In this work, we propose a free-breathing magnetic resonance fingerprinting method that can be used to obtain $B_1^+$-robust quantitative maps of the abdomen in a clinically acceptable time. A three-dimensional MR fingerprinting sequence with a radial stack-of-stars trajectory was implemented for quantitative abdominal imaging. The k-space acquisition ordering was adjusted to improve motion-robustness. The flip angle pattern was optimized using the Cramer-Rao Lower Bound, and the encoding efficiency of sequences with 300, 600, 900, and 1800 flip angles was evaluated. To validate the sequence, a movable multicompartment phantom was developed. Reference multiparametric maps were acquired under stationary conditions using a previously validated MRF method. Periodic motion of the phantom was used to investigate the motion-robustness of the proposed sequence. The best performing sequence length (600 flip angles) was used to image the abdomen during a free-breathing volunteer scan. When using a series of 600 or more flip angles, the estimated $T_1$ values in the stationary phantom showed good agreement with the reference scan. Phantom experiments revealed that motion-related artefacts can appear in the quantitative maps, and confirmed that a motion-robust k-space ordering is essential in preventing these artefacts. The in vivo scan demonstrated that the proposed sequence can produce clean parameter maps while the subject breathes freely. Using this sequence, it is possible to generate $B_1^+$-robust quantitative maps of proton density, $T_1$, and $B_1^+$ under free-breathing conditions at a clinically usable resolution within 5 minutes.
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