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We describe a robust and self-reconfigurable design of a spherical microphone array for beamforming. Our approach achieves a multi-resolution spherical beamformer with performance that is either optimal in the approximation of desired beampattern or is optimal in the directivity achieved, both robustly. Our implementation converges to the optimal performance quickly while exactly satisfying the specified frequency response and robustness constraint in each iteration step without accumulated round-off errors. The advantage of this design lies in its robustness and self-reconfiguration in microphone array reorganization, such as microphone failure, which is highly desirable in online maintenance and anti-terrorism. Design examples and simulation results are presented.