Axisymmetric Spacecraft Research Articles

Smooth Time-Varying Feedback Control of Nonholonomic Systems with Applications to the Attitude Control of Underactuated Spacecraft

This paper studies the control of chained nonholonomic systems by using smooth time-varying feedback. First, by using a time-varying state transformation, the chained nonholonomic system is transformed into a linear time-varying system. Second, with the aid of some properties of a class of parametric Lyapunov equations and time-varying systems theory, smooth time-varying state feedback controller is developed to ensure the exponential convergence of both the system states and controls. Different from existing results, the design parameters in the proposed control strategy are independent of the initial conditions of the system. Third, as an application of the proposed smooth time-varying feedback, the attitude control problem for underactuated axisymmetric spacecraft is addressed. Finally, a numerical simulation is presented to validate the effectiveness of the proposed method.

Time-distributed optimization for shrinking horizon MPC

This paper proposes a strategy for implementing shrinking horizon Model Predictive Control (MPC) using a limited number of optimization iterations at each timestep. Offline and online certification methods are presented for determining a time-varying bound on the number of optimization iterations that ensures the closed-loop system satisfies a specified terminal constraint. An axisymmetric spacecraft spin stabilization example is reported to demonstrate the certification procedure.

Finite-Time Control of a Class of Nonlinear Underactuated Systems with Application to Underactuated Axisymmetric Spacecraft

In this paper, the finite-time control problem of a class of nonlinear underactuated systems is addressed. By using the auxiliary state generated by a time-varying oscillator-like differential equation and constructing a novel Lyapunov-like function, a time-varying dynamic feedback controller is designed for such nonlinear underactuated systems. It is proved that the state of the closed-loop system converges to zero at the finite time and the controls are bounded. As an application, the finite-time tracking problem for underactuated axisymmetric systems is solved. Numerical simulations verify the effectiveness of the proposed methods.

Controlled Change in the Dimensions of an Axisymmetric Spacecraft Descending in the Atmosphere of Mars

In the presented work, a controlled change by dimensions of a spacecraft descending in the atmosphere of Mars is considered. The aim of the work is to obtain a method for calculating the mass and mass-geometric characteristics of a spacecraft when changing its dimensions, which provides angular velocity passive control during the descent of this spacecraft in a low-density atmosphere. In the process of solving this problem, the geometric and mass-geometric characteristics of the descent spacecraft (volume, cross-sectional area, moments of inertia) were calculated. It is assumed that the outer shape of the spacecraft posterior to the incoming flow is a one-sheet rotational hyperboloid, which changes its dimensions during the spacecraft descent in the low-density atmosphere of Mars. As a result of solving the nonlinear programming problem, the minimum and maximum values of the main axial moments of inertia are obtained, which able to spin the spacecraft relative to the longitudinal axis of symmetry. The initial data for solving the nonlinear programming problem are the minimum volume and the maximum cross-sectional area of the hyperboloid, calculated according to the specified intervals of the variable controlling the dimensions of this surface. The method for calculating the mass and mass-geometric characteristics of a spacecraft when changing its dimensions ispresented, which makes it possible to control the magnitude of the angular velocity of a symmetric spacecraft in the low-density atmosphere of Mars without the use of onboard jet engines. In particular, it is shown in the work that as the height of the hyperboloid increases, the moment of inertia about the spacecraft longitudinal axis of symmetry decreases, accompanied by an increase in the moments of inertia about the transverse axes of symmetry. It can be shown that in this case there is an increase in the angular velocity of the spacecraft about the longitudinal axis, which makes it possible to achieve a stable orientation of the spacecraft upon entering the atmosphere. However, a more detailed study of the dynamics ofthe spacecraft relative motionwith a changeable shape in the atmosphere is beyond the scope of this work, but it can be presented in further publications.

Analytical Solution of the Problem on an Axisymmetric Spacecraft Attitude Maneuver Optimal with Respect to a Combined Functional

Analytical Solution of the Problem on an Axisymmetric Spacecraft Attitude Maneuver Optimal with Respect to a Combined Functional

Two-timescale magnetic attitude control of Low-Earth-Orbit spacecraft

Spacecraft attitude stabilization based on active magnetic actuators represents a challenging problem, since the available control torque is constrained on a plane orthogonal to the direction of the local geomagnetic field, making the system instantaneously underactuated. A novel magnetic controller is proposed, driving a satellite flying on a Low-Earth-Orbit to three-axis stabilization on a prescribed attitude in the Nadir-pointing orbit frame. A proof of stability is provided for an idealized configuration (axisymmetric spacecraft with no disturbances). Robustness of the control technique against environmental disturbances, parameter uncertainties, corrupted measurements, and other control implementation issues is then demonstrated by numerical simulations, where the effect of magnetic residual dipoles is mitigated by online estimation.

Synthesis of control of the aircraft angular velocities based on algorithm with a predictive model

An urgent issue is to obtain optimal control laws for nonlinear dynamic objects. The article presents a numerical algorithm to control stabilization of the angular velocities of spacecraft with various axial moments of inertia based on optimization with respect to the Krasovsky functional using the predictive model method. The simulation results are presented. The character of the curves of angular velocity dynamics and control moments obtained in the simulation corresponds to the curves of angular velocity dynamics and control moments obtained in the simulation of control using the analytical law for an axisymmetric spacecraft, which confirms the adequacy of the synthesized algorithm.

Оптимальне демпфування відхилень кутових швидкостей осесиметричного космічного літального апарата

This paper considers the problem of optimal fuel consumption damping of sudden deviations of angular velocities of an axisymmetric spacecraft with a constant speed of rotation around the main axis of symmetry. This assumption has some practical significance and may be due to the creation of artificial gravity on the spacecraft. The idea of artificial gravity due to the rotation of an axisymmetric cylindrical spacecraft is based on the principle of equivalence of the force of gravity and the force of inertia. The urgency of the fuel consumption optimization problem is due to the presence of its limited stock onboard the spacecraft. The optimization problem is solved based on the maximum principle and the phase plane method. The authors of the article determine the structure of optimal fuel consumption processes with three levels of control, and the number of their switches depends on the initial conditions. Synthesized on the phase plane, the optimal switching curves divide the phase plane into eight curvilinear quadrants, which uniquely determine the values of the optimal control effects by the current values of the deviations of the angular velocities of the spacecraft. The problem of the possible presence of a delay in the control loop is proposed to be solved based on the Bess compensation method. To do this, the corresponding optimal curves of switching and disabling the controls are built as geometric locations of points remoted for the time of delay from the found curves of switching and the beginning of coordinates accordingly. It allows us to avoid the emergence of steady self-oscillations in a control contour and to provide a condition of keeping the spacecraft in a given final state after the completion of the stabilization process. Depending on the technical equipment of the spacecraft, two variants of the optimal damping algorithm are offered, namely: an autonomous device in the onboard control system of the spacecraft in the absence of a sufficiently powerful onboard computer, or the optimal damping algorithm, implemented entirely in the onboard computer of the spacecraft in case of its sufficient power.

Velocity pointing error reduction for symmetric spinning spacecraft via a two-burn scheme

During axial thrusting of a symmetric spinning spacecraft, misalignment and center-of-mass offset can cause unwanted body-fixed torques. The two-burn scheme is applied to eliminate velocity pointing error. Solutions for angular velocity, Euler angle, and inertial velocity with nonzero initial conditions are derived in a new form for axisymmetric spacecraft with constant mass. Simulations show that the solutions closely match numerical simulations and the two-burn scheme decrease the velocity pointing error obviously. Based on the solutions, the effect of two-burn scheme is analyzed. The results show that the spacecraft will obtain the minimum velocity pointing error if the burn and coast times are controlled accurately. Also, the two-burn scheme allows for a lower spin rate and the spacecraft can be maneuvered at nonzero initial conditions compared with the continuous thrust scheme.

Global stabilization of the linearized three-axis axisymmetric spacecraft attitude control system by bounded linear feedback

In this paper, the three-axis attitude stabilization of the axisymmetric spacecraft with bounded inputs is studied. By constructing some novel state transformations, saturated linear state feedback controllers are constructed for the considered attitude control system. By constructing suitable quadratic plus integral Lyapunov functions, globally asymptotic stability of the closed-loop systems is proved if the feedback gain parameters satisfy some explicit conditions. By solving some min–max optimization problems, a global optimal feedback gain for the underactuated attitude stabilization system is proposed such that the convergence rate of the linearized closed-loop system is maximized. Numerical simulations show the effectiveness of the proposed approaches.

Attitude Coordinated Control of Multiple Underactuated Axisymmetric Spacecraft

Attitude coordinated control of multiple underactuated spacecraft is studied in this paper. We adopt the parametrization proposed by Tsiotras et al. (1995) to describe attitude kinematics, which has been shown to be very convenient for control of underactuated axisymmetric spacecraft with two control torques. We first propose a partial attitude coordinated controller with angular velocity commands. The controller is based on the exchange of each spacecraft's information with local neighbors and a self-damping term. Under a necessary and general connectivity assumption and by use of a novel Lyapunov function, we show that the symmetry axes of all spacecraft are eventually aligned. Full attitude control of multiple underactuated spacecraft is also considered and a discontinuous distributed control algorithm is proposed. It is shown that the proposed algorithm succeeds in achieving stabilization given that control parameters are chosen properly. Discussions on the cases without self damping are also provided for both partial and full attitude controls. Simulations are given to validate the theoretical results and different steady-state behaviors are observed.

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.

Robust adaptive spin-axis stabilization of a symmetric spacecraft using two bounded torques

The spin-axis stabilization of an axisymmetric spacecraft by two control torques perpendicular to the symmetry axis is addressed. Two control laws are designed to align the symmetry axis along a desired inertial direction despite the revolution around the symmetry axis. The first controller takes a saturated proportional-derivative form and can stabilize the spin-axis to the desired direction with a priori bounded torques in the absence of modeling uncertainties. In order to achieve better robustness, an adaptive controller is then designed to account for the inertia uncertainties and disturbances, in addition to actuator saturation. Numerical examples are presented to demonstrate the advantageous features of the proposed algorithm compared with conventional spin-axis stabilization methods.

Three-axis L1 adaptive attitude control of spacecraft using solar radiation pressure

Based on the [Formula: see text] adaptive control theory, a novel three-axis attitude control system for an axisymmetric spacecraft with uncertain dynamics moving in elliptic orbits, using solar radiation pressure, is derived. The nonaffine-in-control nonlinear spacecraft model includes the gravity gradient torque, the control torque produced by four solar flaps, and external time-varying disturbance moments. For the three-axis attitude control, an [Formula: see text] adaptive control system is designed, which includes a state predictor. A smooth projection algorithm is used to confine the estimated parameters within a desirable set. In the closed-loop system, the designed adaptive law accomplishes three-dimensional attitude control. A special feature of the attitude control system is that it is possible to select large adaptation gains for fast adaptation and to obtain quantifiable performance bounds. Simulation results show that in the closed-loop system, precise roll, yaw, and pitch angle control is accomplished, despite unmodeled nonlinearities, parameter uncertainty, and external disturbance inputs in the model.

A fault-tolerant magnetic spin stabilizing controller for the JC2Sat-FF mission

This paper presents a spin-stabilization algorithm for the Japan Canada Joint Collaboration Satellite-Formation Flying (JC2Sat-FF) mission using magnetic actuation only. It is shown that under a reasonable assumption on the Earth’s magnetic field, the resulting control law is asymptotically stabilizing for an axisymmetric spacecraft, even under the failure of up to two magnetic torque rods and magnetic torque rod saturation. It is also stabilizing under quantization. The satellite motion remains stable under control outages, meaning that the error can be reduced by implementing the control intermittently. The effectiveness of the control law is demonstrated using a high fidelity attitude control system simulator for the JC2Sat-FF satellite.

Nonlinear H_infinity Control Designs with Axisymmetric Spacecraft Control

In this paper, we study nonlinear control of a spacecraft symmetric about its principal axis with two control torques. Using a computationally efficient H ∞ control design procedure, attitude stabilization and command tracking problems of the axisymmetric spacecraft are solved locally. The proposed nonlinear H ∞ control approach uses higher order Lyapunov functions and reformulates the difficult Hamilton―Jacobian―Isaacs inequalities as semidefinite optimization conditions. Sum-of-squares programming techniques are then applied to obtain computationally tractable solutions, from which nonlinear control laws will be constructed. The nonlinear H ∞ control designs for spacecraft are capable of exploiting the most suitable forms of Lyapunov functions for performance improvement.

Rotational Motion Control by Feedback with Minimum L1-Norm

Rotational Motion Control by Feedback with Minimum L1-Norm

Spin-axis stabilisation of underactuated rigid spacecraft under sinusoidal disturbance

Spin-axis stabilisation of spacecraft is a problem of partial stabilisation for non-linear dynamical systems. In this article the analysis of spin-axis stabilisation of underactuated rigid spacecraft in the presence of sinusoidal disturbances is presented. By using the Euler–Poisson form to describe the equations of motion and assuming the disturbances in three axes are decoupled with known frequencies, the paper first studies the problem of the underactuated rigid axisymmetric spacecraft by applying the internal modal principle to eliminate the sinusoidal disturbance. Then the paper turns to the more complicated asymmetric spacecraft, where the boundedness of the angular velocity for the underactuated axis is analysed in detail. The paper also proves the global asymptotic stability of the closed-loop systems for both axisymmetric spacecraft and asymmetric spacecraft by combining the Lyapunov direct method with the LaSalle's theorem. The simulation results show that the proposed control law is effective in the presence of sinusoidal disturbance.

Spacecraft Maneuver and Stabilization for Emergency Atmospheric Entry with One Control Torque

use of control in one axis only. To show the feasibility of such a concept, the technique of single-input/single-output feedback linearization using the Lie derivative method is employed. The problem is solved for different numbers of jets and for different configurations of the inertia matrix. In the case of an axisymmetric spacecraft, the closed-loop stability is analyzed through the zero dynamics of the internal dynamics. In the cases in which the inertia matrix has cross products of inertia different from zero, the internal dynamics becomes practically intractable. In these cases, only an assessment of closed-loop stability coming from the analysis of different simulation cases is provided. The results show that for the proposed concept and control method to be feasible, a specific geometric layout of the actuators is required for each inertia configuration and number of jets employed in the system.

Periodic motions of spinning rigid spacecraft under influence of gravitational and magnetic fields

The motion of a magnetized axisymmetric spacecraft about its center of mass in a circular orbit is considered, taking the gravitational and magnetic effects of the central body into account. Equations of motion of the reduced system are transformed to equations of plane motion of a charged particle under the action of electric and magnetic fields. Stationary motions of the system are determined and periodic motions near to them are constructed using the Lyapounoff theorem of the holomorphic integral.