## 2 Problems
If the action sequence of the 2D lidar and the stepper motor is modified, making the motor start to work earlier and stop working later than the 2D lidar, the acceleration and deceleration of motor shaft will be staggered with the working time of the 2D lidar, as shown in Figure 2. In this way, before the continuous scanning of the 2D lidar, the shaft of the stepper motor has been accelerated and rotates at constant angular velocity \(\omega\). After the 2D lidar stops scanning, the stepper motor starts to decelerate. During the continuous scanning of the 2D lidar, the stepper motor rotates 180\({}^{\circ}\) at constant angular velocity \(\omega\). The advantage of the modified action sequence is that the factors causing the shape error of the 3D point cloud in item 2 and item 4 can be excluded, and the 3D point cloud with correct shape can be obtained. Through the above method, the uncertain shape error of the 3D point cloud can be eliminated, but the uncertain attitude error of the 3D point cloud is still remains to be solved. Due to the error of the photoelectric switch (which is mentioned in item 3), it is impossible to accurately define the initial position of the motor shaft. Due to the uncertainty of the acceleration and deceleration curve (which is mentioned in item 2) and the uncertain time deviation between the starting time of the 2D lidar and the starting time of the motor (which is mentioned in item 4), it is impossible to know how much angular rotation the motor shaft has rotated at the moment the 2D lidar starts to work. Therefore, it is impossible to know the position of the motor shaft when a rotating 2D lidar starts a 3D scan. This will cause the attitude error of the 3D point cloud, and the error is uncertain. Due to the uncertainty of the error, we cannot calibrate it in general way by finding a constant to offset it. Generally speaking, for the calibration of error, if the error to be calibrated is constant (such as mechanical installation error), the calibration of this error will be relatively easy. Because the mechanical installation error is constant, unless the mechanical parts are re-installed. In order to calibrate this kind of error, we can find a constant estimated value for it. In our research, the error to be calibrated is not constant. This increases the difficulty of the calibration of this error. For each 3D scan of our prototype, the true value of this error is different. We cannot find a constant estimated value for it according to the conventional calibration methods. As for why this error is uncertain, we have already analyzed the reasons above. Some factors include some uncertainties (such as uncertain motor acceleration and deceleration curve, uncertain response time of photoelectric switch, uncertain time deviation between the starting time of the 2D lidar and the starting time of the stepper motor), and the combination of these uncertainties leads to the uncertainty of this error. Because this error is shown on the attitude of the 3D point cloud, therefore, we call it uncertain attitude error in our paper. The calibration of the uncertain attitude error of the 3D point cloud is the focus of this paper. To solve this problem, a triangular plate is used as a reference object, which is installed on the rotating unit as part of the prototype. We recognize the corresponding part of the triangular plate in the scanned 3D point cloud, and correct the attitude of the 3D point cloud according to the known position of the triangular plate.