Optimal control of reorientation of a spacecraft using free trajectory method

The problem of optimal control over spatial reorientation of a spacecraft is considered. The functional having a sense of propellant consumption is minimized. The analytical solution to the formulated problem is presented. It is shown that the optimal solution can be found in the class of two-impulse control at which the spacecraft’s turn is performed along a free motion trajectory. In order to improve the accuracy of spacecraft guidance into a specified angular position, methods of control are suggested that realize the method of free trajectories. The synthesized controls are invariant with respect to both external perturbations and parametric errors. The results of mathematical modeling are presented that demonstrate high efficiency of developed control algorithms. Propellant consumption for realizing a programmed turn is numerically estimated taking into account considerable gravitational and aerodynamic moments acting upon the spacecraft.     

Some issues of time-optimal control over a spacecraft programmed turn

The problem of optimal turn of a spacecraft from an arbitrary initial position to a final specified angular position in a minimum time is considered and solved. A case is investigated, when the constraint on spacecraft’s angular momentum during the turn is essential. Based on the quaternion method a solution to the posed problem has been found, and an optimal control program is constructed taking the constraints on controlling moment into account. The optimal control is found in the class of regular motions. A condition (calculation expression) is presented for determining the moment to begin braking with the use of measurements of current motion parameters, which considerably improves the accuracy of putting the spacecraft into a preset position. For a dynamically symmetrical spacecraft the solution to the problem of optimal control by the spacecraft spatial turn is presented in analytical form (expressions in elementary functions). An example of mathematical modeling of the spacecraft motion dynamics under optimal control over reorientation is given.     

Optimal Control of a Spatial Turn of a Spacecraft with Minimal Loading of Construction

The problem of optimal control of a three-dimensional turn of a spacecraft is considered and solved. The turn is performed from an initial angular position into the required final angular position in a specified time and with a minimum value of the functional that represents the degree of loading of the construction. An analytical solution to the formulated problem is presented. It is demonstrated that the optimal (in this sense) control of the spacecraft reorientation can be determined in the class of a regular precession executed by the spacecraft. The instant when braking begins is determined based on the principles of terminal control using the actual kinematical parameters of the spacecraft motion, which substantially increases the accuracy of transferring the spacecraft to a specified position. Data of mathematical modeling are also presented that confirm the efficiency of the described method of controlling the spacecraft's three-dimensional turn.     

Experimental Flight of a Spacecraft with Solar Sail

We analyze the prospects of launching an experimental spacecraft with a solar sail. The problems hindering the implementation of this task are discussed. The ways to solve these problems are pointed out. The feasibility of organization of a system of controlling this spacecraft with a small consumption of propellant mass is briefly investigated.     

Electric transfer optimization for mars sample return mission

The aim of this paper is to analyse an alternative scenario for Mars Sample Return Orbiter mission, where electric propulsion is used for Earth-Mars and Mars-Earth heliocentric cruises and for Mars orbit insertion / escape transfers, whereas chemical propulsion is used for final Mars rendezvous. The problem consists in minimizing the initial vehicle mass to obtain a specific final dry mass in reasonable time. The planetocentric phases correspond to continuous low-thrust trajectories, spiraling around Mars between a low orbit and the influence sphere altitude. The heliocentric phases consist of a succession of low-thrust and coasting arcs with specific departure and arrival conditions at the Earth. For these two types of transfer, efficient optimal control tools exist based on Pontryagin's maximum principle. Thanks to the coordination between planetocentric and heliocentric phases, the solution obtained with these two separate tools gives a good upper bound of the optimal solution in terms of propellant consumption and duration. This optimization procedure is described and finally applied to the proposed mission. The numerical results are presented and compared with the baseline chemical mission solution. The electric option could allow to decrease the spacecraft departure mass but may lead to rather long mission duration.     

The Use of Quaternions in the Optimal Control Problems of Motion of the Center of Mass of a Spacecraft in a Newtonian Gravitational Field: I

The problem of optimal control is considered for the motion of the center of mass of a spacecraft in a central Newtonian gravitational field. For solving the problem, two variants of the equations of motion for the spacecraft center of mass are used, written in rotating coordinate systems. Both the variants have a quaternion variable among the phase variables. In the first variant this variable characterizes the orientation of an instantaneous orbit of the spacecraft and (simultaneously) the spacecraft location in this orbit, while in the second variant only the instantaneous orbit orientation is specified by it. The suggested equations are convenient in the respect that they allow the general three-dimensional problem of optimal control by the motion of the spacecraft center of mass to be considered as a composition of two interrelated problems. In the first variant these problems are (1) the problem of control of the shape and size of the spacecraft orbit and (2) the problem of control of the orientation of a spacecraft orbit and the spacecraft location in this orbit. The second variant treats (1) the problem of control of the shape and size of the spacecraft orbit and the orbit location of the spacecraft and (2) the problem of control of the orientation of the spacecraft orbit. The use of quaternion variables makes this consideration most efficient. The problem of optimal control is solved on the basis of the maximum principle. Several first integrals of the systems of equations of the boundary value problems of the maximum principle are found. Transformations are suggested that reduce the dimensions of the systems of differential equations of boundary value problems (without complicating them). Geometrical interpretations are given to the transformations and first integrals. The relation of the vectorial first integral of one of the derived systems of equations (which is an analog of the well-known vectorial first integral of the studied problem of optimal control) with the found quaternion first integral is considered. In this paper, which is the first part of the work, we consider the models of motion of the spacecraft center of mass that employ quaternion variables. The problem of optimal control by the motion of the spacecraft center of mass is investigated on the basis of the first variant of equations of motion. An example of a numerical solution of the problem is given.     

Control of a spacecraft’s spatial turn with minimum value of the path functional

The problem of optimal (with minimum value of the path functional) control over a spatial reorientation of a spacecraft is considered. Using the quaternion method, an analytical solution to this problem is obtained. For the symmetrical optimality index, the complete solution to the problem of spacecraft reorientation is represented in a closed form. The results of mathematical modeling of the spacecraft motion dynamics are presented, demonstrating the practical efficiency of the developed algorithm of control.     

On the problem of optimal control of the thrust value of the electric propulsion rocket with solar energy source

Under consideration is the optimal control problem on a spacecraft motion in Newtonian central gravity field. With the use of the mathematical model of electrojet propulsion device (EPD) with solar energy source, proposed earlier in paper [1], the dependence of the EPD working substance choice on both the duration of the given dynamic maneuver and the propellant expenditures for its fulfillment is investigated. The efficiency evaluation is carrying out of optimal control of variable valued thrust as well as that for relay mode thrust and relay mode thrust with optimal fixed thrust value.     

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.     

非凸二次约束下航天器姿态机动路径迭代规划方法

针对复杂约束下航天器姿态机动路径规划问题,首先描述和分析了航天器姿态机动过程中面临的动力学和运动学约束、有界约束、姿态指向约束,把姿态指向约束利用非凸二次型进行表述;其次从能量最优角度出发,将该约束机动问题归纳为非凸二次约束二次规划问题;然后引入线性松弛技术,将该问题转化成双线性规划问题,求出其中一个变量的凸包络和凹包络,降低求解复杂度,从而求出原问题的一个线性松弛。同时为了提高求解精度,提出一种基于评价函数的迭代规划算法,利用线性松弛求出的解作为初值,通过评价函数进行迭代规划,最终求出原问题的最优解。仿真结果表明该方法不仅可以满足复杂的姿态约束,得到全局姿态优化路径,而且能够降低能量消耗。     

The Use of Quaternions in the Optimal Control Problems of Motion of the Center of Mass of a Spacecraft in a Newtonian Gravitational Field: III

The results of numerical solution of the problem of a rendezvous in the central Newtonian gravitational field of a controlled spacecraft with an uncontrollable spacecraft moving along an elliptic Keplerian orbit are presented. Two variants of the equations of motion for the spacecraft center of mass are used, written in rotating coordinate systems and using quaternion variables to describe the orientations of these coordinate systems. The problem of a rendezvous of two spacecraft is formulated [1, 2] as a problem of optimal control by the motion of the center of mass of a controlled spacecraft with a movable right end of the trajectory, and it is solved on the basis of Pontryagin's maximum principle. The paper is a continuation of papers [1, 2], where the problem of a rendezvous of two spacecraft has been considered theoretically using the two above variants of the equations of motion for the center of mass of the controlled spacecraft.     

Application of a magnetohydrodynamic element in the control loop of a rotating spacecraft with cavities partially filled with liquid

This paper is a continuation of [1–3] and a generalization of the results for a rotating spacecraft with cavities partially filled with liquid and equipped with an operational magnetohydrodynamic (MHD) element in the loop of its attitude control. This element makes possible the creation of hingeless systems of stabilization and orientation that do not require rocket propellant consumption. The application of an MHD element is considered for stabilization in the mode of spin-up of a spacecraft not having gyroscopic stability.     

Time-optimal maneuvering control of a rigid spacecraft

The time-optimal rest-to-rest maneuvering control problem of a rigid spacecraft is studied in this paper. By utilizing an iterative procedure, this problem is formulated and solved as a constrained nonlinear programming (NLP) one. In this novel method, the count of control steps is fixed initially and the sampling period is treated as a variable in the optimization process. The optimization object is to minimize the sampling period below a specific minimum value, which is set in advance considering the accuracy of discretization. To generate initial feasible solutions of the NLP problem, a genetic-algorithm-based is also proposed such that the optimization process can be started from many different points to find the globally optimal solution. With the proposed method, one can find a time-optimal rest-to-rest maneuver of the rigid spacecraft between two attitudes. To show the feasibility of the proposed method, simulation results are included for illustration.     

Nitrous oxide as a rocket propellant

Nitrous oxide is introduced as a multi-purpose propellant for spacecraft. Potential space applications of this propellant are given. Based on comparison to conventional systems, a multi-mode nitrous oxide propulsion concept is expected to deliver higher performance. Main features of a self-pressurising, nitrous oxide storage system are described. A nitrous oxide catalytic decomposition technique is suggested for restartable spacecraft propulsion. Up-to-date experimental results are presented. A conclusion describes the long-term feasibility of novel nitrous oxide propulsion option concepts.     

On solving the problems of optimization of trajectories of many-revolution orbit transfers of spacecraft

The problem of optimal control over many-revolution spacecraft orbit transfers between circular coplanar orbits of satellites is considered. The spacecraft flight is controlled by a thrust vector of a jet engine with restricted thrust (JERT). The mass expenditure is minimized at a limited time of flight. The optimal control problem is solved based on the maximum principle. The boundary value problem of the maximum principle is solved numerically using the shooting method. A modified computation scheme of the shooting method is suggested (multi-point shooting), as well as a method (correlated with the scheme) of choosing the initial approximation with the use of a solution to the optimization problem in the impulse formulation. The scheme and method allow one to construct many-revolution spacecraft orbit transfers.     

利用喷气装置卸载航天器积累角动量的最小工质损耗控制

讨论利用喷气装置卸载航天器积累的外扰角动量过程中 ,实现最小工质损耗的问题。提出了在航天器绕自己质心转动的过程中实现对这一角动量进行卸载的新思路。文中采用极大值原理求得了最优工质损耗并举出了实例     

基于多目标规划的交会对接推力器指令分配方法

将由控制律得到的控制量转化为推力器控制指令的过程称为推力器指令分配。由于交会对接涉及的推力器配置复杂,且对追踪航天器姿轨控精度的要求很高,因此其推力器指令分配问题十分重要。本文针对该问题,分析了基于线性规划的指令分配方法存在的不足,提出了将推力器指令分配问题转化为非线性多目标规划问题,并应用分枝定界法进行寻优的新方法。新方法可以在指令分配的误差和燃料消耗之间进行折衷,并且考虑了推力器最小开机时间的限制。仿真结果验证了新方法的有效性。     

Control aspects of efficient rocket propulsion systems

The means for enhancing the efficiency of rocket propulsion of spacecraft is considered in terms of the control of propellant consumption, trajectory planning, and in-flight operations management. Particular attention is given to techniques by which all the fuel and oxidizer are consumed completely by mixture adjustment as an example of a terminal control system providing significant propulsion efficiency.     

Development and experimentation of LQR/APF guidance and control for autonomous proximity maneuvers of multiple spacecraft

This work introduces a novel control algorithm for close proximity multiple spacecraft autonomous maneuvers, based on hybrid linear quadratic regulator/artificial potential function (LQR/APF), for applications including autonomous docking, on-orbit assembly and spacecraft servicing. Both theoretical developments and experimental validation of the proposed approach are presented. Fuel consumption is sub-optimized in real-time through re-computation of the LQR at each sample time, while performing collision avoidance through the APF and a high level decisional logic. The underlying LQR/APF controller is integrated with a customized wall-following technique and a decisional logic, overcoming problems such as local minima. The algorithm is experimentally tested on a four spacecraft simulators test bed at the Spacecraft Robotics Laboratory of the Naval Postgraduate School. The metrics to evaluate the control algorithm are: autonomy of the system in making decisions, successful completion of the maneuver, required time, and propellant consumption.     

Qualitative Properties of Orbits for Minimum-Fuel Impulsive Transfers between Circular Coplanar Orbits with a Given Launch Time

The coplanar problem of minimizing propellant consumption in impulsive transfer between circular boundary orbits is investigated. The launch time and the initial configuration of objects on the boundary orbits are specified arbitrarily. The qualitative properties of optimal two-impulse trajectories and their optimality in the class of multi-impulse transfers are studied.