  We propose a robust two-dimensional polynomial beamformer design method,
formulated as a convex optimization problem, which allows for flexible steering
of a previously proposed data-independent robust beamformer in both azimuth and
elevation direction.~As an exemplary application, the proposed two-dimensional
polynomial beamformer design is applied to a twelve-element microphone array,
integrated into the head of a humanoid robot. To account for the effects of the
robot's head on the sound field, measured head-related transfer functions are
integrated into the optimization problem as steering vectors. The
two-dimensional polynomial beamformer design is evaluated using
signal-independent and signal-dependent measures. The results confirm that the
proposed polynomial beamformer design approximates the original fixed
beamformer design very accurately, which makes it an attractive approach for
robust real-time data-independent beamforming.

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