Methods, apparatuses, and systems for robotic insertion of a screw, a rod, or another component of a surgical implant into a patient are disclosed. Synchronous insertion of screws is performed by multiple surgical robots or a single surgical robot having multiple arms and end effectors. The movements of each robotic arm are coordinated into position in preparation of the insertion of multiple surgical implant components at the same time or in the same surgical step. The insertion of the surgical implant components is performed while monitoring the insertion progress. The insertion is completed autonomously or in coordination with a surgeon.