Kinematic calibration under the expectation maximization framework for exoskeletal inertial motion capture system

This study presents a kinematic calibration method for exoskeletal inertial motion capture (EI-MoCap) system with considering the random colored noise such as gyroscopic drift.In this method, the geometric parameters are calibrated by the traditional calibration method at first. Then, in order to calibrate the parameters affected by the random colored noise, the expectation maximization (EM) algorithm is introduced. Through the use of geometric parameters calibrated by the traditional calibration method, the iterations under the EM framework are decreased and the efficiency of the proposed method on embedded system is improved. The performance of the proposed kinematic calibration method is compared to the traditional calibration method. Furthermore, the feasibility of the proposed method is verified on the EI-MoCap system. The simulation and experiment demonstrate that the motion capture precision is significantly improved by 16.79%and 7.16%respectively in comparison to the traditional calibration method.

A Comparative Study on Kinematic Calibration for a 3-DOF Parallel Manipulator Using the Complete-Minimal,Inverse-Kinematic and Geometric-Constraint Error Models

Kinematic calibration is a reliable way to improve the accuracy of parallel manipulators, while the error model dramatically afects the accuracy, reliability, and stability of identifcation results. In this paper, a comparison study on kinematic calibration for a 3-DOF parallel manipulator with three error models is presented to investigate the relative merits of diferent error modeling methods. The study takes into consideration the inverse-kinematic error model, which ignores all passive joint errors, the geometric-constraint error model, which is derived by special geometric constraints of the studied RPR-equivalent parallel manipulator, and the complete-minimal error model, which meets the complete, minimal, and continuous criteria. This comparison focuses on aspects such as modeling complexity, identifcation accuracy, the impact of noise uncertainty, and parameter identifability. To facilitate a more intuitive comparison, simulations are conducted to draw conclusions in certain aspects, including accuracy, the infuence of the S joint, identifcation with noises, and sensitivity indices. The simulations indicate that the complete-minimal error model exhibits the lowest residual values, and all error models demonstrate stability considering noises. Hereafter, an experiment is conducted on a prototype using a laser tracker, providing further insights into the diferences among the three error models. The results show that the residual errors of this machine tool are signifcantly improved according to the identifed parameters, and the complete-minimal error model can approach the measurements by nearly 90% compared to the inverse-kinematic error model. The fndings pertaining to the model process, complexity, and limitations are also instructive for other parallel manipulators.

Kinematic Calibration and Forecast Error Compensation of a 2-DOF Planar Parallel Manipulator

Due to large workspace,heavy-duty and over-constrained mechanism,a small deformation is caused and the precision of the 2-DOF planar parallel manipulator is affected.The kinematic calibration cannot compensate the end-effector errors caused by the small deformation.This paper presents a method combined step kinematic calibration and linear forecast real-time error compensation in order to enhance the precision of a two degree-of-freedom(DOF) planar parallel manipulator of a hybrid machine tool.In the step kinematic calibration phase of the method,the end-effector errors caused by the errors of major constant geometrical parameters is compensated.The step kinematic calibration is based on the minimal linear combinations(MLCs) of the error parameters.All simple and feasible measurements in practice are given,and identification analysis of the set of the MLCs for each measurement is carried out.According to identification analysis results,both measurement costs and observability are considered,and a step calibration including step measurement,step identification and step error compensation is determined.The linear forecast real-time error compensation is used to compensate the end-effector errors caused by other parameters after the step kinematic calibration.Taking the advantages of the step kinematic calibration and the linear forecast real-time error compensation,a method for improving the precision of the 2-DOF planar parallel manipulator is developed.Experiment results show that the proposed method is robust and effective,so that the position errors are kept to the same order of the measurement noise.The presented method is attractive for the 2-DOF planar parallel manipulator and can be also applied to other parallel manipulators with fewer than six DOFs.

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.

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.

Kinematic Calibration of Asymmetricly Actuated 6-DOF 3-PPPS Parallel Mechanism

An asymmetric actuated 3-PPPS parallel mechanism was analyzed in its application to an aircraft wing adjustment process.The posture alignment precision at the wing ends was enhanced with a kinematic calibration method.A constraint equation was built based on a constraint condition that distances among spherical joints of the mechanism were constant,and further eight groups of analytic forward solutions of all poses of the mechanism were solved.An inverse equation of the posture alignment displacements of aircraft wing parts was built based on space vector chains,and a mapping equation of the pose and geometric errors of the posture alignment mechanism containing 39 error sources was derived by differentiating the kinematic equation of the mechanism.After kinematic calibration experiments,the maximum position error of the posture alignment platform dropped from 2.67 mm to 0.82 mm,the maximum angle error decreased from 0.481° to 0.167°,and the posture alignment precision of the aircraft wing end was improved.

Residual index for measurement configuration optimization in robot kinematic calibration

To improve the efficiency and accuracy of kinematic calibration,the selection of measurement configurations is an important issue.In previous research,optimal measurement configurations mainly are selected by maximizing observability indices.However,the traditional observability indices only focus on the identification efficiency of the error parameters,while the purpose of robot kinematic calibration is to improve accuracy.To solve the inconsistency of the purpose between the observability index and calibration,the concept of the residual index to represent the residual distribution of the end effector after robot kinematic calibration with the measurement noise is proposed.Based on the quadratic form minimization of residuals,this article defines a specific residual index,O^(r),which is dimensionless and strictly better with the increase of measurement configurations.The indices are used to select measurement configurations in the kinematic calibration of a 5-DOF 2UPU/SP-RR hybrid robot,and the calibration results show that the proposed residual index is better than the traditional indices in the accuracy and stability of the end effector residual.

Positioning error compensation for parallel mechanism with two kinematic calibration methods

Compared with serial mechanisms, the parallel mechanism(PM) theoretically exhibited higher positioning accuracy, dynamic performance, strength-to-weight ratio, and lower manufacturing cost, but they had not been widely used in the practical application. One key issue, positioning accuracy, which directly affected their performance and was greatly influenced by the errors of kinematic structure parameters was analyzed. To effectively enhance the positioning precision of PMs, a novel modeless kinematic calibration method, namely the split calibration, was presented and its compensation effect of the positioning error was comprehensively compared with that of an integrated method on two different types of PMs. A strange phenomenon-correct and incorrect identified results were derived from two different PMs by the same integrated method, respectivelywhich had not been reported yet was discovered, and the origin of it was revealed utilizing numerical simulations. Finally, respective merits and drawbacks of these two methods obtained in this paper provided underlying insights to guide the practical application of the kinematic calibration for PMs.

Development of an onsite calibration device for robot manipulators

A novel in-contact three-dimensional(3D)measuring device,called MultiCal,is proposed as a convenient,low-cost(less than US$5000),and robust facility for onsite kinematic calibration and online measurement of robot manipulator accuracy.The device hasμm-level accuracy and can be easily embedded in robot cells.During the calibration procedure,the robot manipulator first moves automatically to multiple end-effector orientations with its tool center point(TCP)constrained on a fixed point by a 3D displacement measuring device(single point constraint),and the corresponding joint angles are recorded.Then,the measuring device is precisely mounted at different positions using a well-designed fixture,and the above measurement process is repeated to implement a multi-point constraint.The relative mounting positions are accurately measured and used as prior information to improve calibration accuracy and robustness.The results of theoretical analysis indicate that MultiCal reduces calibration accuracy by 10%to 20%in contrast to traditional non-contact 3D or six-dimensional(6D)measuring devices(such as laser trackers)when subject to the same level of artificial measurement noise.The results of a calibration experiment conducted on a Staubli TX90 robot show that MultiCal has only 7%to 14%lower calibration accuracy compared to a measuring arm with a laser scanner,and 21%to 30%lower time efficiency compared to a 6D binocular vision measuring system,yielding maximum and mean absolute position errors of 0.831 mm and 0.339 mm,respectively.

Design and experimental study of the SPKM165, a five-axis serial-parallel kinematic milling machine

A five-axis serial-parallel kinematic milling machine, the SPKM 165, is introduced. This machine consists of a three-degree of-freedom parallel module and a two-degree-of-freedom serial table. The SPKM 165 is capable of five-face machining. A discussion of the inverse kinematics of the five-axis control is provided. A dimensional synthesis procedure is presented in terms of motion/force transmissibility. Finite-element analysis was used to evaluate the stiffness of a CAD model before the machine was manufactured. Kinematic calibration was implemented to improve the accuracy of the end effector. The results of a calibration experiment are presented. The stiffness of the developed machine was then measured. Milling experiments were conducted, and the test piece showed that the developed machine has satisfactory performance.

A review of structures,verification,and calibration technologies of space robotic systems for on-orbit servicing

Recently,with the rapid development of aerospace technology,an increasing number of spacecraft is being launched into space.Additionally,the demands for on-orbit servicing(OOS)missions are rapidly increasing.Space robotics is one of the most promising approaches for various OOS missions;thus,research on space robotics technologies for OOS has attracted increased attention from space agencies and universities worldwide.In this paper,we review the structures,ground verification,and onorbit kinematics calibration technologies of space robotic systems for OOS.First,we systematically summarize the development of space robotic systems and OOS programs based on space robotics.Then,according to the structures and applications,these systems are divided into three categories:large space manipulators,humanoid space robots,and small space manipulators.According to the capture mechanisms adopted,the end-effectors are systematically analyzed.Furthermore,the ground verification facilities used to simulate a microgravity environment are summarized and compared.Additionally,the on-orbit kinematics calibration technologies are discussed and analyzed compared with the kinematics calibration technologies of industrial manipulators with regard to four aspects.Finally,the development trends of the structures,verification,and calibration technologies are discussed to extend this review work.