最省.结合绕两个旋转轴的姿态机动路径规划方法, 通过姿态机动时序关系的实时分配可实现航天器姿态机动与稳定控制.最后, 通过航天器姿态控制仿真和对比分析, 发现共面双飞轮-单喷气的欠驱动姿态阻尼及姿轨控制方案能够在较少硬件配置下实现对航天器的姿态控制, 且消耗燃料最少.     

On the problem of optimal spacecraft attitude control

The problem of the optimal control of a spacecraft reorientation from an arbitrary initial position into a prescribed final angular position is studied. For optimization, we use a generalized integral index characterizing the complexity of the rotation trajectory from the viewpoint of the “distance covered,” which is the generalized rotation angle that takes into account the different weights of the spacecraft axes in the sense of expenditures (of fuel, time, or another irreplaceable resource) needed to rotate the spacecraft by the same angle. An analytical solution of this problem is obtained. Two versions of the optimal spacecraft slew maneuver problem (using the shortest trajectory) are considered—the quickest maneuver and a maneuver in the prescribed time. The optimal control problem is solved for several types of constraints on the control variables. The time of starting the deceleration is determined based on the actual motion parameters (mismatch angle and angular velocity) using the terminal control principles (based on the angular position and angular velocity measurements). An example and simulation results of the spacecraft dynamics under the optimal control are presented, which demonstrate the practical usefulness of the proposed control algorithms.     

Analysis of factors related to vertical vibration of continuous alternate wheels for omnidirectional mobile robots

Omnidirectional mobile robots (OMRs) are capable of arbitrary motions in arbitrary directions without changing the direction of wheels since they perform 3-DOF (degree of freedoms) motions on a plane. Various omnidirectional wheels including the continuous alternate wheel (CAW) with passive rollers for OMRs have been researched. The CAW has been developed for the purpose of minimizing vibration. The CAW has alternating inner and outer rollers around the wheel which makes nearly continuous contact with the ground. The ideal CAW reduce vibration for certain; however, the real CAW fail to do so due to various errors. In this regard, more research is needed to bring vibration under acceptable tolerance. In this paper, vertical vibration characteristics of the real CAW with tolerance are researched. Simulation models of CAWs are implemented using flexible body dynamics of Recurdyn. To verify vibration characteristics of the model, simulation results are compared with experimental results from the improved CAW with five rollers set (CAW5). Vertical vibration is affected by various factors: geometry errors, the gap, the thickness of flexible body, the angular velocity, the alignment angle, the load and the elasticity of flexible body, etc. To efficiently analyze the effects of various factors, dynamic simulations are conducted using Taguchi method. As a result, it is found that the main factors which affect vibration are the angular velocity and the alignment angle followed by the geometry errors, the load, the elasticity of flexible body, the thickness of flexible body and the gap. This process can be applied to the analysis of the other omnidirectional wheels with passive rollers.     

Output attitude tracking for flexible spacecraft

In this work a class of nonlinear controllers has been derived for spacecraft with flexible appendages. The control aim is to track a given desired attitude. First, a static controller based on the measure of the whole state is determined. Then, a dynamic controller is designed; this controller does not use measures from the modal variables, and the variables measured are the parameters describing the attitude and the spacecraft angular velocity. Finally, it is shown that a relaxed version of the tracking problem can be solved when the only measured variable is the spacecraft angular velocity. Simulations show the performances of such control schemes.     

On the coupled dynamics of small spacecraft and elastic deployable appendages

A thorough investigation of the dynamics of finite-mass satellites with a deployable elastic arm is presented. This work is focused on the interaction between spacecraft rigid body motion and its flexible arm dynamics during the deployment process. The classical Newton–Euler formulation and the Lagrangian approach are applied to the study of the dynamics of spacecraft and its deploying arm. Utilizing a non-Newtonian floating frame to define the arm elastic deformation field, the interactions between the spacecraft and its moving arm have been simulated. Complete equations of motion show that the spacecraft motion induces dynamical stiffness on the arm; in addition, axial and lateral motions of the deploying elastic arm change the spacecraft mass-characteristics and thus influence the spacecraft’s rigid body motions. The overall dynamic behavior is highly dependent on spacecraft mass characteristics in addition to the “arm deployment time (ADT)”. The results of case studies clearly indicate that some assumptions previously applied in appendage dynamic analysis are not conservative and produce erroneous results. This study realistically investigates the dynamics of elastic deploying appendages by considering finite-mass characteristics for small and massy spacecraft. The results reveal that for massive spacecraft the arm’s flexible dynamics is mainly excited through deployment, while for small spacecraft the energy transfers to the arm base and the spacecraft rigid body motion is considerably stimulated. Moreover, this work has further highlighted the effects of ADT in the overall system response. The findings of this work show that the energy distribution between arm’s elastic dynamics and spacecraft rigid body motions is an important factor in the design of any control system to limit unwanted arm-tip motions.     

Analytical solution of the optimal slew problem for an axisymmetric spacecraft in the class of conical motions

The traditional problem is discussed of an optimal spacecraft slew in terms of minimum energy costs. The spacecraft is considered as a rigid body with one symmetry axis under arbitrary boundary conditions for the angular position and angular velocity of the spacecraft in the quaternion formulation. Using substitutions of variables, the original problem is simplified (in terms of dynamic Euler equations) to the optimal slew problem for a rigid body with a spherical mass distribution. The simplified problem contains one additional scalar differential equation. A new analytical solution is presented for this problem in the class of conical motions, leading to constraints on the initial and final values of the angular velocity vector. In addition, the optimal slew problem is modified in the class of conical motions to derive an analytical solution under arbitrary boundary conditions for the angular position and angular velocity of the spacecraft. A numerical example is given for the conical motion of the spacecraft, as well as examples showing the closeness of the solutions of the traditional and modified optimal slew problems for an axisymmetric spacecraft.     

考虑测量不确定和输入饱和的充液航天器自适应鲁棒控制

本文研究了三轴稳定充液航天器控制系统中同时存在测量不确定,外部未知干扰,参数不确定和控制输入饱和的鲁棒自适应姿态机动控制问题.建模过程中,将晃动液体燃料等效为粘性球摆模型,采用动量矩守恒定律推导出充液航天器的耦合动力学方程.提出了一种将反步控制方法结合非线性干扰观测器和指令滤波器的鲁棒饱和输出反馈复合控制策略,该控制策略不仅能继承反步控制方法的优点,而且通过引入非线性干扰观测器实现对未知外部干扰,参数不确定以及测量不确定的补偿,还能利用指令滤波器处理控制力矩输入饱和的不利影响.基于Lyapunov稳定性分析方法证明了系统状态变量的渐进稳定性.仿真结果验证了提出控制方法的有效性和鲁棒性.     

Attitude control of spacecraft simulator without angular velocity measurement

In this paper the attitude control of a spacecraft simulator using Reaction Wheels (RW) as the actuators is investigated. The main goal of the current study is to bring the RWs to the rest at the end of the maneuver without angular velocity measurement. A modified feedback linearization controller is applied by considering the Euler angles of the simulator as the output and the RWs angular momentums as the internal state variables. The stability of the proposed controller and the internal dynamics is analyzed using Lyapunov theory. Two modified sliding mode observers are designed to estimate the angular velocities of the spacecraft attitude control subsystem simulator. The proposed observers do not use the control input and the detailed knowledge of the model and thus it can be implemented easily. The global stability of the system is proved. The proposed controller and observers are finally evaluated numerically and experimentally on an attitude spacecraft simulator.     

Analytical Solution of the Minimum Time Slew Maneuver Problem for an Axially Symmetric Spacecraft in the Class of Conical Motions

The conventional problem of the time-optimal slew of a spacecraft considered as a solid body with a single symmetry axis subject to arbitrary boundary conditions for the attitude and angular velocity is considered in the quaternion statement. By making certain changes of variables, the original dynamic Euler equations are simplified, and the problem turns into the optimal slew problem for a solid body with a spherical distribution of mass containing one additional scalar differential equation. For this problem, a new analytical solution in the class of conical motions is found; in this solution, the initial and terminal attitudes of the space vehicle belong to the same cone realized under a bounded control. A modification of the optimal slew problem in the class of generalized conical motions is made that makes it possible to obtain its analytical solution under arbitrary boundary conditions for the attitude and angular velocity of the spacecraft. A numerical example of a spacecraft’s conical motion and examples demonstrating the proximity of the solutions of the conventional and modified optimal slew problems of an axially symmetric spacecraft are discussed.     

Special control mode in the problem of optimal turn of an arbitrary rigid body (spacecraft)

The problem of optimal turn of spacecraft as a rigid body of arbitrary dynamic configuration under arbitrary boundary conditions with respect to angular position and angular velocity of spacecraft in the quaternion formulation is considered. The optimality criterion is a functional that combines time and the integral value of the control vector magnitude spent for the spacecraft turn. A special control mode of the spacecraft is studied. Examples of calculations are given.     

Special control regime in optimal turn problem of spherically symmetric spacecraft

The optimal turn problem of a spacecraft as a solid body with spherical mass distribution for arbitrary boundary conditions with respect to the spacecraft angular position and angular velocity is considered in the quaternion formulation. The functional combining the time and the integral absolute value of the control vector applied for the spacecraft turn is used as the optimality criterion. The special control regime of the spacecraft is studied, the isolated character of this regime is demonstrated. Examples of calculations are presented.     

欠驱动刚体航天器姿态运动规划的遗传算法

研究欠驱动刚体航天器姿态的非完整运动规划问题．航天器利用3个动量飞轮可以控制其姿态和任意定位,当其中一轮失效,航天器姿态通常表现为不可控．在系统角动量为零的情况下,系统的姿态控制问题可转化为无漂移系统的运动规划问题．基于优化控制理论,提出了求解欠驱动刚体航天器的姿态运动控制遗传算法,并且数值仿真表明：该方法对欠驱动航天器姿态运动的控制是有效的．