# Oscillating Saw Calibration for mandibular Osteotomy Robots
###### Abstract  
Accurate oscillating saw tool calibration is an important task for mandibular osteotomy robots to perform precise cutting operations. However, in contrast to traditional tool calibration which just calibrates the tool center position (TCP) or the tool feed axis, both the position and the plane orientation of the saw should be carefully calibrated. Therefore, aiming at this problem, in this paper, we propose a method to carry out oscillating saw calibration by employing an optical stereo vision tracking system. At first, hand-eye calibration is conducted to ascertain the spatial pose of the vision frame within the manipulator's base frame. Subsequently, employing a probe, the positions of the sawtooth points on the oscillating saw plane are captured within the vision frame. These positions are then translated to the manipulator's end-effector frame using the positional elimination algorithm proposed in this paper. Finally, the pose of the oscillating saw plane within the manipulator's end-effector frame is extrapolated from the positions of the three sawtooth points. The result shows that the position errors of the points on the oscillating saw plane are within 0.25 mm and the variance of the plane normal direction is 1.95\({}^{\circ}\) in the five experiments. This approach enables accurate calibration of the oscillating saw plane's position and orientation within the manipulator's end-effector frame. Furthermore, it mitigates the necessity of continual adjustments to the joint angles of the manipulator as required by the \"six-point method\". However, this approach is hinged upon the availability of precision-oriented 3D positioning equipment. mandibular osteotomy robot; oscillating saw calibration; tool calibration +
Footnote †: journal: Appliedrobot-assisted mandibular osteotomy, it is necessary to accurately calibrate the pose of the OSP in robot end-effector frame, so that the oscillating saw can accurately reach the cutting pose and complete cutting. Calibrating the OSP is an indispensable task in modern robotic surgical applications, serving as a form of tool calibration and demanding meticulous attention to plane attributes. Tool calibration needs to select an appropriate tool center point (abbreviated to TCP) and obtains its position (abbreviated to TCPP) and the tool center point frame (abbreviated to TCPF) in the robot end-effector frame [7]. Although there are many works in the literature on tool calibration, to the best of our knowledge, there is no published method for OSP calibration. There are two main reasons for this. Firstly, the existing literature mainly focuses on the tool calibration encompassing point and line attributes but does not include the tool calibration with plane attributes. Arc welding robots prioritize calibration accuracy for the TCPP over the TCPF [8], whereas drilling robots and medical puncture robots require a high calibration accuracy for both the feed-axis within the TCPF and the TCPP [9]. In stark contrast, mandibular osteotomy robots need to accurately calibrate the TCPP and each axis of the TCPF. Secondly, the methods of tool calibration are primarily classified into contact methods based on spatial constraints and non-contact methods based on 3D measuring equipment [9]. Contact-based calibration of the OSP is characterized by a notable intricacy in operational procedures and complexity. Conversely, non-contact calibration methodologies for the OSP, while offering operational simplicity, may occasionally encounter challenges in achieving precise positioning of sawtooth points on the plane. Thus, it becomes imperative to engage in dedicated research endeavors to further advance the domain of OSP calibration. In this paper, we introduce a method to address OSP calibration for mandibular osteotomy robots. The challenge of OSP calibration is reformulated as determining the positions of three sawtooth points (abbreviated to TSPP) within the manipulator's end-effector frame. This method consists of three steps.