A novel algorithm based on nonlinear optimization for parameters calibration of wheeled robot mobile chasses

Spatial configuration and time synchronization technology are the key to achieve high precision positioning of visual inertial system. The premise is to calibrate the internal and external parameters of the camera, the IMU (inertial measurement unit) bias and the external parameters between the camera and the IMU. In the traditional calibration method, the work of external parameter calibration is carried out offline, and it is generally completed in the initialization stage before being put into use, and it is assumed that the external parameters of each sensor will not change during the long-term operation. However, in complex practical working environments, sensor suites consisting of cameras and low-cost IMU often have time delay problems due to device processes, and visual inertia systems may be subjected to physical shocks from outside. Therefore, it is often necessary to face the failure of initial external parameters due to uncertain factors such as external shocks, time delays, mechanical structure adjustments or cumulative deformation under long-term work. In view of the above background, this paper constructs an online calibration model of monocular IMU based on the feature that the online calibration method can correct the external parameter deviation in real time and the constraint factor of the natural environment. Firstly, the external parameters of monocular camera and IMU are initialized based on physical space constraints, and the initial values to be optimized are obtained. Finally, the problem of matching the structural features in the online calibration process is solved by using the method of matching the structural features in the vertical main direction, and the objective optimization function of reprojection error considering the point and structure line is constructed. The Jacobian matrix of the reprojection error is given, and the decreasing direction of the optimization function is determined. The global optimal solution of the external parameters of camera and IMU is obtained in the online calibration.

Camera calibration is the most important aspect of computer vision research. To address the issue of insufficient precision, therefore, a high precision calibration algorithm for binocular stereo vision camera using deep reinforcement learning is proposed. Firstly, a binocular stereo camera model is established. Camera calibration is mainly divided into internal and external parameter calibration. Secondly, the internal parameter calibration is completed by solving the antihidden point of the camera light center and the camera distortion value of the camera plane. The deep learning fitting value function is used based on the internal parameters. The target network is established to adjust the parameters of the value function, and the convergence of the value function is calculated to optimize reinforcement learning. The deep reinforcement learning fitting structure is built, the camera data is entered, and the external parameter calibration is finished by continuous updating and convergence. Finally, the high precision calibration of the binocular stereo vision camera is completed. The results show that the calibration error of the proposed algorithm under different sizes of checkerboard calibration board test is only 0.36% and 0.35%, respectively, the calibration accuracy is high, the value function converges quickly, and the parameter calculation accuracy is high, the overall time consumption of the proposed algorithm is short, and the calibration results have strong stability.

The GaoFen-4 (GF-4) remote sensing satellite is China’s first civilian high-resolution geostationary optical satellite, which has been launched at the end of December 2015. To guarantee the geometric quality of imagery, this paper presents an on-orbit geometric calibration method for the area-array camera of GF-4. Firstly, we introduce the imaging features of area-array camera of GF-4 and construct a rigorous imaging model based on the analysis of the major error sources from three aspects: attitude measurement error, orbit measurement error and camera distortion. Secondly, we construct an on-orbit geometric calibration model by selecting and optimizing parameters of the rigorous geometric imaging model. On this basis, the calibration parameters are divided into two groups: external and internal calibration parameters. The external parameters are installation angles between the area-array camera and the star tracker, and we propose a two-dimensional direction angle model as internal parameters to describe the distortion of the areaarray camera. Thirdly, we propose a stepwise parameters estimation method that external parameters are estimated firstly, then internal parameters are estimated based on the generalized camera frame determined by external parameters. Experiments based on the real data of GF-4 shows that after on-orbit geometric calibration, the geometric accuracy of the images without ground control points is significantly improved.

Abstract. The GaoFen-4 (GF-4) remote sensing satellite is China’s first civilian high-resolution geostationary optical satellite, which has been launched at the end of December 2015. To guarantee the geometric quality of imagery, this paper presents an on-orbit geometric calibration method for the area-array camera of GF-4. Firstly, we introduce the imaging features of area-array camera of GF-4 and construct a rigorous imaging model based on the analysis of the major error sources from three aspects: attitude measurement error, orbit measurement error and camera distortion. Secondly, we construct an on-orbit geometric calibration model by selecting and optimizing parameters of the rigorous geometric imaging model. On this basis, the calibration parameters are divided into two groups: external and internal calibration parameters. The external parameters are installation angles between the area-array camera and the star tracker, and we propose a two-dimensional direction angle model as internal parameters to describe the distortion of the areaarray camera. Thirdly, we propose a stepwise parameters estimation method that external parameters are estimated firstly, then internal parameters are estimated based on the generalized camera frame determined by external parameters. Experiments based on the real data of GF-4 shows that after on-orbit geometric calibration, the geometric accuracy of the images without ground control points is significantly improved.

We conducted a systematic investigation into independent on-orbit geometric calibration, with the aim of applying it to linear agile optical satellite (AOS). Using a combination of multi-attitude images, a complete full-link independent calibration method chain was achieved, in which both the internal and external systematic parameters could be calibrated using the self-constraint of these images, as distinct from the absolute constraints identified from ground calibration sites. In accordance with the capacity for restraint associated with the self-constraint of the images and the geometric characteristics of the systematic errors in the imaging model, the calibration parameters that were deemed suitable for mathematical estimation under this self-constraint, as well as capable of compensating for the systematic errors, were determined by two equivalent compensations. Subsequently, a stepwise calibration for the estimation of external and internal parameters was conducted, where the corresponding points, matched from two separate combinations of multi-attitude images, were applied to the external and internal calibrations, respectively. With an aided elevation, the optimal calibration parameters were achieved under these conditions without the use of a ground control point (GCP). Finally, a set of innovative experiments were conducted on rigorously simulated data to verify the theoretical accuracy and feasibility of this method. The experimental results indicated that the method could achieve an overall theoretical accuracy of around 0.002 arc seconds, and showed good geometric consistency for all charge-coupled device (CCD) detectors.

The calibration of the camera's internal and external parameters is the basis for constructing a three-dimensional world from a two-dimensional plane. It is also the basis for corresponding point matching and image stitching. The accuracy of camera parameter calibration directly affects the accuracy of the restoration of the three-dimensional world. The internal parameters of the camera have been fixed since the factory, no need for frequent calibration, but the external parameters of the camera vary with the installation position of the camera. For the driving recorder, it needs to be re-calibrated after each repositioning. Therefore, it is particularly important to find a simple, efficient and high-precision external parameter calibration method. The calibration method based on chessboard grids or control points has the disadvantages of large amount of engineering, complicated operation, low efficiency, etc. Based on the geometric characteristics of roads with fixed width and parallel lane lines, this paper proposes a solution for external camera calibration using 3 sets of parallel lane lines within flat roads. The method of calculating the external parameters of the on-board camera is to establish conditional constraint equations by selecting equally spaced control points on different lane lines, and then use the least square method to calculate the optimal value of the rotation matrix from the camera coordinate system to the vehicle coordinate system, the height of the camera to the ground, and of the x and z coordinates of the lane line control point in the vehicle coordinate system simultaneously. The method is simple and easy to implement, and the calibration accuracy meets the requirements of high-precision lane-level navigation map production, combining with the vehicle coordinates measured by GPS and the lane line coordinates under the vehicle coordinate system, the lane lines under the earth coordinate system can be solved, providing a basis for the calibration of external parameters of the driving recorder and the production of high-precision maps.

<div class="section abstract"><div class="htmlview paragraph">In the field of automatic driving, the combination of 3D LIDAR and inertial measurement unit (IMU) is a common sensor configuration scheme in laser point-cloud localization, high-precision map making and point-cloud target detection. So it is critical to calibrate LIDAR and IMU accurately. At present, due to the large volume and high cost of 3D LIDAR with high-line-number(Such as 64 lines or 128 lines), the configuration scheme of using multiple low-line-number 3D LIDARs appears in the automatic driving vehicle sensing system. However, the common calibration methods are not suitable for multi 3D LIDARs and IMU parameters calibration on autonomous vehicle, which have the disadvantages of cumbersome implementation and low accuracy. In this paper, a joint calibration test platform composed of dual LIDARs and IMU is assembled, and a method of precise automatic calibration based on GPS/RTK data is proposed. Firstly, the initial parameters of the main 3D LIDAR and IMU are obtained by hand-eye calibration method, and then the motion distortion of the point cloud are removed by using the pose information. After global and local optimization of nearest neighbor error, the conversion parameters from the main LIDAR to IMU are obtained. Then, the remaining LIDARs are calibrated with the main LIDAR by combining coarse registration and fine registration, and finally realize the automatic calibration of external parameters of the entire system. The experimental results show that the proposed method has high calibration accuracy for the system composed of multiple 3D LIDARs and IMU, and the calibration effect is stable.</div></div>

The fusion of camera and lidar plays an important role in the field of robotic perception. The accurate external parameter calibration is a necessary prerequisite for sensor fusion. Herein, an auxiliary calibration device with distinctive geometric features was designed to address the problems of low accuracy and poor robustness associated with external parameter calibrations of camera and lidar. Moreover, a coarse-to-fine two-stage calibration method was proposed for the external parameters of the camera and lidar. The first stage of the method is the extraction of multiple groups of two-dimensional (2D) and three-dimensional (3D) lines corresponding to the edge of the calibration device from the image and lidar point cloud that yields a unique initial estimation of the external parameters. In the second stage, the 2D–3D center point of the sphere of the calibration device was detected, and the initial external parameters were further optimized using a nonlinear optimization method. The proposed method provides two different features that add stability against noise to the calibration system. Both simulated and actual experiments show that the method can yield high-precision external parameters without an initial value. Compared to state-of-the-art methods, our method has advantages in terms of accuracy. the calibration system has a certain degree of noise resistance and stability under different laser noise and vertical resolution.

The air pollution in the planetary boundary layer (PBL) at a height of about 1 km is considered. Assuming stationarity and horizontal homogeneity of the underlying surface, the turbulent state in the PBL is completely determined by the following external parameters: the Rossby number, one parameter for thermal stratification and two for baroclinicity. The turbulent state in the PBL under the same conditions is also determined completely by the following internal parameters: one for thermal stratification and two for baroclinicity. If the internal or external parameters completely determine the PBL turbulent state, then they should completely determine the diffusion processes in it. That is why for the analysis of pollution data, it is recommended that these representative meteorological parameters should be used rather than selected ones. The external parameters which may be obtained from synoptic data have a definite advantage for statistical processing of air pollution data. This is clearly of importance for forecasting. On the other hand, the connection between pollution and the internal parameters is comparatively well-studied theoretically. That is why for the prediction of pollution, it is necessary to know the dependence between the internal and external parameters, as given by the resistance law. An example of statistical processing of air pollution data in the PBL is treated in terms of the external parameters. In addition, an example is given of a theoretical prediction of pollution using synoptic data.

Microsoft Kinect is a new and robust 3D camera, which can be used for indoor scene and 3D model reconstruction. It contains an infrared projector, an infrared camera and a RGB camera, color and depth map can be captured in one scene at the same time and run at a speed of 30 frames per second. As a handhold device, Kinect is low-cost and portable compared with lidar, but its accuracy is low. The internal parameters of both infrared camera and RGB camera, as well as their relative pose, are pre-calibrated in factory, however these average values can't meet the need of high-precision applications and parameters vary from device to device. So if we want to improve the precision of Kinect, the calibration should be done at first. In this article, we attempt to use indoor control field to calibrate Kinect sensor, and get the accurate internal parameters of both cameras and their relative pose. Different from some compute vision methods, the 3d coordinate of control points should be measured in our coordinated system and one image is enough fine to compute the internal and external parameters. As Kinect can't get the IR stream and color stream simultaneously, we get the depth and color image at first, then cover the infrared projector and get the IR image, while an infrared compensation lamp is used to make the IR map clear. We separately detect the control points in the color and IR image for getting their corresponding image points, then gain their distance values from depth image based-on IR image points. Our algorithm contains four steps: 1) Initializing the internal parameters of infrared camera and RGB camera with Zhang's method. For RGB camera, collinearity equation is applied to establish the relationship between control points and their RGB image points, then estimating external parameters and refining internal parameters based-on least square adjustment. For infrared camera, transform IR image points to Kinect 3D coordinate with their distance value and initialized internal parameters to establish the point-to-point correspondence with control points, then calculate external parameters and refining internal parameters using iterative closest points method. Furthermore, we assume a model to improve the precision of distance value, in which three additional parameters should be estimated. 2)Projecting the control points to IR and RGB image coordinate separately which consider as ideal points, and regard the corresponding image points as real points, we can estimate the distortion parameters of infrared and RGB camera. 3) Iterating 1)2) steps until it is convergence. 4) Using the external parameters of both cameras to calculate their relative pose. In our experiment, 36 control points are measured, part of them (about 20) can be seen in one image. We usually use 15 points of them to estimate parameters and others consider as check points. The results show that our method can get high precision calibration parameters which projection mean square error lower than 0.5 pixels, and the mean square error of transforming depth image points to RGB image points lower than 1.0 pixels.

A mobile robot must know its position in order to operate autonomously. The process of determining the robot's absolute position from sensor data is called robot localization. Sonar, inertial, RF, and laser sensors can all be used for navigation and localization purposes. These sensors can achieve good accuracy when operating in certain conditions. For example, sonar is useful when operating in a mapped environment containing known obstacles. Inertial sensors have trouble with drift, which is accentuated when moving continuously for long periods of time. By merging the results from multiple sensors, the accuracy over a wider range of conditions can be obtained. This work proposes a technique of merging heterogeneous signals from inertial and RF sensors. Since sensors have errors associated with their readings, the robot's state will be represented probabilistically. Based on the sensors used in this work, the robot's position, velocity, and acceleration will be estimated using a joint probability distribution function (PDF). At each time step, this PDF will be updated based on the RF readings and then updated again based on the readings from the inertial sensor. The proposed algorithm will be applied to simulation of an uncluttered, level environment. The accuracy of the localization algorithm is compared to the accuracies obtained by other localization algorithms. The results show better localization accuracy when using the RF and inertial sensors together.

External parameter calibration of laser scanner based on the combination of plane-control-based and plane-constraints-based methods

Strapdown inertial navigation system (SINS) requirements are very demanding on gyroscopes and accelerometers as well as on calibration. To improve the accuracy of SINS, high-accuracy calibration is needed. Adding the accelerometer nonlinear scale factor into the model and reducing estimation errors is essential for improving calibration methods. In this paper, the inertial navigation error model is simplified, including only velocity and tilt errors. Based on the simplified error model, the relationship between the navigation errors (the rates of change of velocity errors) and the inertial measurement unit (IMU) calibration parameters is presented. A tracking model is designed to estimate the rates of change of velocity errors. With a special calibration procedure consisting of six rotation sequences, the accelerometer nonlinear scale factor errors can be computed by the estimates of the rates of change of velocity errors. Simulation and laboratory test results show that the accelerometer nonlinear scale factor can be calibrated with satisfactory accuracy on a low-cost three-axis turntable in several minutes. The comparison with the traditional calibration method highlights the superior performance of the proposed calibration method without precise orientation control. In addition, the proposed calibration method saves a lot of time in comparison with the multi-position calibration method.

To better solve the attitude of robots with high precision using low cost inertial measurement unit (IMU), we design novel calibration methods, namely twelve positions calibration method, method based on ellipsoid fitting and eight positions calibration method, to effectively calibrate accelerometer, magnetometer and gyroscope, respectively. An attitude estimator using data from the multi-sensors calibrated by our proposed methods was designed based on Kalman Filter, with its estimated value of the attitude prediction deviation fed back to the predicted value as the prediction deviation at the end of each filtering period. Finally, relevant experiments are designed to verify the validity of the proposed attitude solution method as well as the proposed calibration methods, with results showing that the roll and pitch angle measured by the attitude measurement unit have an effective resolution of 0.1° and the yaw angle has an effective resolution of 1°. The innovation of this paper is that the proposed calibration methods can be carried out with simple tools, eliminating the need for expensive and complicated multi-axis turntables, and the designed attitude measurement unit based on calibrated low cost IMU’s inertial sensors has smaller size, higher resolution in roll and pitch, and much lower cost compared with the commercial MTi-G-710. The accuracy of the attitude solution for such IMU is high enough for the application on robots.

The fusion of 3D LiDAR and colour cameras requires the most accurate possible calibration of external parameters. In this paper, we reduce the edge errors of the LiDAR by selecting planar feature constraints. A new calibrator is used in the execution of our approach. A checkerboard calibration board is used to firstly solve the camera’s internal parameters. Next, a regular pyramid with checkerboard on three sides and a checkerboard calibration board is used as the calibrator to scan, extract the intersection of four planes as the feature points, and finally solve the external parameters of the LiDAR and the camera by registering the feature points. In addition, the method collects and processes multiple sets of data and introduces a global optimisation mechanism for loop closure detection to reduce cumulative errors.