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The imaging and characterization of a larger range of exoplanets, down to young Jupiters and exo-Earths will require accessing very high contrasts at small angular separations with an increased robustness to aberrations, three constraints that drive current instrumentation development. This goal relies on efficient coronagraphs set up on extremely large diameter telescopes such as the Thirty Meter Telescope (TMT), the Giant Magellan Telescope (GMT), or the Extremely Large Telescope (ELT). However, they tend to be subject to specific aberrations that drastically deteriorate the coronagraph performance: their primary mirror segmentation implies phasing errors or even missing segments, and the size of the telescope imposes large spiders, generating low-wind effect as already observed on the Very Large Telescope (VLT)/SPHERE instrument or at the Subaru telescope, or adaptive-optics-due petaling, studied in simulations in the ELT case. The ongoing development of coronagraphs has then to take into account their sensitivity to such errors. We propose an innovative method to generate coronagraphs robust to primary mirror phasing errors and low-wind and adaptive-optics-due petaling effect. This method is based on the apodization of the segment or petal instead of the entire pupil, this apodization being then repeated to mimic the pupil redundancy. We validate this so-called Redundant Apodized Pupil (RAP) method on a James Webb Space Telescope-like pupil composed of 18 hexagonal segments segments to align, and on the VLT architecture in the case of residual low-wind effect.