Robot–patient registration for optical tracker-free robotic fracture reduction surgery

•Fracture state which is a three-dimensional positional relationship between bones in real-world is simulated in the virtual space of the navigation system.•Refined registration which adopts particle swarm optimization with the minimum cross-reprojection error based on bidirectional X-ray images was proposed.•Attachable robot features were developed to address the unrecognizable features due to crossed occlusion between the robot and bone.•Average translational and rotational errors of the phantom experiments were 1.88 mm and 2.45°, respectively, and the corresponding errors in the ex-vivo experiments were 2.64 mm and 3.32°.