Standard Dual Quaternion Optimization and Its Applications in Hand-Eye Calibration and SLAM

Several common dual quaternion functions,such as the power function,the magnitude function,the 2-norm function,and the kth largest eigenvalue of a dual quaternion Hermitian matrix,are standard dual quaternion functions,i.e.,the standard parts of their function values depend upon only the standard parts of their dual quaternion variables.Furthermore,the sum,product,minimum,maximum,and composite functions of two standard dual functions,the logarithm and the exponential of standard unit dual quaternion functions,are still standard dual quaternion functions.On the other hand,the dual quaternion optimization problem,where objective and constraint function values are dual numbers but variables are dual quaternions,naturally arises from applications.We show that to solve an equality constrained dual quaternion optimization(EQDQO)problem,we only need to solve two quaternion optimization problems.If the involved dual quaternion functions are all standard,the optimization problem is called a standard dual quaternion optimization problem,and some better results hold.Then,we show that the dual quaternion optimization problems arising from the hand-eye calibration problem and the simultaneous localization and mapping(SLAM)problem are equality constrained standard dual quaternion optimization problems.

New self-calibration approach to space robots based on hand-eye vision

To overcome the influence of on-orbit extreme temperature environment on the tool pose(position and orientation) accuracy of a space robot,a new self-calibration method based on a measurement camera(hand-eye vision) attached to its end-effector was presented.Using the relative pose errors between the two adjacent calibration positions of the space robot,the cost function of the calibration was built,which was different from the conventional calibration method.The particle swarm optimization algorithm(PSO) was used to optimize the function to realize the geometrical parameter identification of the space robot.The above calibration method was carried out through self-calibration simulation of a six-DOF space robot whose end-effector was equipped with hand-eye vision.The results showed that after calibration there was a significant improvement of tool pose accuracy in a set of independent reference positions,which verified the feasibility of the method.At the same time,because it was unnecessary for this method to know the transformation matrix from the robot base to the calibration plate,it reduced the complexity of calibration model and shortened the error propagation chain,which benefited to improve the calibration accuracy.

Research on Hand-eye Calibration Technology of Visual Service Robot Grasping Based on ROS

For the hand-eye calibration of the vision service robot,the traditional hand-eye calibration tech-nology can’t be realized which because the service robot is independently developed and there is no teaching device to feed back the pose information of the service robot in real time.In this paper,a hand-eye calibration method based on ROS(Robot Operating System)is proposed.In this method,ROS system is used to accurately control the arm of the service robot to rotate in different positions for many times.Meanwhile,the head camera of the service robot takes images of a fixed point in the scene.Then,the nonlinear equations were established ac-cording to the homography matrix of the two images and the position and pose information of the ROS system,and the accurate hand-eye relationship was optimized by the least square method.Finally,an experimental platform is built and the proposed hand-eye calibration method is verified.The experiment results show that the method is easy to operate,simple algorithm and correct result,which verifies the effectiveness of the algorithm and provides conditions for the realization of humanoid grasping of visual service robot.

Geometric Calibration Method of Robot Based on Measurement System Including Position and Orientation Parameters

Industrial robot which can acquire high accuracy has been widely used in automatic assembly.Usually,the geometric parameter of industrial robot should be inspected during manufacturing and application.High precision measurement equipment was utilized to acquire the position and orientation of robot’s end⁃effector,when calibrating the geometric parameter of robot.A kind of measurement system based on a draw⁃wire encoder was presented,since the current measurement equipment has some disadvantages,such as the cost and the requirements of working environment are high.According to this kind of measurement system,a sort of geometric calibration method of robot was presented including position and orientation parameters.The uncertain arc length of the cable length between robot end⁃effector and the measurement can be exactly acquired according to the position and orientation parameters.The pose⁃solving model of robot end⁃effector was associated with the kinematic model of robot,and robot’s geometric parameter can be computed by using the least⁃squares methods.Validate instance was conducted,the result showed that the optimal number of the calibration pose was 47 with little improvement in accuracy,even if increasing the number of calibration pose.Robot calibration experiment was performed and the results showed that the absolute accuracy of robot decreased from 4.32 mm to 0.87 mm after calibration,which improved the robot’s absolute accuracy effectively.

Effective Self-calibration for Camera Parameters and Hand-eye Geometry Based on Two Feature Points Motions

A novel and effective self-calibration approach for robot vision is presented, which can effectively estimate both the camera intrinsic parameters and the hand-eye transformation at the same time. The proposed calibration procedure is based on two arbitrary feature points of the environment, and three pure translational motions and two rotational motions of robot endeffector are needed. New linear solution equations are deduced, and the calibration parameters are finally solved accurately and effectively. The proposed algorithm has been verified by simulated data with different noise and disturbance. Because of the need of fewer feature points and robot motions, the proposed method greatly improves the efficiency and practicality of the calibration procedure. © 2017 Chinese Association of Automation.

An Overview of Calibration Technology of Industrial Robots

With the continuous improvement of automation,industrial robots have become an indispensable part of automated production lines.They widely used in a number of industrial production activities,such as spraying,welding,handling,etc.,and have a great role in these sectors.Recently,the robotic technology is developing towards high precision,high intelligence.Robot calibration technology has a great significance to improve the accuracy of robot.However,it has much work to be done in the identification of robot parameters.The parameter identification work of existing serial and parallel robots is introduced.On the one hand,it summarizes the methods for parameter calibration and discusses their advantages and disadvantages.On the other hand,the application of parameter identification is introduced.This overview has a great reference value for robot manufacturers to choose proper identification method,points further research areas for researchers.Finally,this paper analyzes the existing problems in robot calibration,which may be worth researching in the future.

Design of a Two-Step Calibration Method of Kinematic Parameters for Serial Robots

Serial robots are used to handle workpieces with large dimensions, and calibrating kinematic parameters is one of the most efficient ways to upgrade their accuracy. Many models are set up to investigate how many kinematic parameters can be identified to meet the minimal principle, but the base frame and the kinematic parameter are indistinctly calibrated in a one-step way. A two-step method of calibrating kinematic parameters is proposed to improve the accuracy of the robot＇s base frame and kinematic parameters. The forward kinematics described with respect to the measuring coordinate frame are established based on the product- of-exponential （POE） formula. In the first step the robot＇s base coordinate frame is calibrated by the unit quaternion form. The errors of both the robot＇s reference configuration and the base coordinate frame＇s pose are equivalently transformed to the zero-position errors of the robot＇s joints. The simplified model of the robot＇s positioning error is established in second-power explicit expressions. Then the identification model is finished by the least square method, requiring measuring position coordinates only. The complete subtasks of calibrating the robot＇ s 39 kinematic parameters are finished in the second step. It＇s proved by a group of calibration experiments that by the proposed two-step calibration method the average absolute accuracy of industrial robots is updated to 0.23 mm. This paper presents that the robot＇s base frame should be calibrated before its kinematic parameters in order to upgrade its absolute positioning accuracy.

CALIBRATION OF A 6-DOF SPACE ROBOT USING GENETIC ALGORITHM

The kinematic error model of a 6-DOF space robot is deduced, and the cost function of kinematic parameter identification is built. With the aid of the genetic algorithm （GA） that has the powerful global adaptive probabilistic search ability, 24 parameters of the robot are identified through simulation, which makes the pose （position and orientation） accuracy of the robot a great improvement. In the process of the calibration, stochastic measurement noises are considered. Lastly, generalization of the identified kinematic parameters in the whole workspace of the robot is discussed. The simulation results show that calibrating the robot with GA is very stable and not sensitive to measurement noise. Moreover, even if the robot＇s kinematic parameters are relative, GA still has strong search ability to find the optimum solution.

Optimal measurement configurations for kinematic calibration of six-DOF serial robot

An optimal measurement pose number searching method was designed to improve the pose selection method.Several optimal robot measurement configurations were added to an initial pre-selected optimal configuration set to establish a new configuration set for robot calibration one by one.The root mean squares (RMS) of the errors of each end-effector poses after being calibrated by these configuration sets were calculated.The optimal number of the configuration set corresponding to the least RMS of pose error was then obtained.Calibration based on those poses selected by this algorithm can get higher end-effector accuracy,meanwhile consumes less time.An optimal pose set including optimal 25 measurement configurations is found during the simulation.Tracking errors after calibration by using these poses are 1.54,1.61 and 0.86 mm,and better than those before calibration which are 7.79,7.62 and 8.29 mm,even better than those calibrated by the random method which are 2.22,2.35 and 1.69 mm in directions X,Y and Z,respectively.

An approach to measure the pose of RHJD4-1 arc welding robot for calibration

A measurement setup used for robot calibration was designed to meet the requirement of off line programming technique. The robot end effector pose (position and orientation) can be calculated indirectly by using this setup. The setup has been applied to RHJD4 1 arc welding robot. The experimental results show the method of pose measuring using the measurement setup is simple and reliable to finish pose measuring for robot calibration. In addition, the setup can measure the position repeatability of robot.

Robot stereo vision calibration method with genetic algorithm and particle swarm optimization

Accurate stereo vision calibration is a preliminary step towards high-precision visual posi- tioning of robot. Combining with the characteristics of genetic algorithm （GA） and particle swarm optimization （PSO）, a three-stage calibration method based on hybrid intelligent optimization is pro- posed for nonlinear camera models in this paper. The motivation is to improve the accuracy of the calibration process. In this approach, the stereo vision calibration is considered as an optimization problem that can be solved by the GA and PSO. The initial linear values can be obtained in the frost stage. Then in the second stage, two cameras＇ parameters are optimized separately. Finally, the in- tegrated optimized calibration of two models is obtained in the third stage. Direct linear transforma- tion （DLT）, GA and PSO are individually used in three stages. It is shown that the results of every stage can correctly find near-optimal solution and it can be used to initialize the next stage. Simula- tion analysis and actual experimental results indicate that this calibration method works more accu- rate and robust in noisy environment compared with traditional calibration methods. The proposed method can fulfill the requirements of robot sophisticated visual operation.

Monocular Visual-Inertial and Robotic-Arm Calibration in a Unifying Framework

Reliable and accurate calibration for camera,inertial measurement unit(IMU)and robot is a critical prerequisite for visual-inertial based robot pose estimation and surrounding environment perception.However,traditional calibrations suffer inaccuracy and inconsistency.To address these problems,this paper proposes a monocular visual-inertial and robotic-arm calibration in a unifying framework.In our method,the spatial relationship is geometrically correlated between the sensing units and robotic arm.The decoupled estimations on rotation and translation could reduce the coupled errors during the optimization.Additionally,the robotic calibration moving trajectory has been designed in a spiral pattern that enables full excitations on 6 DOF motions repeatably and consistently.The calibration has been evaluated on our developed platform.In the experiments,the calibration achieves the accuracy with rotation and translation RMSEs less than 0.7°and 0.01 m,respectively.The comparisons with state-of-the-art results prove our calibration consistency,accuracy and effectiveness.

Robot Calibration Using Active Vision-based Measurement

This paper presents an efficient robot calibration method with non-contact vision metrology. Using the coplanar pattern to calibrate camera made the active-vision-based end-effector pose measurement be a feasible and costeffective way. Kinematic parameter errors were linearized and identified through two-step procedure, thus the singular and non-linear condition was overcome. These errors were then compensated using inverse model method. The whole calibration process is flexible, easy to implement and prevents the error propagation from the earlier stages to the later ones. Calibration was performed on MOTOMAN SV3industrial robot. Experiment results show that the proposed method is easy to setup and with satisfactory accuracy.

Using a 3D Interval Type-2 Fuzzy Interpolation System to Improve Modeless Robots Measurement and Calibration Accuracy

This paper is an extended research for a novel technique used in the pose error compensations of the robot and manipulator calibration process based on an IT2FEI （interval type-2 fuzzy error interpolation） method. Robot calibrations can be classified into model-based and modeless methods. A model-based calibration method normally requires that the practitioners understand the kinematics of the robot therefore may pose a challenger for field engineers. An alternative yet effective means for robot calibration is to use a modeless method; however with such a method there is a conflict between the calibration accuracy of the robot and the number of grid points used in the calibration task. In this paper, an interval type-2 fuzzy interpolation system is applied to improve the compensation accuracy of the robot in its 3D workspace. An on-line type-2 fuzzy inference system is implemented to meet the needs of on-line robot trajectory planning and control. The simulated results given in this paper show that not only robot compensation accuracy can be greatly improved, but also the calibration process can be significantly simplified, and it is more suitable for practical applications.

Analytical/Numerical Modelling of Two Parallel Robots as Laser Calibration Instruments Controlled by Classical/Intelligent Schemes

Industrial metrology deals with measurements in production environment. It concerns calibration procedures as well as control of measurement processes. Measuring devices have been evolving from manual theodolites, electronic theodolites, robotic total stations, to a relatively new kind of laser-based systems known as laser trackers. Laser trackers are 3D coordinate measuring devices that accurately measure large （and relatively distant） objects by computing spatial coordinates of optical targets held against those objects. In addition, laser trackers are used to align truthfully large mechanical parts. However, such aligning can be done in moving parts, for instance during robot calibration in a welding line. In this case, serial robots are controlled in order to keep a prescribed trajectory to accomplish its task properly. Nevertheless, in spite of a good control algorithm design, as time goes by, deviations appear and a calibration process is necessary. It is well known that laser tracker systems are produced by very well established enterprises but their laser products may result expensive for some （small） industries. We offer two parallel robot-based laser tracker systems models whose implementation would result cheaper than sophisticated laser devices and takes advantage of the parallel robot bondages as accuracy and high payload. The types of parallel robots evaluated were 3-SPS-1-S and 6-PUS. Modelling of the parallel robots was done by analytical and numerical techniques. The latter includes classical and artificial intelligence-based algorithms. The control performance was evaluated between classical and intelligent controllers.

A calibration and compensation method for an industrial robot with high accuracy harmonic reducers

Industrial serial robots need high stiffness to keep absolute pose accuracy and meet the requirements in practical applications. However, the weak stiffness feature of robot joints and the payloads affected on robot end-effector, which will also increase the pose error of robot. Especially, the existing calibration methods often consider under no-payload condition without discussing the payload state. In this paper, we report a new industrial serial robot composed by a new harmonic reducer: Model-Y, based on high accuracy and high stiffness, and a kinematic parameter calibration algorithm which is based on a harmonic reducer forcedeformation model. To decrease the accuracy effects of payload, an iterative calibration method for kinematic parameters with payload situation was proposed. Simulation and experiments are conducted to verify the effectiveness of the proposed calibration method using the self-developed industrial serial robot. The results show a remarkably improved accuracy in absolute position and orientation with the robot's payload range. The position mean error has 70% decreased to 0.1 mm and the orientation mean error diminished to less than 0.01° after calibration with compensation. Additionally, online linear and circular tests are carried out to evaluate the position error of the robot during large-scale spatial and low-speed continuous movement. The accuracy is consistent with the previous calibration results, indicating the effectiveness and advantages of the proposed strategy in this article.

Novel method to calibrate kinematic parameters for mobile robots

In order to reduce the system errors of dead reckoning and improve the localization accu- racy, a new model for systematic error of mobile robot was defined and a UMBmark-based method for calibrating and compensating systematic error was presented. Three dominant reasons causing systematic errors were considered： imprecise average wheel diameter, uncertainty about the effec- tive wheelbase and unequal wheel＇ s diameter. The new model for systematic errors is considering the coupling effect of the three factors during the localization of mobile robot. Three coefficients to calibrate average wheel diameter, effective wheelbase, left and right wheels＇ diameter were ob- tained. Then these three coefficients were used to make improvements on robot kinematic equations. The experiments on the dual-wheel drive mobile robot DaNI show that the presented method has achieveda significant improvement in the location accuracy compared with the UMBmark calibration.

Kinematic Calibration of a Six-Legged Walking Machine Tool

This paper presents the kinematic calibration of a novel six-legged walking machine tool comprising a six-legged mobile robot integrated with a parallel manipulator on the body.Each leg of the robot is a 2-universal-prismatic-spherical(UPS)and UP parallel mechanism,and the manipulator is a 6-PSU parallel mechanism.The error models of both subsystems are derived according to their inverse kinematics.The objective function for each kinematic limb is formulated as the inverse kinematic residual,i.e.,the deviation between the actual and computed joint coordinates.The hip center of each leg is first identified via sphere fitting,and the other kinematic parameters are identified by solving the objective function for each limb individually using the least-squares method.Thus,the kinematic parameters are partially decoupled,and the complexities of the error models are reduced.A calibration method is proposed for the legged robot to overcome the lack of a fixed base on the ground.A calibration experiment is conducted to validate the proposed method,where a laser tracker is used as the measurement equipment.The kinematic parameters of the entire robot are identified,and the motion accuracy of each leg and that of the manipulator are significantly improved after calibration.Validation experiments are performed to evaluate the positioning and trajectory errors of the six-legged walking machine tool.The results indicate that the kinematic calibration of the legs and manipulator improves not only the motion accuracy of each individual subsystem but also the cooperative motion accuracy among the subsystems.

Design of Calibration Experiments for Identification of Manipulator Elastostatic Parameters

The paper is devoted to the elastostatic calibration of industrial robots, which is used for precise machining of large-dimensional parts made of composite materials. In this technological process, the interaction between the robot and the workpiece causes essential elastic deflections of the manipulator components that should be compensated by the robot controller using relevant elastostatic model of this mechanism. To estimate parameters of this model, an advanced calibration technique is applied that is based on the non-linear experiment design theory, which is adopted for this particular application. In contrast to previous works, it is proposed a concept of the user-defined test-pose, which is used to evaluate the calibration experiments quality. In the frame of this concept, the related optimization problem is defined and numerical routines are developed, which allow generating optimal set of manipulator configurations and corresponding forces/torques for a given number of the calibration experiments. Some specific kinematic constraints are also taken into account, which insure feasibility of calibration experiments for the obtained configurations and allow avoiding collision between the robotic manipulator and the measurement equipment. The efficiency of the developed technique is illustrated by an application example that deals with elastostatic calibration of the serial manipulator used for robot-based machining.

Ultrasound calibration with ladder phantom at multiple depths for breast biopsy navigation system

Ultrasound guided breast biopsy navigation system with a graphical user interface and a passive robotic needle holder is developed to increase the performance and reliability of the radiologist.Ultrasound calibration and tool tip calibration are required before using the system.A ladder phantom is developed to be used for ultrasound calibration in real time system with only one ultrasound image required.The passive robotic needle holder structure results in an identity matrix for the makes the rotation matrix;therefore,only translation and scaling are required in the system.This method can be applied to multiple ultrasound depths,which has a relationship at each depth and a relationship to the ultrasound image on the display.The results show high accuracy(<1 mm.)and rapid calibration(5–10 minutes)which is suitable for a real time system like a breast biopsy navigation system based on tests with a breast phantom.