End-effector Position Error Research Articles

Design and kinematics of a novel rigid-flexible coupling hybrid robot for aeroengine blades in situ repair

PurposeThis paper aims to present the mechanical design and kinematics of a novel rigid-flexible coupling hybrid robot to develop a promising aeroengine blades in situ repair technology.Design/methodology/approachAccording to requirements analysis, a novel rigid-flexible coupling hybrid robot is proposed by combining a three degrees of freedom (DOF) parallel mechanism with a flexible continuum section. Then the kinematics models of both parallel mechanism and flexible continuum section are derived respectively. Finally, based on equivalent joint method, a two-step numerical iterative inverse kinematics algorithm is proposed for the whole robot: (1) the flexible continuum section is equivalently transformed to a 2-DOF spherical joint, thus the approximate analytical inverse kinematic solution can be obtained; (2) the accurate solution is derived by an iterative derivation of both parallel mechanism and flexible continuum section.FindingsTo verify structure scheme and the proposed kinematics modeling method, numerical simulations and prototype experiments are implemented. The results show that the proposed kinematics algorithm has sufficient accuracy and computational efficiency in the whole available workspace, that is end-effector position error and orientation error are less than 0.2 mm and 0.01° respectively, and computation time is less than 0.22s.Originality/valueA novel rigid-flexible coupling hybrid robot for aeroengine blades in situ repair is designed. A two-step numerical iterative inverse kinematics algorithm is proposed for this unique hybrid robots, which has good accuracy and computational efficiency.

Robot error compensation strategy based on error sensitivity

Abstract Due to the errors in manufacturing and assembly, there are differences between the actual model and the theoretical model of the robot, which affects the positioning accuracy of the robot end-effector. In order to improve the accuracy of robot end-effector position, a robot error compensation strategy based on error sensitivity is proposed.Firstly, the robot kinematic model is established by Denavit-Hartenberg (D-H) method, and the sensitivity of end-effector position error is analyzed. According to the influence degree of different kinematic parameters on the robot end-effector position accuracy in the whole workspace, different weights are given to different kinematic parameters. {\color{red}Secondly, the kinematic error model is established, and the redundancy of the error parameter matrix is analyzed to obtain an independent error model. Thirdly, based on the error sensitivity analysis, a Weighted Levenberg-Marquard (WLM) algorithm with adaptive penalty factor is proposed, and the kinematic parameters are iteratively identified.} Finally, an error compensation experiment is carried out by using a universal serial six-degree-of-freedom robot. The experimental results show that the maximum error, mean absolute error and root mean square error of the position error on the test set are reduced by 90.75%, 89.86% and 95.64% respectively. The research in this paper provides a theoretical basis for robot end error compensation.

Development of a Novel Retinal Surgery Robot Based on Spatial Variable Remote Center-of-Motion Mechanism

Abstract This article reports the design, modeling, and experiments of a novel retinal surgery robot based on spatial variable remote center-of-motion (RCM) mechanism. The general design criteria for parallel mechanisms are proposed, and the planar five-bar mechanisms are evaluated and selected. The planar-spatial evolution process, including the parallel connection of the planar mechanism and the equivalent substitution of joints, is adopted to develop a spatial variable RCM mechanism and then the robot. The mobility and singularity of the robot are analyzed, and the forward/inverse kinematics and workspace are modeled. Dimension optimization is conducted based on a comprehensive performance indicator that characterizes the motion range of linear actuators and the global dexterity performance index of robot. The prototyped robot is fabricated and assembled, and the kinematic calibration is performed. The position error of end-effector is within 34 μm, and both the position error and deviation of the RCM point are within 23 μm. The robot is demonstrated to reach the desired position and execute the RCM motion with high precision simultaneously.

Inverse kinematics of six degrees of freedom robot manipulator based on improved dung beetle optimizer algorithm

Inverse kinematics is a basic problem in robotics, which aims to solve the robot’s joint angles according to the end effector’s position and orientation. This paper proposed an improved spiral search multi-strategy dung beetle optimizer (DBO) algorithm for solving the inverse kinematics problem. The improved DBO algorithm considers not only the error between the target value and the current value but also the previous position of the robot to ensure minimum displacement during the movement. To solve the end position error and orientation error of the robot end effector more accurately, the quaternion is introduced as a penalty factor in the optimization objective function, which is of great significance for reducing the orientation error. Through the improved DBO algorithm, the position error is still accurate, and the orientation error is reduced from 9.5901 to 1.8718. Experimental results show that the proposed algorithm outperforms other swarm-intelligent algorithms in terms of accuracy and convergence speed. Overall, the proposed spiral search multi-strategy DBO algorithm provides an effective and efficient solution to the inverse kinematics problem in robotics.

Research on accurate morphology predictive control of CFETR multi-purpose overload robot

The CFETR multipurpose overload robot (CMOR) is a critical component of the fusion reactor remote handling system. To accurately calculate and visualize the structural deformation and stress characteristics of the CMOR motion process, this paper first establishes a CMOR kinematic model to analyze the unfolding and working process in the vacuum chamber. Then, the dynamic model of CMOR is established using the Lagrangian method, and the rigid-flexible coupling modeling of CMOR links and joints is achieved using the finite element method and the linear spring damping equivalent model. The co-simulation results of the CMOR rigid-flexible coupled model show that when the end load is 2000 kg, the extreme value of the end-effector position error is more than 0.12 m, and the maximum stress value is 1.85 × 108 Pa. To utilize the stress-strain data of CMOR, this paper designs a CMOR morphology prediction control system based on Unity software. Implanting CMOR finite element analysis data into the Unity environment, researchers can monitor the stress strain generated by different motion trajectories of the CMOR robotic arm in the control system. It provides a platform for subsequent research on CMOR error compensation and extreme operation warnings.

Structural Optimization of 4-DOF Agricultural Robot Arm

The shortage of human labor is increasing; thus, more agricultural machinery and equipment are expected to enter the agricultural sector. One of the agricultural machinery widely studied nowadays involves robot arms. Therefore, developing robot arms is a hot issue in this field. The ideal structure of the robot arm with optimal length is currently gaining popularity and being used in many sectors, such as manufacturing and agriculture. This is closely related to the dynamic structure of agricultural areas. Therefore, this study uses the forward kinematic modeling method to design an optimal robot arm to achieve a specific coordinate in a dynamic environment. The robot in this study arm mimics the boom and arm installed on a tractor. The forward kinematic problem in this study is defined using the Denavit-Hartenberg (DH) convention method. The DH convention is commonly used to solve kinematic analysis problems of a robot arm. Simulation of kinematic modeling is performed using MATLAB software. This study studies various optimization algorithms to compare the performance of algorithms that can achieve the optimal length with minimum errors. The comparison between artificial bee colony (ABC) and particle swarm optimization (PSO) is studied. At the end of the study, the best algorithm was selected for the robot arm design with a four-degree-of-freedom (4-DOF). The best algorithm, i.e., the PSO algorithm, is evaluated by calculating mean square error (MSE of 0.00108527), root mean square error (RMSE of 0.01678), mean absolute error (MAE of 0.004286081), and end-effector position error (error of 0.080557045), where the best algorithm has the lowest value of error.

Quantifying the Effects of Network Latency for a Teleoperated Robot.

The development of teleoperated devices is a growing area of study since it can improve cost effectiveness, safety, and healthcare accessibility. However, due to the large distances involved in using teleoperated devices, these systems suffer from communication degradation, such as latency or signal loss. Understanding degradation is important to develop and improve the effectiveness of future systems. The objective of this research is to identify how a teleoperated system's behavior is affected by latency and to investigate possible methods to mitigate its effects. In this research, the end-effector position error of a 4-degree-of-freedom (4-DOF) teleultrasound robot was measured and correlated with measured time delay. The tests were conducted on a Wireless Local Area Network (WLAN) and a Virtual Local Area Network (VLAN) to monitor noticeable changes in position error with different network configurations. In this study, it was verified that the communication channel between master and slave stations was a significant source of delay. In addition, position error had a strong positive correlation with delay time. The WLAN configuration achieved an average of 300 ms of delay and a maximum displacement error of 7.8 mm. The VLAN configuration showed a noticeable improvement with a 40% decrease in average delay time and a 70% decrease in maximum displacement error. The contribution of this work includes quantifying the effects of delay on end-effector position error and the relative performance between different network configurations.

Lie Group Formulation and Sensitivity Analysis for Shape Sensing of Variable Curvature Continuum Robots With General String Encoder Routing

This article considers a combination of actuation tendons and measurement strings to achieve accurate shape sensing and direct kinematics of continuum robots. Assuming general string routing, a methodical Lie group formulation for the shape sensing of these robots is presented. The shape kinematics is expressed using arc-length-dependent curvature distributions parameterized by modal functions, and the Magnus expansion for Lie group integration is used to express the shape as a product of exponentials. The tendon and string length kinematic constraints are solved for the modal coefficients and the configuration space and body Jacobian are derived. The noise amplification index for the shape reconstruction problem is defined and used for optimizing the string/tendon routing paths, and a planar simulation study shows the minimal number of strings/tendons needed for accurate shape reconstruction. A torsionally stiff continuum segment is used for experimental evaluation, demonstrating mean (maximal) end-effector absolute position error of less than 2% (5%) of total length. Finally, a simulation study of a torsionally compliant segment demonstrates the approach for general deflections and string routings. We believe that the methods of this article can benefit the design process, sensing, and control of continuum and soft robots.

Comprehensive Compensation Method for Motion Trajectory Error of End-Effector of Cable-Driven Parallel Mechanism

The accuracy of the end-effector motion trajectory is a critical performance indicator for cable-driven parallel mechanisms. This study aims to address the problem of trajectory error during the end-effector motion in a cable-driven parallel mechanism. It proposes a comprehensive compensation method based on the simultaneous application of the improved sparrow search algorithm and the cable length space error compensation algorithm, leveraging kinematic analysis. To compensate for the motion trajectory error of the end-effector caused by the geometric parameter error, the study establishes the kinematic model of the cable-driven parallel mechanism using the vector method. It creates the end-effector position error model and motion trajectory error model using the differential kinematic theory, analyzes the impact of the geometric parameter error on the motion trajectory error, constructs the kinematic parameter identification matrix, and uses an improved sparrow search algorithm to compensate for the position error of the motion trajectory interpolation point. For the motion trajectory error of the end-effector caused by non-geometric parameter error, the study analyzes the intrinsic correlation between the adjacent position error of the end-effector and the variation of the cable length using the error similarity theory. It then compensates for the position error of the interpolation point of the trajectory using a cable length space interpolation compensation method to enhance the motion trajectory accuracy of the end-effector. The study experimentally verifies the proposed comprehensive compensation method for end-effector motion trajectory error on a 4-cable-driven 2-DOF parallel mechanism, which reduces the motion trajectory error of the end-effector by 75%.

Mathematical modeling and simulation of the inverse kinematic of a redundant robotic manipulator using azimuthal angles and spherical polar piecewise interpolation

In this study, smooth trajectory generation and the mathematical modeling of the inverse kinematics and dynamics of a redundant robotic manipulator is considered. The path of the end-effector of the robotic manipulator is generated – along a particular set of via-points – in a system of spherical coordinates by combining the Hermite polar piecewise interpolants that approximate each intermediate radial distance on the reference plane using the azimuthal angle and each corresponding point height of the path computed in the rotating radial plane through the corresponding polar angle. The smoothness of the end-effector path is guaranteed by the use of quintic Hermite piecewise interpolants having functional continuity, while the inverse kinematics and inverse dynamics used to compute the coordinates of the joints and the equations of motion of the robotic manipulator are considered for optimum trajectory planning. Optimization solutions to minimize the joint velocities, the end-effector positioning error, the traveling time and mechanical energy, or the consumed power, are presented. The direct computation of the joints trajectory and a optimal trajectory with minimization of the end-effector position error while preserving trajectory smoothness of the joints are considered. To assess and verify the approach numerical examples – implemented in Matlab – are introduced, and the outcomes are examined.

Null-Space Minimization of Center of Gravity Displacementof a Redundant Aerial Manipulator

Displacements of the base during trajectory tracking are a common issue in the control of aerial manipulators. These are caused by reaction torques transferred to the base due to the manipulator motion and, in particular, to the motion of its center of gravity. We present a novel approach to reduce base displacements of a kinematically redundant aerial manipulator by using null-space projection in the inverse kinematic control. A secondary objective function minimizes the horizontal displacement of the manipulator center of gravity. We test this algorithm on different trajectories for both three and four degrees of freedom (DOF) manipulators in a simulation environment. The results comparing our algorithm with inverse kinematic control without the null-space projection show up to an 80% reduction in the end-effector position error and an average of about 56% reduction in maximum base displacement. The simulation implementation also runs faster than in real-time in our code implementation. We provide a workspace analysis based on multiple stopping criteria such as excessive base displacement, joint velocities and end-effector position error for the 3 and 4 DOF manipulators. As expected, the 4 DOF manipulator has a larger workspace.

Performance Analysis of Hybrid Kinematic Mechanism for Fusion Reactor Maintenance

The hybrid kinematic mechanism (HKM) as an alternative remote handling subsystem of the Demonstration Fusion Power Plant (DEMO) breeding blanket (BB) is undergoing extensive theoretical analysis and feasibility verification. In this paper, the forward and inverse kinematic models of the HKM are derived by combining the Newtonian iterative method and the analytical method. Cartesian space trajectory planning is designed based on the trajectories of the HKM lifting of inboard and outboard BBs. The continuous smooth inverse kinematic solutions in the HKM joint space are obtained based on the polynomial interpolation method. For the characteristics of the HKM piston thread driving, the end-effector position error caused by the degradation of the spherical joint into a universal joint is analyzed and calculated. During the lifting of the left inboard BB, there is a maximum absolute error ∆P = 3.1 mm, and as the error continues to expand to the bottom of the BB it causes a risk of collision. Combining the overall effects of driving control, rigid–flexible coupling, etc., on position accuracy, an open-loop variable parameter error compensation plan based on the Levenberg–Marquardt (LM) nonlinear damping least-squares algorithm is proposed and validated in this paper. The simulation results show that the maximum absolute error after compensation is less than 1 mm as the mesh density increases, and the absolute position accuracy can be further improved by local mesh encryption. This study verifies the feasibility of the HKM as a BB remote handling subsystem and provides an option for high-precision control of the HKM.

Application of Half-Derivative Damping to Cartesian Space Position Control of a SCARA-like Manipulator

In classical Cartesian space position control, KD, the end-effector follows the set-point trajectory with a stiffness expressed in the directions of the external coordinates through the stiffness matrix, K, and with a damping proportional to the first-order derivatives of errors of the external coordinates through the damping matrix, D. This work deals with a fractional-order extension of the Cartesian space position control, KDHD, which is characterized by an additional damping term, proportional to the half-order derivatives of the errors of the external coordinates through a second damping matrix, HD. The proposed Cartesian position control scheme is applied to a SCARA-like serial manipulator with elastic compensation of gravity. Multibody simulation results show that the proposed scheme was able to reduce the tracking error, in terms of mean absolute value of the end-effector position error and Integral Square Error, with the same amount of Integral Control Effort and comparable maximum actuation torques.

Coordinated Pose Control of Mobile Manipulation With an Unstable Bikebot Platform

Bikebot manipulation has advantages of the single-track robot mobility and manipulation dexterity. We present a coordinated pose control of mobile manipulation with the stationary bikebot. The challenges of the bikebot manipulation include the limited steering balance capability of the unstable bikebot and kinematic redundancy of the manipulator. We first present the steering balance model to analyze and explore the maximum steering capability to balance the stationary platform. A balancing equilibrium manifold is then proposed to describe the necessary condition to fulfill simultaneous platform balance and posture control of the end-effector. A coordinated planning and control design is presented to determine the balance-prioritized posture control under kinematic and dynamic constraints. Extensive experiments are conducted to demonstrate the mechatronic design for autonomous plant inspection in agricultural applications. The results confirm the feasibility to use the bikebot manipulation for plant inspection with end-effector position and orientation errors about 5 mm and 0.3 degs, respectively.

Zero Reaction Torque Trajectory Tracking of an Aerial Manipulator through Extended Generalized Jacobian

Aerial manipulators are used in industrial and service robotics tasks such as assembly, inspection, and maintenance. One of the main challenges in aerial manipulation is related to the motion of the UAV base caused by manipulator disturbance torques and forces, which jeopardize the precision of the robot manipulator. In this paper, we propose two novel inverse kinematic control methods used to track a trajectory with an aerial manipulator while also considering resultant UAV base motions. The first method is adapted from the generalized Jacobian formulation used in space robotics and includes the change in system momentum resulting from gravity and UAV control forces in the inverse kinematic control equation. This approach is simulated for a 2 and 3 degree-of-freedom aerial manipulator tracking trajectories with the end-effector. Although the end-effector position error is approximately zero throughout the simulated task, we see significant undesired UAV base motions of several centimeters in magnitude. To ameliorate this by exploiting the kinematic redundancy, we modify the generalized Jacobian by adding an additional task constraint which minimizes the reaction torques from the manipulator, to form the extended generalized Jacobian. While the second approach results in improved precision and reduced base motion by an order of magnitude as compared to the generalized Jacobian, a drawback is the reduction in the available workspace as the solution seeks to minimize the manipulator center of gravity translation. We also demonstrate and compare both approaches in a load picking task. All the algorithms are completed computationally faster than real time in the MATLAB simulations, illustrating their potential for application in real-world experiments.

A Dual Fuzzy-Enhanced Neurodynamic Scheme for Model-Less Kinematic Control of Redundant and Hyperredundant Robots

Tracking control of redundant and hyperredundant manipulators is a fundamental and critical problem in practical applications. In order to effectively decrease the end-effector position errors, a novel dual fuzzy-enhanced neurodynamic (DFEN) scheme is put forward for solving the position error accumulation problem followed by achieving accurate tracking control results. The proposed scheme is established based on a zeroing neurodynamic approach in conjunction with two fuzzy adjustment units that are capable of tuning the control parameters by monitoring the tracking error. Moreover, the DFEN scheme can effectively solve the tracking problem without requiring knowing <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> knowledge of the kinematic model of the robot. The convergence and the stability of the proposed approach are demonstrated by theoretical analysis. The effectiveness, accuracy, and robustness of the proposed DFEN scheme are verified on the simulative redundant manipulator, continuum robot, and hybrid robot (integrating the redundant manipulator and the continuum robot). A practical experiment is provided to validate the proposed scheme as well.

Fractional Order KDHD Impedance Control of the Stewart Platform

In classical impedance control, KD, the steady-state end-effector forces are imposed to be proportional to the end-effector position errors through the stiffness matrix, K, and a proper damping term is added, proportional to the first-order derivatives of the end-effector position errors according to the damping matrix, D. This paper presents a fractional-order impedance control scheme, named KDHD, in which an additional damping is added, proportional to the half-order derivatives of the end-effector position errors according to the half-derivative damping matrix, HD. Since the finite-order digital filters which implement in real-time the half-order derivatives modify the steady-state stiffness of the end-effector—which should be defined exclusively by the stiffness matrix—a compensation method is proposed (KDHDc). The effectiveness of this approach is validated by multibody simulation on a Stewart platform. The proposed impedance controller represents the extension to multi-input multi-output robotic systems of the PDD1/2 controller for single-input single-output systems, which overperforms the PD scheme in the transient behavior.

The Kinematic Calibration of an Industrial Robot With an Improved Beetle Swarm Optimization Algorithm

The article proposes a kinematic calibration method based on an improved beetle swarm optimization algorithm for an industrial robot to finish drilling and riveting. Specifically, a preference random substitution method to improve the update strategy was presented, which comprises a new boundary-processing strategy that avoids stagnation states and local optimization traps by adopting a dynamic parameter adjustment strategy to increase the speed and stability of searches. The effectiveness of the proposed method was verified by simulations and calibration experiments involving a robot drilling and riveting system with an industrial robot KUKA KR500L340-2. In addition, comparisons were conducted with linear least-squares, particle swarm optimization, and beetle swarm optimization algorithms. According to the results of calibration simulations and experiments, the fitness function value of the proposed algorithm can decrease rapidly in the first 20 iterations, while the mean value of the end-effector position error is reduced from 2.95mm to 0.20mm by using the proposed algorithm. Compared with other three algorithms, the positioning accuracy is improved by more than 60&#x0025;.

Application of the Half-Order Derivative to Impedance Control of the 3-PUU Parallel Robot

This paper presents an extension of impedance control of robots based on fractional calculus. In classical impedance control, the end-effector reactions are proportional to the end-effector position errors through the stiffness matrix K, while damping is proportional to the first-order time-derivative of the end-effector coordinate errors through the damping matrix D. In the proposed approach, a half-derivative damping is added, proportional to the half-order time-derivative of the end-effector coordinate errors through the half-derivative damping matrix HD. The discrete-time digital implementation of the half-order derivative alters the steady-state behavior, in which only the stiffness term should be present. Consequently, a compensation method is proposed, and its effectiveness is validated by multibody simulation on a 3-PUU parallel robot. The proposed approach can be considered the extension to MIMO robotic systems of the PDD1/2 control scheme for SISO mechatronic systems, with potential benefits in the transient response performance.

Assistive Sliding Mode Control of a Rehabilitation Robot with Automatic Weight Adjustment.

There are approximately 13 million new stroke cases worldwide each year. Research has shown that robotics can provide practical and efficient solutions for expediting post-stroke patient recovery. This simulation study aimed to design a sliding mode controller (SMC) for an end-effector-based rehabilitation robot. A genetic algorithm (GA) was designed for automatic controller weight adjustment. The optimal weights were obtained by minimizing a cost function comprising the end-effector position error, robot input, robot input-rate, and patient input. To promote safe tuner optimization, a model of the human arm was incorporated to generate the human joint torque. A computed-torque proportional derivative controller (CTPD) was designed for the human arm to approximate the central nervous system (CNS) motor control. This controller was adjusted to simulate rehabilitation effects and patient adaptation. The tuner was optimized for a trajectory tracking task with an assistive high-level control scheme. The simulation results showed lower cost compared to seven manual weight settings. The optimal weights provided good tracking performance and suitable robot inputs. This research provides a framework to conduct various simulations before testing our controller on human subjects. The preliminary results of this study will be used as the starting point for online adaptive controller tuning, which will be examined in our future research.