This phase III trial compares the effects of robot-assisted radical prostatectomy (RARP) with or without vesicopexy on urinary continence (a person's ability to control their bladder) and quality of life in patients with cancer of the prostate. RARP is the most adopted surgical approach for treatment of prostate cancer that has not spread to other places in the body (non-metastatic). Urinary incontinence (inability to control the bladder) is one of the most common complications of RARP, impacting patients' quality of life and psychological well-being. Different techniques have been proposed to improve urinary continence following RARP. Vesicopexy is one technique that restores the bladder to its normal position in the body after RARP. This study aims to evaluate whether RARP with vesicopexy may improve urinary continence and quality of life after surgery in prostate cancer patients.