Underactuated Attitude Control of Small Satellites

• Hardware redundancies - Due to limitations on mass, power, and financial resources, sometimes fully redundant actuators are not feasible, especially for small spacecrafts. Furthermore, hardware redundancies are not always effective since these may also fail.
• Hybrid control by the combinations of the remaining actuators - The recoveries of several spacecrafts (BIRDs, FUSE, MAP and etcs) show that: through this explicit methodology, stabilization of the spacecraft can be obtained but not permit fine control; the low level actuators usually decrease control performances greatly and even make the spacecraft easily suffer from resources supply due to charging problems.

In the last decade, the problem of underactuated attitude control has received considerable interests. Underactuated attitude control means to use one or two actuators to realize three axes stabilization or tracking problem. This stems not only from a theoretical point of view but also from the practical value of the results. On the theoretical perspective, it has been established that underactuated attitude system has strong nonlinear properties and hence solution based on a linearization are not practical; on other side, underactuated attitude control strategy only needs less than three actuators to perform control algorithms, which can also be used to deal with the failure of one actuator.

In this project, the problem how to realise three-axis stabilization with two Control Moment Gyros (CMGs) is under consideration. The aims of this project are:

• Derive a design framework for nonlinear control of underactuated spacecrafts
• Investigate 3 axis controllability using a pair of CMGs
• Connect actuator mechanical configuration, actuator capacity and controller parameters to controllability and attitude accuracy

So far, the achievements we have obtained are:

• Investigation of existing design methods for underactuated systems
• Identify CMG configurations used for controller design
  1. two CMGs with beta=0 degrees
  2. two CMGs in a pyramid configuration
• For those models set-up controller optimisation frameworks
• Identify a measure for performance
• Analyse the convergence manifold and identify a measure for its size in respect to design parameters
• Identify solvability of the HJI inequality.
• Analyse the approximate solution and in general solvability of 1st order solution – draw conclusions on solvability
• Modify optimisation task
• Suggest alternative dynamic configurations that might have solutions or the overall solvalibility from Hoo control point of view
• Analyse application of numerical solutions of HJI inequalities

The responses below demonstrate 3-axis controllability using 2 CMGs. The actuator’s gimbal axes are aligned along one principal axis on the spacecraft. The non-smooth Lyapunov control law is further tuned by analysing the solution of the associated Hamiltonian-Jacobi-Isaacs (HJI) inequality. As a result, optimal controller parameters are derived to generate a dissipative closed-loop system.

Ongoing activities:

• Experimental validation of results
• Analysis of tracking, transient rate and attitude accuracy