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Abstract: Abstract Background Periodic and slow target motion is tracked by synchronous motion of the treatment beams in robotic stereotactic body radiation therapy (SBRT). However, spontaneous, non-periodic displacement or drift of the target may completely change the treatment geometry. Simple motion compensation is not sufficient to guarantee the best possible treatment, since relative motion between the target and organs at risk (OARs) can cause substantial deviations of dose in the OARs. This is especially evident when considering the temporally heterogeneous dose delivery by many focused beams which is typical for robotic SBRT. Instead, a reoptimization of the remaining treatment plan after a large target motion during the treatment could potentially reduce the actually delivered dose to OARs and improve target coverage. This reoptimization task, however, is challenging due to time constraints and limited human supervision. Purpose To study the detrimental effect of spontaneous target motion relative to surrounding OARs on the delivered dose distribution and to analyze how intra-fractional constrained replanning could improve motion compensated robotic SBRT of the prostate. Methods We solve the inverse planning problem by optimizing a linear program. When considering intra-fractional target motion resulting in a change of geometry, we adapt the linear program to account for the changed dose coefficients and delivered dose. We reduce the problem size by only reweighting beams from the reference treatment plan without motion. For evaluation we simulate target motion and compare our approach for intra-fractional replanning to the conventional compensation by synchronous beam motion. Results are generated retrospectively on data of 50 patients. Results Our results show that reoptimization can on average retain or improve coverage in case of target motion compared to the reference plan without motion. Compared to the conventional compensation, coverage is improved from 87.83 \% to 94.81 \% for large target motion. Our approach for reoptimization ensures fixed upper constraints on the dose even after motion, enabling safer intra-fraction adaption, compared to conventional motion compensation where overdosage in OARs can lead to 21.79 \% higher maximum dose than planned. With an average reoptimization time of 6 s for 200 reoptimized beams our approach shows promising performance for intra-fractional application. Conclusions We show that intra-fractional constrained reoptimization for adaption to target motion can improve coverage compared to the conventional approach of beam translation while ensuring that upper dose constraints on VOIs are not violated.