End-effector Position Research Articles

Impulsive tracking synchronization control of networked robotic manipulator systems in the task space

This study investigates the impulsive tracking synchronization control of networked robotic manipulator systems based on Lagrangian systems. In the task space, the end-effector positions of networked robotic manipulators can synchronize and track a desired trajectory by designing an impulsive controller. Based on impulsive control, some algebraic synchronization criteria are derived. As a direct application of the theoretical results, tracking synchronization of six double-link robotic manipulators in the task space is discussed in detail. Numerical simulations are given to demonstrate the effectiveness and feasibility of the proposed control strategy.

Improved Bald Eagle Search Optimization Algorithm for the Inverse Kinematics of Robotic Manipulators.

The inverse kinematics of robotic manipulators involves determining an appropriate joint configuration to achieve a specified end-effector position. This problem is challenging because the inverse kinematics of manipulators are highly nonlinear and complexly coupled. To address this challenge, the bald eagle search optimization algorithm is introduced. This algorithm combines the advantages of evolutionary and swarm techniques, making it more effective at solving nonlinear problems and improving search efficiency. Due to the tendency of the algorithm to fall into local optima, the Lévy flight strategy is introduced to enhance its performance. This strategy adopts a heavy-tailed distribution to generate long-distance jumps, thereby preventing the algorithm from becoming trapped in local optima and enhancing its global search efficiency. The experiments first evaluated the accuracy and robustness of the proposed algorithm based on the inverse kinematics problem of manipulators, achieving a solution accuracy of up to 10-18 m. Subsequently, the proposed algorithm was compared with other algorithms using the CEC2017 test functions. The results showed that the improved algorithm significantly outperformed the original in accuracy, convergence speed, and stability. Specifically, it achieved over 70% improvement in both standard deviation and mean for several test functions, demonstrating the effectiveness of the Lévy flight strategy in enhancing global search capabilities. Furthermore, the practicality of the proposed algorithm was verified through two real engineering optimization problems.

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.

Control analysis of an underactuated bio-inspired robot

Abstract This article is devoted to the control of bio-inspired robots that are underactuated. These robots are composed of tensegrity joints remotely actuated with cables, which mimic the musculoskeletal system of the bird neck. A computed torque control (CTC) is applied to these robots as well as an original control called pseudo computed torque control (PCTC). This new control uses the dynamics and the pseudo-inverse of the Jacobian matrix. The stability of the two proposed controls is then analyzed through linearization of the dynamic model and expression of the closed-loop transfer function in the Laplace domain. We show that, depending on the desired trajectory, the CTC can be unstable when the controlled variables are the end effector position and orientation. For a robot with many joints and a limited number of cables, the CTC is always unstable. Instead, the PCTC shows a large domain of stability. The analysis is complemented by experimental tests demonstrating that the CTC and PCTC exhibit similar performance when the CTC is stable. Furthermore, the PCTC maintains stability on trajectories where the CTC becomes unstable, showing robustness to perturbations as well.

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.

Tip and vibration control of space robots using estimated flexible coordinates

This paper provides an extension to previous work on end-effector control of flexible space manipulators. Those works considered the use of a special output called the μ-tip rate for feedback control of desired end-effector trajectories with simultaneous vibration control. Implementation of this special output requires measurement of end-effector position or the use of flexible forward kinematics to determine it. For the latter, one requires measurements of the joint angles and flexible coordinates. The second of these is difficult to measure in space scenarios, so this paper looks at the use of an estimation scheme to approximate it and use it in a task-space control law. Multiple simulations are conducted to investigate the use of these approximated elastic coordinates in robustly controlling a one-link and two-link flexible manipulator with a payload mass. The error between desired and actual trajectory is calculated, and the results are juxtaposed with results from a joint-space feedback scheme. There is an emphasis on comparing the estimated elastic coordinates with the actual simulated coordinates. Using the estimated elastic coordinates to determine the end-effector location via forward kinematics, yielded similar results to when the actual elastic coordinates were used. Overall, the estimation equation used is shown to provide reasonable end-effector tracking results with the end-effector being able to track various types of trajectories.

Simple Inverse Kinematics Computation Considering Joint Motion Efficiency.

Inverse kinematics (IK) is an important and challenging problem in the operation of industrial manipulators. This study proposes a simple IK calculation scheme for an industrial serial manipulator. The proposed technique can calculate appropriate values of the joint variables to realize the desired end-effector position and orientation while considering the motion costs of each joint. Two scalar functions are defined for the joint variables: one is to evaluate the end-effector position and orientation, whereas the other is to evaluate the motion efficiency of the joints. By combining the two scalar functions, the IK calculation of the manipulator is formulated as a numerical optimization problem. Furthermore, a simple algorithm for solving the IK via the aforementioned optimization is constructed on the basis of the simultaneous perturbation stochastic approximation with a norm-limited update vector (NLSPSA). The proposed scheme considers not only the accuracy of the position and orientation of the end-effector but also the efficiency of the robot movement. Therefore, it yields a practical result of the inverse problem. Moreover, the proposed algorithm is simple and easy to implement owing to the high-calculation efficiency of NLSPSA. Finally, the effectiveness of the proposed method is verified through numerical examples using a redundant manipulator.

Vision-Based Force Estimation for Minimally Invasive Telesurgery Through Contact Detection and Local Stiffness Models

In minimally invasive telesurgery, obtaining accurate force information is difficult due to the complexities of in-vivo end effector force sensing. This constrains development and implementation of haptic feedback and force-based automated performance metrics, respectively. Vision-based force sensing approaches using deep learning are a promising alternative to intrinsic end effector force sensing. However, they have limited ability to generalize to novel scenarios, and require learning on high-quality force sensor training data that can be difficult to obtain. To address these challenges, this paper presents a novel vision-based contact-conditional approach for force estimation in telesurgical environments. Our method leverages supervised learning with human labels and end effector position data to train deep neural networks. Predictions from these trained models are optionally combined with robot joint torque information to estimate forces indirectly from visual data. We benchmark our method against ground truth force sensor data and demonstrate generality by fine-tuning to novel surgical scenarios in a data-efficient manner. Our methods demonstrated greater than 90% accuracy on contact detection and less than 10% force prediction error. These results suggest potential usefulness of contact-conditional force estimation for sensory substitution haptic feedback and tissue handling skill evaluation in clinical settings.

Simultaneous compensation of geometric and compliance errors for robotics with consideration of variable payload effects

In order to satisfy the high accuracy requirements of robotic applications, it is necessary to consider not only the geometric errors but also the compliance errors which are caused by the self-gravity of the link and the external payloads. A general error model is developed based on the modified Denavit-Hartenberg (DH) model. For the parameters in the error model, there is a coupling between the compliance coefficients and the link parameters, making it difficult to use only the compliance coefficients to compute the compliance errors due to external payloads. As the external payload for the robot manipulator varies, the parameter identification of the model should be conducted again. In this paper, a novel algorithm using a variable payload method is proposed to first identify the compliance coefficients using different payloads and end effector position information. Second, the kinematic parameter errors and link parameters are identified with the given compliance coefficients. Then, the algorithm generates a modified trajectory using the calibrated DH tables for the precision compensation. Simulation and experimental results demonstrate that the positioning accuracy can be improved by 80 % to 90 % even under different payloads. The root mean square, mean, maximum, and standard deviation of the residual errors by using the proposed algorithm could outperform the conventional kinematic algorithm.

Self-correcting gripping robotic arm for QR code based on hand-eye calibrationv

During the operation of a robotic arm, the inaccuracy of the end-effector position can seriously affect the overall performance of the robot. In order to significantly reduce the positional error of the actuator with minimal cost, we adopt a 2D code-assisted positioning method based on the principle of hand-eye calibration to negatively feedback correct the coordinates of the end-effector. This method establishes a robotic arm-camera system, which improves the performance and accuracy of the robotic arm.

A Comparative study of pseudoinverse and damped least squares approaches in inverse kinematics for a 5-DOF hydraulic arm

Abstract This paper presents a comparative study of two iterative methods for solving the inverse kinematics problem on a hydraulically actuated 5-DOF arm with non-standard geometries. The work aims to determine the joint angles required to achieve a desired end effector position and orientation, which indicates a specific displacement of the hydraulic actuators. A simulation model is used with the Pseudoinverse and damped least squares methods. The results show that using the model with both methods can be utilized to solve the inverse kinematics problem. The damped Least Squares method exhibits higher accuracy and robustness to singularities than the Pseudoinverse method, however, the Pseudoinverse method is more computationally efficient and can give results close to the damped least squares method but with some modifications. The paper concludes with implications of the findings and recommendations for future research, particularly in the application of these methods to real-world hydraulically actuated robotic systems.

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.

Shape Reconstruction of Extensible Continuum Manipulator Based on Soft Sensors.

Continuum manipulators can improve spatial adaptability and operational flexibility in constrained environments by endowing them with contraction and extension capabilities. There are currently desired requirements to quantify the shape of an extensible continuum manipulator for strengthening its obstacle avoidance capability and end-effector position accuracy. To address these issues, this study proposes a methodology of using silicone rubber strain sensors (SRSS) to estimate the shape of an extensible continuum manipulator. The way is to measure the strain at specific locations on the deformable body of the manipulator, and then reconstruct the shape by integrating the information from all sensors. The slender sensors are fabricated by a rolling process that transforms planar silicone rubber sensors into cylindrical structures. The proprioceptive model relationship between the strain of the sensor and the deformation of the manipulator is established with considering the phenomenon of torsion of the manipulator caused by compression. The physically extensible continuum manipulator equipped with three driving tendons and nine SRSS was designed. Comprehensive evaluations of various motion trajectories indicate that this method can accurately reconstruct the shape of the manipulator, especially under end-effector loads. The experimental results demonstrate that the mean (maximum) absolute position error of the endpoint is 1.61% (3.45%) of the manipulator length.

Deep reinforcement learning and decoupling proportional-integral-derivative control of a humanoid cable-driven hybrid robot

Aiming at the application of robots in service, medical treatment, rehabilitation, and other fields, a humanoid cable-driven hybrid robot by imitating the structure of human arm is designed in this article. The robot is composed of a cable–spool–pulley system, series mechanism, and coaxial spherical parallel mechanism, which can achieve six degrees of freedom movement in space. A challenge with cable driving is that the movement of the rear end joints (such as pitch and roll) can alter the length or tension of the cable driven by the frontend joints, resulting in joint coupling. This interference can lead to a decrease in the motion accuracy of the robotic arm. In addition, it also affects the durability of cables or mechanical components such as bearings and pulleys. Considering the joint motion coupling phenomenon caused by the cable-driven, the decoupling method is proposed, and the kinematic model of the robot is established. To solve the nonlinear coupling characteristics and the uncertainty of the dynamics parameters, a controller is proposed for the humanoid cable-driven hybrid robot, combining proportional-integral-derivative (PID) control based on decoupling method (DC-PID) and the double delay deep deterministic policy gradient (TD3) deep reinforcement learning algorithm. The trajectory tracking of the end-effector position and orientation are controlled by using DC-PID and TD3. And the simulation results show that the proposed control method has good trajectory tracking and convergence performance according to trajectory tracking error and training reward. Finally, the humanoid cable-driven hybrid robot prototype is developed. The experimental results of coupling compensation show that the average maximum error of the joint is reduced by 77.58% after considering the coupling compensation of the joint. The results of the controller validation experiments show that the DC-PID controller reduces the maximum error in each axis by 11.54%, 35.29%, and 40.16%, respectively, compared to the open-loop experiments.

Understanding human–robot interaction forces: a new mechanical solution

Nowadays, robots hold crucial roles in an increasing number of different fields, highlighting an ongoing transition to ever-closer collaboration between humans and machines. In this context, this new technological era has brought out safety issues and, consequently, robots need to be monitored with an appropriate control architecture and human–machine interaction forces should be correctly estimated. For this purpose, friction, inertia, external perturbation, and the intrinsic dynamic of the robots should be monitored. This specific work starts from the need to monitor human–robot interaction forces to ensure safety for users. A successful case study concerning the integration of additional sensors on a wrist robot that directly interacts with humans is shown. Its limits have been the inability to directly measure forces applied by users and the impossibility to know accurately the end-effector position. Firstly, introducing a force/torque sensor, the detection of the forces applied by the user to the robot has been enabled. The user’s force data have been used to measure force dissipation and, together with the smoothness of operation, to compare three different embeddable mechanisms. Moreover, the integration of a linear encoder allowed measuring the instantaneous end-effector position on a non-actuated linear guideway, consequently knowing the motor torque value and the force applied by the robot to the user. This has been compared to the interaction force estimated from the motor torques without the linear sensor. The error assessed between the force measured with the encoder and estimated without it is about 12.9%. These results demonstrate the importance of this new embedded system to detect human–machine interaction forces in an accurate way and prevent safety issues.

Multitask control of aerial manipulator robots with dynamic compensation based on numerical methods

This paper presents a control scheme for aerial manipulators which allows to solve different motion problems: end-effector position control, end-effector trajectory tracking control and path-following control. The scheme has two cascaded controllers: i) the first controller is a minimum norm controller based on numerical methods, it solves the three motion control problems just by modifying the controller references. Also, since the aerial manipulator robot is a redundant system, i.e., it has extra degrees of freedom to accomplish the task, it is possible to set other control objectives in a hierarchical order. As a secondary objective of the control it is proposed to maintain a desired configuration for the robotic arm during the task. ii) The second cascade controller is designed to compensate the dynamics of the system which main objective is to drive the velocity errors to zero. The coupled dynamic model of the robotic system (hexarotor and robotic arm) is presented. This model is usually developed as a function of the forces and torques. However, in this work, it is written as a function of reference velocities which are usual references for these vehicles. The proposed control algorithms are given with the corresponding stability and robustness analysis. Finally, to validate the control scheme, experimental tests are performed in a partially structured environment with an aerial manipulator conformed by an aerial platform and a 3DOF robotic arm.

Trajectory Planning, Kinematics, and Experimental Validation of a 3D-Printed Delta Robot Manipulator

This paper presents the implementation, trajectory planning, kinematics, and experimental validation of an open-source 3D-printed delta robot manipulator. The robot’s hardware consists of three servo motors, an Arduino Uno microcontroller, and a Pulse Width Modulation (PWM) servo module. The software includes a trapezoidal velocity profile planner and an inverse and forward kinematics solver to calculate the motor angles required to achieve a desired end-effector position in task space. The 3D printed parts were obtained from an open-source Thingiverse project and assembled to form the robot’s kinematic structure. The robot’s performance was evaluated in terms of its accuracy, repeatability, and maximum speed for a pick-and-place task. Experimental results show that the robot can achieve a positioning accuracy of 2.2 mm, with a top speed of 0.4 m/s, 30 picks per minute, and load carrying capacity up to 200 g. These results are satisfactory, considering the ease of assembly and the cost-effectiveness of the robot. The comparison of the calculated motor angles with actual motor angles obtained through additional potentiometer wires soldering shows promising results. The proposed robot’s cost-effective characteristics, utilization of open-source additive manufacturing, and motion planning algorithms make it suitable for various applications, including education, research, and small-scale industrial applications.

Model-Free Intelligent Control for Space Soft Robotic Manipulators

Given the advantages of softness, lightness, low cost, and interaction safety, inverse kinematic modeling and control of soft actuators has caused a research boom. However, in realizing dexterous manipulation of space large soft manipulators, it is much more difficult to achieve precise control not only because of the greater accumulation of errors in the multiple degrees of freedom and nonlinear properties of soft materials at large scales but also because of the inability of directly solving the inverse kinematics in the cases of singular pure elongation. In this work, a model-free intelligent kinematic control strategy is proposed for these problems that exhibit a mapping relationship between the output end-effector position and the input pressure. For multiple-degree-of-freedom robots, especially pneumatic soft manipulators, traditional inverse kinematic modeling methods are complex and inverse Jacobian matrix solution often encounters geometric singularities. To address this issue, this paper proposes an inverse kinematics–multilayer perceptron (IK-MLP) method for soft manipulators. In this strategy, the trained intelligent controller can be applied to control pneumatic manipulators without establishing a traditional inverse kinematic model. The control algorithm is experimentally tested based on the ground experiment system of the space soft manipulator. Simulations and experiments are carried out to validate the given model-free intelligent controller, proving that the IK-MLP method can effectively solve the singularity of inverse kinematics.

Visual Servo Control for Workspace Navigation of Nanorobot End-Effector Inside SEM

Despite of the promising advancements in the last decade, the majority of scanning electron microscope (SEM)-based nanomanipulation tasks remain manually performed. Even in automated tasks, human intervention is required, at least during the task preparatory stage, where both the object of interest and robot end-effector are adequately enclosed in the field of view (FOV) of SEM at moderate magnification. This paper proposes a fully automated visual servo control method for workspace navigation of nanorobot end-effector that actively maintains the end-effector position offset from the center of FOV during passive working scene zooming and translation operations. We also propose using the scaling image Jacobian matrix theory to adaptively establish the hand-eye relationship of the nanorobotic system at uncalibrated magnifications, without the need for hardware regulation. This proposed method for workspace navigation is applicable to almost all commercial nanomanipulation systems. To the authors’ best knowledge, there has been no dedicated research on this problem in the literature. Experiments show that the proposed method significantly improves workspace navigation efficiency by about two-thirds, even for a skilled operator. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Workspace navigation refers to the process of moving the FOV to visually enclose the object or feature of interest at a moderate magnification, which is prerequisite for initializing either an automated or manual nanomanipulation task. This process involves consecutive zooming of the SEM in and out, as well as translating the sample stage, which can cause the end-effector to move out of the FOV. Therefore, it is necessary to move the robot end-effector with visual assistance along workspace navigation to avoid unexpected collisions. Typically, skilled operators perform this process manually in almost all nanomanipulation tasks, which is tedious and time-consuming. Therefore, developing an automated visual servo control method for workspace navigation of end-effector will significantly contribute to the nanomanipulation community.