Rune Schlanbusch

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.

On the stability and stabilization of quaternion equilibria of rigid bodies

We study attitude control of rigid bodies on quaternion coordinates under three mathematically different perspectives, depending on how the system dynamics are assumed to evolve. In the first case, we suppose that one equilibrium point is chosen a priori and a continuous controller is used under the assumption that the rigid body always spins in the same direction. In the second case, we relax the assumption that the sense of rotation is constant. Finally, a third scenario is considered in which hybrid (switching) control is used to choose the direction in which to spin, that is, both equilibria are continuously considered with regard to less energy consumption. It is showed that each of three scenarios must be treated in a different theoretical setting. A comparative study in simulations is also provided.

Hybrid attitude tracking of rigid bodies without angular velocity measurement

In this paper we address the problem of output-feedback attitude control of a rigid body in quaternion-coordinate space through a hybrid (switching) PD+ based tracking controller; we establish stability for all initial values in a compact subset which may be arbitrarily enlarged by increasing the control gains. Assumptions used in the literature such as supposing that the initial states lay in a determined compact set or that the attitude error norm is smaller than π rad for all time, are removed by including a switching law. Simulation results are presented to corroborate our theoretical findings, showing that the system stabilises as expected, even when the initial estimated velocity error is large.

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.

Underactuated translational control of a rigid spacecraft

In this paper we consider a spacecraft with one main thruster for translational control and reaction wheels for full attitude control. This is an underactuated control problem, which in this paper is solved using backstepping in order to couple the position tracking problem with the attitude. Assuming that the thrust is non-zero the nonlinear tracking control law is shown to be uniformly globally exponentially stable, and simulations validate these results.

PD+ attitude control of rigid bodies with improved performance

We address the problem of state feedback attitude control of a rigid body in quaternion coordinate space through a modified PD+ tracking controller. The control law ensures faster convergence to the desired operating point during attitude maneuver, while keeping the gains small for station keeping. A direct consequence is a drop in energy consumption when affected by sensor noise. More precisely, we show uniform asymptotic stability for the system without perturbations and uniform practical asymptotic stability in the presence of unknown, bounded input disturbances. Simulation results illustrate the performance improvement with respect to classic PD+ control, especially in the presence of input perturbations.

Hybrid attitude tracking of output feedback controlled rigid bodies

In this paper we address the problem of output feedback attitude control of a rigid body in quaternion coordinate space through a PD+ based tracking controller using switching technique to obtain stability for all initial values. Assumptions on earlier results where either the initial state is considered bounded, or the attitude error for all time is less than 180 degrees, is removed by applying switching technique, also including hysteresis for robust stability. More precisely, we show uniform asymptotic stability in the large of a set containing the origin for the closed-loop system in the presence of unknown, bounded input disturbances. Simulation results are presented to verify our theoretical findings, showing that the system stabilizes as expected, even with high initial estimated velocity error.

Reaction wheel design for CubeSats

This paper presents a reaction wheel design for CubeSats where it takes the limitation of size and mass into consideration. It presents an overview of which altitudes it is feasible to use magnetic torquers for momentum dumping as well as presenting equations for customizing reaction wheels for a CubeSat mission. The reaction wheels are then simulated for different CubeSat sizes and proved capable of performing attitude maneuvers. During these simulations a non-linear passivity-based sliding surface controller is used which through Lyapunov stability theory has been shown to be uniformly asymptotically stable.

Spacecraft formation reconfiguration with dynamic collision avoidance

In this paper we present three different solutions to the collision avoidance problem for spacecraft formations based on the Null-Space Based (NSB) behavioral control concept. In the first case, a constant sized sphere of safety area is centered on each spacecraft and obstacle, and the collision avoidance task is activated when this area is entered using a constant repulsive gain similar to what has been proposed for robotics in earlier publications. In the second case we make use of a variable state dependent gain for increasing the level of repulsiveness for each safety sphere to completely avoid collisions. In the third case the sphere is resized based on the relative position and velocity vectors, such that evasive maneuvers are initiated earlier when on collision course, but kept small when passing by. Through Lyapunov analysis we show that the equilibriumpoint of the follower spacecraft dynamics in closed-loop with a sliding surface based controller is uniformly globally exponentially stable when no collisions are detected, and that collisions will not occur when the collision avoidance task is active by scaling the variable state dependent gain. Simulation results are presented comparing the performance of the proposed methods during a formation reconfiguration maneuver.

Underactuated Waypoint Tracking of a Fixed-Wing UAV*

Abstract In this paper a new method of performing waypoint tracking is shown for underactuated fixed-wing uavs. The position error can be mapped onto the desired axis using a desired rotation matrix, while the velocity error can be mapped to the desired axis using a desired angular velocity. With all errors defined along one axis, the tracking problem is easily solved using only one thruster. A velocity controller is derived which makes sure that the uav tracks a desired total velocity moving towards the next waypoint, while a sliding surface attitude controller is designed to track the desired attitude. The impact of saturation on the attitude controller is also studied where it is shown that the actuators will desaturate in finite time, through a change in the reference trajectory. Using both controllers, a solution to the problem of waypoint tracking of an underactuated uav is proposed, and simulations have been performed that support the theoretical results.