Raymond Kristiansen

Satellite Attitude Control by Quaternion-Based Backstepping

In this brief, a tracking controller is presented to stabilize the attitude of a micro satellite via integrator backstepping and quaternion feedback. The controller is shown to render the equilibrium points in the closed-loop system uniformly asymptotically stable. Simulations are performed using satellite parameters from the ESEO mission under the European Space Agencys SSETI project.

Brief paper: Spacecraft coordination control in 6DOF: Integrator backstepping vs passivity-based control

In this paper, we present three nonlinear control solutions for 6DOF spacecraft formation control, adopted from Euler-Lagrange system theory. The quaternion parametrization results in dual equilibrium points in the closed loop system, and the controllers are proved to render these uniformly asymptotically stable. We also present a theoretical comparison of the three control solutions, together with simulation results to visualize the performance of the controllers.

Brief paper: Spacecraft relative rotation tracking without angular velocity measurements

We present a solution to the problem of tracking relative rotation in a leader-follower spacecraft formation using feedback from relative attitude only. The controller incorporates an approximate-differentiation filter to account for the unmeasured angular velocity. We show uniform practical asymptotic stability (UPAS) of the closed-loop system. For simplicity, we assume that the leader is controlled and that we know orbital perturbations; however, this assumption can be easily relaxed to boundedness without degrading the stability property. We also assume that angular velocities of spacecraft relative to an inertial frame are bounded. Simulation results of a leader-follower spacecraft formation using the proposed controller structure are also presented.

Satellite attitude control by quaternion-based backstepping

In this paper a result on attitude control of a microsatellite by integrator backstepping based on quaternion feedback is presented, and the controller is shown to make the closed loop equilibrium points asymptotic stable in the sense of Lyapunov. This is a part of a study of possible control methods for the spacecraft European Student Earth Orbiter (ESEO), a spacecraft included in the Student Space Exploration and Technology Initiative (SSETI) project initiated by ESA. The spacecraft is actuated by four reaction control thrusters and one reaction wheel, and simulation results based on data from the satellite are presented.

Brief paper: Spacecraft formation reconfiguration with collision avoidance

In this paper we present a behavioral control solution for reconfiguration of a spacecraft formation using the Null-Space Based (NSB) concept. The solution is task based, and aims to reconfigure and maintain a rigid formation while avoiding collisions between spacecraft. A model of relative translation is derived, together with a passivity-based sliding surface controller which globally stabilizes the equilibrium point of the closed-loop system. The NSB control method is implemented by giving each task different priorities and then calculating desired velocity and a Jacobian matrix for each spacecraft and each task. The velocity vector for each task is then projected into the null-space for higher prioritized tasks to remove conflicting velocity components. Simulation results are presented, showing that each spacecraft moves into the predefined formation without breaking any rules for the higher priority tasks, and all collisions are avoided.

Output Feedback Control of Relative Translation in a Leader-Follower Spacecraft Formation

We present a solution to the problem of tracking relative translation in a leader-follower spacecraft formation using feedback from relative position only. Three controller configurations are presented which enables the follower spacecraft to track a desired reference trajectory relative to the leader. The controller design is performed for different levels of knowledge about the leader spacecraft and its orbit. The first controller assumes perfect knowledge of the leader and its orbital parameters, and renders the equilibrium points of the closed-loop system uniformly globally asymptotically stable (UGAS). The second controller uses the framework of the first to render the closed-loop system uniformly globally practically asymptotically stable (UGPAS), with knowledge of bounds on some orbital parameters, only. That is, the state errors in the closed-loop system are proved to converge from any initial conditions to a ball in close vicinity of the origin in a stable way, and this ball can be diminished arbitrarily by increasing the gains in the control law. The third controller, based on the design of the second, utilizes adaptation to estimate the bounds that were previously assumed to be known. The resulting closed-loop system is proved to be uniformly semiglobally practically asymptotically stable (USPAS). The last two controllers assume boundedness only of orbital perturbations and the leader control force. Simulation results of a leader-follower spacecraft formation using the proposed controllers are presented.

Adaptive Output Feedback Control of Spacecraft Relative Translation

We address the problem of tracking relative translation in a leader-follower spacecraft formation using position feedback and under parameter uncertainty (spacecraft mass) and uncertainty in the leader variables (true anomaly rate and rate of change). We only assume boundedness of orbital perturbations and the leader control force but with unknown bounds. Under these conditions we propose a controller that renders the closed-loop system delta-weakly uniformly semiglobally practically asymptotically stable. In particular, the domain of attraction can be made arbitrarily large by picking convenient gains, and the state errors in the closed-loop system are proved to converge from any initial condition within the domain of attraction to a ball in close vicinity of the origin in a stable way; moreover, this ball can be diminished to a maximum precision by increasing the gains in the control law. Simulation results of a leader-follower spacecraft formation using the proposed controller are presented

PD+ Based Output Feedback Attitude Control of Rigid Bodies

We address the problem of output feedback attitude control of a rigid body in quaternion coordinate space via a modified PD+ based tracking controller. Angular velocity is replaced by a low-gain dynamic extension. The controller ensures fast convergence to the desired operating point during transient maneuvers, while keeping the gains small. This contributes to diminishing the sensitivity to measurement noise hence, energy consumption may be expected to drop along with a decrease of the residual. More precisely, we show uniform practical asymptotic stability of the equilibrium point for the closed loop system in the presence of unknown, bounded input disturbances. Simulation results illustrate the performance improvement with respect to PD+ based output feedback control with static gains.

Modelling of Actuator Dynamics for Spacecraft Attitude Control

S PACECRAFT mission success is often highly dependent on the performance and robustness of the attitude control system, which consists of different types of actuators, such as reaction control thrusters, reaction wheels, and magnetic actuators. Solutions to spacecraft attitude control problems often rely on inherent assumptions that the onboard actuators are able to deliver the exact torque desired by the attitude controller at a specified time. The actuators are thus assumed to have no dynamics, or the actuator dynamics are assumed to be fast enough to allow them to be neglected. Although this has shown to be a sufficient approach in the past, it is obvious that attitude actuators, as all electromechanical devices, have dynamics that might impact controller performance. With an increasing demand for high-precision attitude control for purposes such as formation control and optical intersatellite links, the necessity of including actuator dynamics within the control solution is increasingly evident. Mathematical modelling of the complex and nonideal dynamical behavior of actuators and its influence on spacecraft attitude control is a cumbersome task. This dynamical behavior has traditionally been found through laboratory testing, and the subsequent controller design has been influenced by these considerations. One example in this direction is the requirement of reaction thruster response delays being less than the duration of the minimum activation pulse of the actuator. There exist, however, theoretical results from themodelling and analysis of actuator dynamics, such as in [1], in which the effect of unmodelled fast actuator dynamics on the output feedback stabilization of feedback linearizable systems is studied. Similarly, in [2,3], the robust stabilization of a class of nonlinear systems in the presence of unmodelled actuator and sensor dynamics is investigated. More applicable results for our purpose are found in [4,5], in which general multiple-input/multiple-output (MIMO) linear actuator models for underwater vehicle thrusters with dynamics are presented. Because underwater vehicle thrusters are essentially propellers connected to dc motors, analogous to, for example, reaction wheels for spacecraft attitude control, is it possible to describe other actuators with the same model subject to minor changes and tuning. In this paper, we substantiate a unified mathematical model of various attitude control actuators for space applications, in particular, reaction thrusters, reaction wheels, and magnetic torquers. The general actuator dynamical model is based on the marine technology work of [5], appropriately fitted to the aforementioned actuator categories. To describe time delays in the response of actuators such as, for example, thrusters, an expansion of the general actuatormodel is suggested.

Quaternion-Based Backstepping Control of Relative Attitude in a Spacecraft Formation

In this paper we present a solution to the problem of controlling relative attitude in a leader-follower spacecraft formation, with focus on the rotation path for the follower spacecraft. Mathematical models of relative attitude kinematics and dynamics are presented, and a nonlinear control law designed by use of integrator backstepping is used to control the relative attitude in the formation. The resulting control law is proved to result in asymptotically stable equilibrium points in the closed loop system, and by a convenient choice of backstepping variables, it is ensured that a proper rotation path is used. Simulation results for a leader-follower spacecraft formation are presented to illustrate the performance of the presented control law