This paper addresses the leader-following attitude consensus problem for a group of spacecraft when at least one follower can access the leader's attitude and velocity relative to the inertial space. A nonlinear distributed observer is designed to estimate the leader's states for each follower. The observer possesses one important and novel feature of keeping attitude and angular velocity estimation errors on second-order sliding modes, and thus provides finite-time convergent estimates for each follower. Further, quaternion-based hybrid homogeneous controllers recently developed for single spacecraft are extended and then applied, by establishing a separation principle with the proposed observer, to track the leader's attitude motion. As a result, global finite-time attitude consensus is achieved on the entire attitude manifold, with either full-state measurements or attitude-only measurements, as long as the network topology among the followers is undirected and connected. Numerical simulations are presented to demonstrate the performance of the proposed methods.
In this work feedback control laws are designed for achieving three-axis attitude stabilization of inertial pointing spacecraft using only magnetic torquers. The designs are based on an almost periodic model of geomagnetic field along the spacecraft's orbit. Both attitude plus attitude rate feedback, and attitude only feedback are proposed. Both feedback laws achieve local exponential stability robustly with respect to large uncertainties in the spacecraft's inertia matrix. The latter properties are proved using general averaging and Lyapunov stability. Simulations are included to validate the…
This paper studies formation control of an arbitrary number of spacecraft based on a serial network structure. The leader controls its absolute position and absolute attitude with respect to an inertial frame, and the followers control its relative position and attitude with respect to another spacecraft assigned by the serial network. The unique feature is that both the absolute attitude and the relative attitude control systems are developed directly in terms of the line-of-sight observations between spacecraft, without need for estimating the full absolute and relative attitudes, to improve…
Spacecraft attitude control using only magnetic torques is a periodic time-varying system as the Earth magnetic field in the spacecraft body frame changes periodically while the spacecraft circles around the Earth. The optimal controller design therefore involves the solutions of the periodic Riccati differential or algebraic equations. This paper proposes an efficient algorithm for the periodic discrete-time Riccati equation arising from a linear periodic time-varying system $(\A,\B)$, which explores and utilizes the fact that $\A$ is time-invariant and only $\B$ is time-varying in the system…
The paper develops a Model Predictive Controller for constrained control of spacecraft attitude with reaction wheel actuators. The controller exploits a special formulation of the cost with the reference governor like term, a low complexity addition of integral action to guarantee offset-free tracking of attitude set points, and an online optimization algorithm for the solution of the Quadratic Programming problem which is tailored to run in fixed-point arithmetic. Simulations on a nonlinear spacecraft model demonstrate that the MPC controller achieves good tracking performance while satisfyin…
A global model is presented that can be used to study attitude maneuvers of a rigid spacecraft in a circular orbit about a large central body. The model includes gravity gradient effects that arise from the non-uniform gravity field and characterizes the spacecraft attitude with respect to the uniformly rotating local vertical local horizontal coordinate frame. An accurate computational approach for solving a nonlinear boundary value problem is proposed, assuming that control torque impulses can be applied at initiation and at termination of the maneuver. If the terminal attitude condition is …
Relative attitude formation control systems are developed for multiple spacecraft, based on the line-of-sight measurements between spacecraft in formation. The proposed control systems are unique in the sense that they do not require constructing the full attitudes of spacecraft and comparing them to obtain the relative attitudes indirectly. Instead, the control inputs are directly expressed in terms of line-of-sight measurements to control relative attitude formation precisely and efficiently. It is shown that the relative attitudes almost globally asymptotically track their desired relative …
This paper discusses spacecraft control using variable-speed CMGs. A new operational concept for VSCMGs is proposed. This new concept makes it possible to approximate the complex nonlinear system by a linear time-varying system (LTV). As a result, an effective control system design method, Model Predictive Control (MPC) using robust pole assignment, can be used to design the spacecraft control system using VSCMGs. A nice feature of this design is that the control system does not have any singular point. A design example is provided. The simulation result shows the effectiveness of the proposed…
Two popular types of spacecraft actuators are reaction wheels and magnetic torque coils. Magnetic torque coils are particularly interesting because they can be used for both attitude control and reaction wheel momentum management (desaturation control). Although these two tasks are performed at the same time using the same set of actuators, most design methods deal with only one of the these tasks or consider these two tasks separately. In this paper, a design with these two tasks in mind is formulated as a single problem. A periodic time-varying linear quadratic regulator design method is the…
We consider the problem of jointly estimating the attitude and spin-rate of a spinning spacecraft. Psiaki (J. Astronautical Sci., 57(1-2):73--92, 2009) has formulated a family of optimization problems that generalize the classical least-squares attitude estimation problem, known as Wahba's problem, to the case of a spinning spacecraft. If the rotation axis is fixed and known, but the spin-rate is unknown (such as for nutation-damped spin-stabilized spacecraft) we show that Psiaki's problem can be reformulated exactly as a type of tractable convex optimization problem called a semidefinite opti…
This paper addresses the problem of distributed coordination control of spacecraft formation. It is assumed that the agents measure relative positions of each other with a non-zero, unknown constant sensor bias. The translational dynamics of the spacecraft is expressed in Euler-Lagrangian form. We propose a novel distributed, model independent control law for synchronization of networked Euler Lagrange system with biased measurements. An adaptive control law is derived based on Lyapunov analysis to estimate the bias. The proposed algorithm ensures that the velocities converge to that of leader…
This paper discusses translation and attitude control in spacecraft rendezvous and soft docking. The target spacecraft orbit can be either circular or elliptic. The high fidelity model for this problem is intrinsically a nonlinear system but can be viewed as a linear time varying system (LTV). Therefore, a model predictive control (MPC) based design is proposed to deal with the time-varying feature of the problem. A robust pole assignment method is used in the MPC-based design because of the following merits and/or considerations: (a) no overshoot of the relative position and attitude between …
This paper presents a continuous optimization approach to DCOC and its application to spacecraft high-precision attitude control. The approach computes a control input sequence that maximizes the time-before-exit by solving a nonlinear programming problem with an exponentially weighted cost function and purely continuous variables. Based on results from sensitivity analysis and exact penalty method, we prove the optimality guarantee of our approach. The practical application of our approach is demonstrated through a spacecraft high-precision attitude control example. A nominal case with three …
The spacecraft attitude tracking problem is addressed with actuator faults and uncertainties among inertias, external disturbances, and, in particular, state estimates. A continuous sliding mode attitude controller is designed using attitude and angular velocity estimates from an arbitrary stable stand-alone observer. Rigorous analysis shows that the controller ensures robust stability of the entire closed-loop system as long as the observer yields state estimates with uniformly ultimately bounded estimation errors. In addition, a sequential Lyapunov analysis is utilized to obtain a convergent…
The general objective of this Ph.D. thesis is to study the dynamics and control of rigid and flexible spacecraft supported by a high-fidelity numerical simulation environment. The demand for greater attitude pointing precision, attitude maneuvering or recovery with the increased use of lightweight and flexible materials necessitates the consideration of flexible dynamics in the control strategy. These highly nonlinear dynamics which increase the order of the system are extremely difficult to model with high degree of accuracy. A general model for attitude and flexible dynamics for a class of s…
Optimization of body configuration and joint-driven attitude stabilization for transformable spacecrafts under solar radiation pressure
Institute of Space and Astronautical Science（宇宙航空研究开发机构空间与宇航科学研究所）；Japan Aerospace Exploration Agency（日本宇宙航空研究开发机构）；Tokyo Institute of Technology（东京工业大学）
A deterministic attitude estimator for a rigid body under an attitude dependent potential is studied. This estimator requires only a single direction measurement to a known reference point at each measurement instant. The measurement cannot completely determine the attitude, but an attitude estimation scheme based on this measurement is developed; a feasible set compatible with the measurement is described and it is combined with an attitude dynamics model to obtain an attitude estimate. The attitude is globally represented by a rotation matrix, and the uncertainties are described by ellipsoid…
Spacecraft attitude control using only magnetic torques is a time-varying system. Many designs were proposed using LQR and H-infinity formulations. The existence of the solutions depends on the controllability of the linear time-varying systems which has not been established. In this paper, we will derive the conditions of the controllability for this linear time-varying systems.
A minimum-time reorientation of an axisymmetric rigid spacecraft controlled by three torques is studied. The orientation of the body is modeled such that the attitude kinematics are representative of a spin-stabilized spacecraft. The optimal control problem considered is shown to have a switching control structure. Moreover, under certain assumptions, the solutions contain segments that lie on a singular arc. A numerical optimization study is performed using a recently developed method that is designed to accurately solve bang-bang and singular optimal control problems. The optimality conditio…
