Adaptive control of spacecraft formation flying

Model reference adaptive control block diagram, source: https://doi.org/10.1371/journal.pone.0172761.g004

Adaptive control laws, as the name suggest are control laws that change or adapt to incoming disturbances. Hence, these control laws are capable of working on nonlinear systems where disturbances may not be exactly known.

Increasingly complicated space missions are being made feasible with the use of multiple spacecrafts flying in formation. Formation flying of satellites has many advantages namely better coverage of the earth, more resolution in data, larger aperture for remote sensing and communication applications and an increase in redundancy. As always these benefits come at a trade-off; in the case of formation flying the challenge lies in the coordination and maintaining satellite formation with minimal error and human intervention.

Tackling the problem of maintaining formation in satellites seemed challenging; nevertheless kindled my interests. As a student of control theory, I in consultation with my colleagues came up with the idea to use an adaptive control approach to tackle the problem of satellite formation keeping. We decided on using model reference adaptive control (MRAC) strategies to develop control laws for spacecrafts with complicated formations in high earth orbits. The MRAC strategy has two basic elements (i) a plant with uncertain dynamics, and (ii) the reference system with known dynamics. The MRAC strategy is to match the uncertain dynamics to the desired dynamics by adaptively generating control inputs.

In this work, we use the Clohessy-Wiltshire equations to model the relative dynamics of the satellites. We use the data from Magentospheric Multiscale Mission (MMS), which has four satellites in flying in high earth orbit with a tetrahedron formation that changes with time. To model the extrinsic disturbances realistically, we use solar radiation pressure. We show that the MRAC control law developed in this project works well to maintain the satellite formation in time. We also use a perturbation-based technique to minimize secular growth. Further detatils of this work can be found in the full paper.