# Oscillating Saw Calibration for mandibular Osteotomy Robots
## 5 Discussion  
Oscillating saw calibration can be attributed to tool calibration with planar orientation information, which is transformed into the problem of TSPP calibration. This means that three sawtooth points on the oscillating saw can be regarded as the TCP, respectively (TSPP), and from this the frame of the oscillating saw can be determined.  
To make up for time-consuming and labor-consuming traditional tool calibration methods, an optic stereo vision system is employed. The optic stereo vision system should be accurately registered to the manipulator's base frame by head-eye calibration. In our simulation experiment, different head-eye calibration methods were tested, and the results showed that no matter which head-eye calibration method is used to obtain the initial value, the best result can be obtained as long as the nonlinear optimization process is employed.  
To obtain a better TCP position, the data for the TSPP should be redundant, ensuring that the collected samples are evenly distributed in space, for example 40 groups. The concurrent simulation experiments also demonstrate that the positional elimination method proposed in this paper yields a higher precision compared to the direct transformation of frames for obtaining the TSPP.  
In practice, 15 groups of data could be selected to reduce operations. In the five physical experiments, the obtained average error of the TCP was 0.25 mm, and the angular error of the tool plane's normal vector was less than 1.93\({}^{\circ}\). The experimental results meet the requirements for performing osteotomy surgery.  
The method proposed in this paper is achieved by using an optical localization system to obtain the coordinates of three predefined sawtooth points on the oscillating saw. Traditional contact tool calibration methods [7; 8; 10; 11; 12; 13; 14] mainly calibrate the TCP point of the tool and involve continual adjustments of the manipulator's pose to ensure the TCP contact with a fixed point in space. The traditional contact method is cumbersome to operate, and the method proposed in this paper obviates the need for continuous adjustments of the manipulator's pose. Non-contact tool calibration methods [9; 20; 21] rely on precise localization of the TCP point by the visual system, and in this paper, a customized probe is employed to ensure the visual system's accuracy in TCP point localization. In contrast to visual positioning techniques, the utilization of probe-based positioning offers a solution to the challenges posed by small sawtooth point dimensions and difficulties in identifying reflective materials. To the best of our knowledge, this is the first paper presenting a tool calibration method capable of accurately calibrating both the tool position and orientation.  
The limitations of this method are (1) The need for a high-precision visual measurement system, such as the NDI Vecra optical localization tracking system used in this experiment (Northern Digital), with an RMS of 0.15 mm. (2) The oscillating saw needs to be kept in the initial position during the calibration process. It is not difficult to avoid causing the tool to swing and shift when measuring the coordinates of the sawtooth points with an optical probe.