Automated laser surgery with sensor fusion is an important problem in medical robotics since it requires precise control of mirrors used to steer the laser systems. The propagation of the laser beam should satisfy the geometric constraints of the surgical site but the relation between the number of mirrors and the design of the optical path remains an unsolved problem. Furthermore, different types of surgery (e.g. endoscopic vs open surgery) can require different optical designs with varying number of mirrors to successfully steer the laser beam to the tissue. A generalized method for controlling the laser beam in such systems remains an open research question. This paper proposes an analytical model for a laser-based surgical system with an arbitrary number of mirrors, which is referred as an "-mirror" robotic system. This system consists of three laser inputs to transmit the laser beam to the tissue surface through number of mirrors, which can achieve surface scanning, tissue resection and tissue classification separately. For sensor information alignment, the forward and inverse kinematics of the -mirror robot system are derived and used to calculate the mirror angles for laser steering at the target surface. We propose a system calibration method to determine the laser input configuration that is required in the kinematic modelling. We conduct simulation experiments for a simulated 3-mirror system of an actual robotic laser platform and a 6-mirror simulated robot, both with 3-laser inputs. The simulation experiments for system calibration show results of maximum position offset smaller than 0.127 mm and maximum angle offset smaller than 0.05° for the optimal laser input predictions.