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Nonlinear Sampled-data Attitude Stabilization of Underactuated Spacecraft

Periodic Reporting for period 1 - SAT STABILIS (Nonlinear Sampled-data Attitude Stabilization of Underactuated Spacecraft)

Reporting period: 2015-10-01 to 2017-09-30

The Attitude Determination and Control System (ADCS) has a major impact on the efficiency of space missions. Its task is to control the orientation (attitude) of a satellite in space to a high pointing accuracy and maintain stability, in order to meet key mission requirements imposed by the payload and the electrical power and communication subsystems. However, several space missions suffered disastrous consequences due to failures in ADCS actuators that remained uncooperative. In actuator failure mode, the number of controlled inputs is reduced, from three necessary independent actuators, to two, converting a fully-actuated system to an underactuated one, leading to destabilization. The impact of underactuation on performance degradation is more catalytic in small satellites, since here reaction wheel redundancy is not a feasible option, due to mass, power and financial resources. A viable alternative, to ensure high mission reliability, is to stabilize the spacecraft with the remaining actuators. The underlying underactuated control problem to be addressed is challenging, since the underactuated system is non-holonomic, admitting only non-standard, non-smooth stabilizing feedback. State-of-the-art controllers, though continuous in nature, are inevitably implemented digitally on the on-board computer, leading to loss of performance and instabilities.

Under this framework, the overall objectives set for the SAT STABILIS project were to:

• Conduct theoretical investigations in order to derive ad-hoc digital control solutions based on nonlinear sampled-data control methodologies for active, high precision, three-Axis Attitude Stabilization (3-AAS) of underactuated satellites subject to reaction wheel failures.

• Verify and validate the robustness and applicability of the innovative attitude control algorithms developed, by performing extensive software simulations and implementing them on the embedded processor of an attitude control experimentation platform.

• Deploy a plan for in-orbit technology demonstration and testing of the project outcomes on a CubeSat like nano-satellite.

The control algorithms conceived offer a fail-safe operation mode without significant performance degradation, improving the reliability of the attitude control system, a catalytic factor for the nowadays emerging small satellite technology. The project stays in line with the EU’s space policy, which considers the small satellite market crucial for human activities and the Space Horizon 2020 objectives to enable advances in space technologies.
In the methodology contributed, both the kinematic and dynamic equations were considered, avoiding cascaded control that leads to inadmissible torque levels. The continuous-time models were transformed into normal forms. In order to consider the effect of sampling from the beginning in the design process, the approach followed was based on an equivalent nonlinear discrete-time model of the normal forms, the Exact Sampled Representation (ESR). The ESRs obtained, from a computation point of view, have the appealing characteristic of finite computability, a property that permits to design discrete-time controllers without approximations. Multi-rate sampled-data techniques were implemented on the ESR models, where the control variables are adequately kept piecewise constant over fractions of the sampling period. The multiple changes of the control variables in the inter-sampling interval produce the increased number of degrees of freedom required to achieve one step dead beat control, invert the input-state map and achieve robust stabilization via an adequate feedback control strategy.

The performance of the novel algorithms was validated with extensive Model-In the-Loop simulations on the MATLAB/Simulink environment and, in more realistic conditions, by developing a more sophisticated design tool that includes an orbit propagator, the complete spacecraft equations, an Unscented Kalman Filter for attitude determination, the dynamics of the reaction wheels including PWM signals and saturation effects and environmental disturbances. This flexible tool gives the potentiality to design and test sampled-data based algorithms also for the fully actuated spacecraft. Various on-orbit attitude control operations, during all phases of the mission, like detumbling, desaturation, nadir pointing and ground station tracking have been simulated.

The applicability of the methodology was confirmed by the means of a hardware prototype built, based on a spherical air-bearing that offers friction-free motion on three rotational axes, equipped with an embedded STM32F4 microprocessor, an MPU-9250 9-axis MEMS sensor and three Maxon EC 45 flat 70W brushless DC motors with press-fitted aluminum flywheels and driven by ESCON 36/3 EC servo controllers.

The software tool designed, if further developed, could be marketed, targeting at the CubeSat market. The control methodology conceived can be implemented as a fail-safe mode on the OBC of a microsatellite. This twofold exploitation potentiality and the resulting IPR handling are currently under investigation in collaboration with G.A.U.S.S. Srl, a spin-off of the Sapienza University, with launch services, design and manufacturing of microsatellites activities.

The project outcomes will be disseminated through open access publications. They were presented at the ‘Open DIAG’ events held at the host institution, where projects and activities conducted are presented to students and will be presented in the framework of the Sapienza Aerospace Research Centre and of the ‘Master in Satelliti e Piattaforme Orbitanti’. The prototype platform will be used to motivate pupils of all levels towards science, research and innovation, promote EU investment in research and science and highlight control principles in space, in the framework of a digital festival held in 18 cities all over Greece, under the aegis of the Ministry of Education.
The progress, beyond the state-of-the-art, of the derived advanced nonlinear ad-hoc sampled-data controllers comprises:

• Considering the full satellite kinematic and dynamic equations, thus avoiding torque saturation, proven to be a problem with designs based on cascaded control systems.
• Considering the digital aspects intervening in the practical case, like the digital implementation on the on-board computer or the need for actuator PWM signals, by accounting for the first time the effect of sampling during the design phase.
• Maintaining performance in terms of pointing accuracy and stability, despite the inevitable non-smooth nature of the controllers, intrinsic to the nature of the control problem.

The ability to maintain three-axis pointing is also jeopardized in the presence of redundant reaction wheels (Kepler, FUSE, Hubble missions), so that unavoidably, a two reaction wheel operation mode should be planned in order to avoid an uncontrollable vehicle state, confer pointing capability and assure a continued science program on space missions. The outcomes of the SAT STABILIS project, if implemented on the OBC, offer a fault-tolerant solution in order to prepare for a potential underactuation situation. Many aspects of our approach can also be applied to other classes of underactuated mechanical systems, which are abundant in real life, including mobile robots and vehicles, underwater vehicles, space robots, the multi-body spacecraft, robotic manipulators.
SAT STABILIS Image For Publication