GNC functional architecture design and implementation of the LISA drag-free control system
Authors:   Sener Aeroespacial, Tres Cantos, Spain, Sánchez Maestro Raúl , Veenman Joost , Cardin Jorge , Grzymisch Jonathan , Preda Valentin 
Published: January 2024

The LISA (Laser Interferometer Space Antenna) mission is one of the most challenging endeavours to be undertaken by ESA whose objective is to study gravitational waves. The mission consists of three identical spacecraft in a triangular formation, with an inter-satellite distance of 2.5 million km, flying in a heliocentric orbit. Each spacecraft contains two test masses (TM) that are confined within an electrode housing with electrostatic sensing and actuation capability. Two telescopes are present, pointing towards the two other spacecraft, which includes a sophisticated optical metrology system to measure the distance between TMs of opposing spacecraft with pico-metre accuracy. In order to maintain formation tracking, the angle between the telescopes is variable so that it can keep the opposing spacecraft within its field of view (FoV).

The science phase of the LISA DFACS (Drag-Free Attitude Control System) consists of leaving the TMs in free fall in the direction of the line-of-sight (LoS) between spacecraft while being suspended in the other directions using the electrostatic sensors and actuators. The spacecraft will perform a drag-free control by following the TMs’ geodesic path using micro-Newton thrusters while simultaneously maintaining formation via attitude control and corresponding telescope angle commands. The stringent pointing requirements to maintain formation is achieved via laser measurements providing relative angles with respect to the LoS between spacecraft.

A study was carried out for ESA by SENER Aeroespacial as part of a development risk mitigation activity in Phase A/B1 with the objective to investigate control system architectures and advanced design methodologies. The full nonlinear DKE models, which include all the degrees of freedom (DoF) of the coupled spacecraft dynamics were developed by Deimos Engenharia to perform the validation activities of the GNC (Guidance, Navigation and Control).

The LISA spacecraft, once placed in a heliocentric orbit, will execute a sequence of operations that consists of:

- Inertial pointing of the individual spacecraft (including slew manoeuvre to target)

- Release of the two test masses (either sequentially or simultaneously)

- Acquisition of the flight formation

- Science observations

Within the activity, a full-fledged GNC was designed and implemented that is capable of autonomously executing the above sequence, including all the necessary functions for mode management, guidance, navigation (state determination) and control and the switch between sensor/actuator HW depending on the phase within the sequence.

This paper presents the design process of the GNC. Considering the large quantity of work performed, a general overview is provided of the design activities covering various aspects of relevance. In particular, the following topics will be addressed:

- GNC functional architecture and control problem formulation

- Guidance strategy of the formation acquisition

- Spacecraft attitude estimation filter based on the TM dynamics

The topics related to the control design as well as the validation and verification (V&V) campaign are addressed in an accompanying paper.

The LISA DFACS needs to control a total of 16DoF, which are the spacecraft attitude, the relative attitude and position of the two TMs and the inter-telescope angle. Needless to say, it is a complex MIMO (Multiple Input Multiple Output) system that needs a proper assessment. In fact, as the three spacecraft transition through the various phases in the above sequence, the number of DoFs to control varies as well. This requires a careful design of the control architecture and control problem formulation as it drives both the GNC functional architecture and the intended control design and analysis methodologies.

One of the critical areas is the formation acquisition, which involves a dedicated scan and search strategy that combines attitude manoeuvres with inter-telescope angle commands. The telescopes emit a laser beam, which is captured by the Constellation Acquisition Sensor (CAS) of the opposing spacecraft. One of the main challenges is the fact that there is no communication exchange between spacecraft hence they do not know if the other spacecraft have observed the incoming laser beams so that it can “stop” scanning. A systematic search strategy has been designed to cope with these issues, which has shown to be successful in Monte Carlo simulations.

The formation acquisition requires a high attitude pointing accuracy and stability in order to obtain a lock between spacecraft due to the very narrow FoV of the laser beam. The Star Trackers (STR) are not expected to provide the necessary accuracy to guarantee a successful acquisition. Therefore, a Kalman filter was developed that uses the dynamics and electrostatic actuation of the TMs to improve the spacecraft attitude estimation during the search and scanning pattern. The presence of actuation errors and Solar Radiation Pressure (SRP) lead to drift issues, which necessitates the inclusion of the STR measurements within the filter to ensure bounding the state propagation errors, which is crucial as the duration of the acquisition can take up to 48 hours.

The performed study has successfully led to a complete GNC design, capable of autonomously transitioning through all the modes while meeting all the control pointing requirements in a Monte Carlo campaign within a detailed nonlinear simulation environment.