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Fast inertia property estimation via convex optimization for the asteroid redirect mission

Accurate inertia property estimation is critical to the success of the upcoming asteroid redirect mission. The inertia tensor, center of mass, and total mass of the spacecraft-asteroid combined rigid body must be accurately estimated so that solar electric propulsion can be used to redirect an asteroid into an orbit around the Earth. This paper develops an efficient algorithm to solve for those properties. The estimation is framed as a least squares minimization problem subject to convex constraints. A standard least squares approach is not sufficient due to a matrix rank deficiency arising from the fact that a pure torque cannot be applied to the asteroid after capture. The constrained least squares minimization framework allows for fast inertia estimation with a convex optimization solver, in the sense that accurate estimates can be made with only a few force inputs and response measurements. Simulations are performed in MATLAB R2013B using the CVX 2.1 convex optimization solver to assess the algorithm's performance in a typical mission scenario.