Transcranial Magnetic Stimulation (TMS) is a non-invasive method for brain stimulation, commonly employed in depression treatment and pre-operative planning. With an average session duration of 30 minutes, the manual handling and positioning of the TMS coil during the treatment may become strenuous for the operator. Robotized TMS systems can help automate the overall process. Our study introduces the TMS Robotic Assistant (TMS-RA) as an end-to-end system integrated with a commercial navigated TMS. TMS-RA utilizes online calibration, eliminating additional calibration steps needed before each TMS session. Furthermore, it can be adapted for use with mobile-based nTMS systems commonly found in clinics. We have implemented an error-compensation scheme to mitigate positioning errors, effectively constraining both position and orientation errors to final mean values of 1.18 mm and $0.57°}$. Comparing our system with a highly experienced medical expert, it is more precise and has significantly lower orientation errors, with a $3°}$ difference, while the position errors were slightly worse but remained comparable.