Nadjim M. Horri

Practical Implementation of Attitude-Control Algorithms for an Underactuated Satellite

The challenging problem of controlling the attitude of satellites subject to actuator failures has been the subject of increased attention in recent years. The problem of controlling the attitude of a satellite on all three axes with two reaction wheels is addressed in this paper. This system is controllable in a zero-momentum mode. Three-axis attitude stability is proven by imposing a singular quaternion feedback law to the angular velocity trajectories.Two approaches are proposed and compared to achieve three-axis control: The first one does not require angular velocity measurements and is based on the assumption of a perfect zero momentum, while the second approach consists of tracking the desired angular velocity trajectories. The full-state feedback is a nonlinear singular controller. In-orbit tests of the first approach provide an unprecedented practical proof of three-axis stability with two control torques. The angular velocity tracking approach is shown to be less efficient using the nonlinear singular controller. However, when inverse optimization theory is applied to enhance the nonlinear singular controller, the angular velocity tracking approach is shown to be the most efficient. The resulting switched inverse optimal controller allows for a significant enhancement of settling time, for a prescribed level of the integrated torque.

Attitude stabilization of an underactuated satellite using two wheels

Failure of mechanical controllers onboard a satellite is a well-known phenomenon that has already occurred during several space missions. Particularly disastrous for attitude control is the loss of thrusters in one or more axes, or in the case studied here, the loss of a reaction wheel. Of course it has been standard practice to employ redundant actuators (e.g. 4 wheels) so that in the event of losing one wheel, full 3-axis control may still be possible. As an interesting alternative to this expensive solution, we present here a theory, which shows how full 3- axis control can still be achieved, despite losing one of the reaction wheels from a standard orthogonal 3-wheel configuration (or even two wheels failures ftom the expensive solution using a redundant 4-wheel configuration). Using a novel nonlinear time invariant and discontinuous approach, we show that the attitude is precisely and rapidly restored, without transient oscillations, to the required earth pointing.

Optimal geometric motion planning for a spin-stabilized spacecraft

Abstract A method requiring low-computational overhead is presented which generates low-torque reference motions between arbitrary orientations for a spin-stabilized spacecraft. The initial stage solves a constrained optimal control problem deriving analytical solutions for a class of smooth and feasible reference motions. Specifically, for a quadratic cost function an application of Pontryagin’s maximum principle leads to a completely integrable Hamiltonian system that is, exactly solvable in closed-form, expressed in terms of several free parameters. This is shown to reduce the complexity of a practical motion planning problem from a constrained functional optimization problem to an unconstrained parameter optimization problem. The generated reference motions are then tracked using an augmented quaternion feedback law, consisting of the sum of a proportional plus derivative term and a term to compensate nonlinear dynamics. The method is illustrated with an application to re-point a spin-stabilized agile micro-spacecraft using zero propellant. The low computational overhead of the method enhances its suitability for on-board motion generation.

Gain-Scheduled Inverse Optimal Satellite Attitude Control

Despite the theoretical advances in optimal control, satellite attitude control is still typically achieved with linear state feedback controllers, which are less efficient but easier to implement. A switched controller is proposed, based on inverse optimal control theory, which circumvents the complex task of numerically solving online the Hamilton-Jacobi-Bellman (HJB) partial differential equation of the global nonlinear optimal control problem. The inverse optimal controller is designed to minimize the torque consumption pointwise, while imposing the stabilization rate of a linear benchmark controller. The controller is then modified by gain scheduling to achieve a tradeoff enhancement compared with the benchmark controller, while maintaining torque saturation limits. The extent to which performance can be enhanced is shown to be dependent on the controller parameters. A controller tuning analysis shows how a design settling time limit can be achieved, within the problems constraints on the maximum torque and the total integrated torque. The proposed optimization approach is globally stabilizing and presents low implementation complexity, which is highly desirable given the limited resources onboard satellites.

STRaND-2: Visual inspection, proximity operations & nanosatellite docking

The Surrey Training Research and Nanosatellite Demonstrator (STRaND) programme has been success in identifying and creating a leading low-cost nanosatellite programme with advanced attitude and orbit control system (AOCS) and experimental computing platforms based on smart-phone technologies. The next demonstration capabilities, that provide a challenging mission to the existing STRaND platform, is to perform visual inspection, proximity operations and nanosatellite docking. Visual inspection is to be performed using a COTS LIDAR system to estimate range and pose under 100 m. Proximity operations are controlled using a comprehensive guidance, navigation and control (GNC) loop in a polar form of the Hills Clohessy Wiltshire (HCW) frame including J2 perturbations. And finally, nanosatellite docking is performed at under 30 cm using a series of tuned magnetic coils. This paper will document the initial experiments and calculations used to qualify LIDAR components, size the mission thrust and tank requirements, and air cushion table demonstrations of the docking mechanism.

Optimal satellite attitude control: a geometric approach

Optimal nonlinear control remains one of the most challenging subjects in control theory despite a long research history. In this paper, we present a geometric optimal control approach, which circumvents the tedious task of numerically solving online the Hamilton Jacobi Bellman (HJB) partial differential equation, which represents the dynamic programming formulation of the nonlinear global optimal control problem. Our approach makes implementation of nonlinear optimal attitude control practically feasible with low computational demand onboard a satellite. Optimal stabilizing state feedbacks are obtained from the construction of a Control Lyapunov function. Based on a phase space analysis, two natural dual optimal control objectives are considered to illustrate the application of this approach to satellite attitude control: Minimizing the norm of the control torque subject to a constraint on the convergence rate of a Lyapunov function, then maximizing the convergence rate of a Lyapunov function subject to a constraint on the control torque. Both approaches provide ease of implementation and achieve robust optimal trade-offs between attitude control rapidity and torque expenditure, without computational issues.

Optimal Momentum Unloading of Reaction Wheels in the Presence of Attitude Control Errors

The attitude of low earth orbiting (LEO) satellites is typically controlled by reaction wheels, which exchange angular momentum with the platform without consuming propellant. However, the momentum of wheels is known to build up and reach wheel speed saturation under the effect of external disturbance torques such as gravity gradient torques, aerodynamics torques, solar radiation torques and erroneous control torques from thrusters and magnetic torquers. As a consequence, the control torque required for attitude stabilization can no longer be generated by the wheels. To prevent this phenomenon, the momentum of the reaction wheels has to be rapidly unloaded by magnetic torquers and/or thrusters. The momentum desaturation must be fast but energy efficient. In this work, we consider different optimal control approaches to achieve this momentum dumping task.

Three-Axis Attitude Control of a Satellite in Zero Momentum Mode Using a Tilted Wheel Methodology

Generation of control torque for highly agile satellite missions is generally achieved with momentum exchange devices, such as reaction wheels and control moment gyros (CMGs) with high slew maneuverability. However, the generation of a high control torque from the respective actuators requires high power and thus a large mass. This paper proposes a novel type of control actuator that will generate torques in all three principal axes of a rigid satellite using only a spinning wheel and a simple tilt mechanism. The tilt mechanism will rotate the spin axis of the wheel (tilt the generated angular momentum vector) about two additional axes thereby generating high control torque about the axes orthogonal to the wheel spin axis. Torque will also be generated about the wheel spin axis through the increase or decrease of the wheel angular speed. This newly proposed actuator generates control torque through controlled precession of the spinning wheel while the tilt angle and the tilt rates are computed without the use of the popular pseudo-inverse calculation obtained with CMGs leading to no singularities being experienced during nominal wheel operation. This paper describes the fundamental mathematical dynamic model of the system and numerical simulations are used to demonstrate the agile three-axis attitude control capability that guarantees a highly efficient trade-off between torque capability, mass, and power consumption. The system actuator sizing is based on slew rates of up to two degrees per second.

Gain scheduled inverse optimal control for fine pointing of a spacecraft camera

The problem of controlling a system modeled as two coupled bodies, a spacecraft and a camera, is considered here. These two bodies are connected by active truss members forming a system of springs and piezoelectric actuators to damp out vibrations. There is also a satellite mounted reaction wheel cluster to perform slew maneuvers. An inverse optimal controller is designed to control the attitude of the satellite and improve the pointing performance of its large earth observation camera. It is based on gain scheduled minimum-norm optimization. A gain scheduling strategy is used in this paper to achieve an optimal tradeoff between settling time and integrated torque, under torque saturation constraints. Simulation results show that the proposed controller compares favorably with a conventional quaternion error feedback controller, which is used as a benchmark.