Robot Kinematics Research Articles

A Hybrid Digital Twin Scheme for the Condition Monitoring of Industrial Collaborative Robots

Industrial collaborative robots play an essential role in smart manufacturing because they improve productivity while also ensuring workplace safety. However, the development of prognostic and health management systems to ensure the reliability of these robots has been a major challenge due to the lack of fault data. This paper proposed a digital twin scheme based on the fusion of the robot kinematic and dynamic models’ information down to the powertrains (i.e., the joints motor, and gear) along with the control algorithms and uncertainty accommodation based upon deep learning. The presented digital twin concept has the potential to propel simulation-based fault prediction. We also highlight and discuss challenges and opportunities around the development of the hybrid digital twin for condition monitoring of industrial collaborative robots.

Research on optimal path planning technology for industrial robots based on improved IDE algorithm

Abstract Realizing efficient and accurate positional movement of industrial robots is one of the key technologies to accelerate industrial development. In this paper, a four-wheel-drive McNamee mobile robot is selected as the research object, and the improved IPSO-IDE algorithm is proposed, which is combined with a PID controller to realize the accurate positioning and optimal path planning of industrial machines. The experimental results of robot kinematic parameter calibration show that the distance error of the robot calibrated with the algorithm is greatly reduced, and not only that, the IPSO-IDE algorithm reduces the average distance error of the robot to only 0.124 mm, which is much smaller than that of the PSO algorithm and the DE algorithm. The IPSO-IDE algorithm is capable of planning the optimal motion path in a short time, as demonstrated by the results of robot map environment simulation experiments. In the simulated map environment of 10 m × 10 m, the convergence speed of the algorithm’s planning path is 12.69 seconds, and the generated optimal path length is 15.0221 m, which is better than other algorithms. In conclusion, the proposed IPSO-IDE algorithm has an excellent performance in terms of path-planning capabilities for industrial robots.

Laser Scanner-Based Robotic Coordinate Measuring Machine

The objectives of the research presented in this paper are to design, integrate and demonstrate a robotic Coordinate Measuring Machine (CMM) for digitizing 3D geometries of objects to be used in reverse-engineering applications. The paper describes the mathematical model, the integration of the light detection and ranging (LiDAR) sensor with the automated positioning system and the programming used to attain the technology. The digital reconstruction of an object’s 3D model is achieved by applying forward robot kinematics along with homogeneous transforms to the point cloud detected by the LiDAR. The object’s geometric features are determined using 2nd-order polynomial best fitted curves of the scanned point clouds using the bisquare fit method. The CMM uses forward robot kinematics along with homogeneous transforms to programmatically compensate for geometric positioning errors resulting from deviations in position and orientation of the CMM components during assembly and from deviations in position and orientation of the workpiece when it is located in its mounting device. The instrument is shown to reconstruct with remarkable qualitative accuracy the 3D model of a turbine blade. Using a better-quality detecting sensor, the instrument can be used as well in automated quality control and inspection applications.

Smooth Distances for Second-Order Kinematic Robot Control

Smooth Distances for Second-Order Kinematic Robot Control

夹持-拉断式苹果采摘机器人设计与实验

For the standardized apple orchards in China, which are mainly dwarfed and densely planted, firstly, according to the spatial distribution characteristics of fruits within the tree canopy, a clamping-pull-off apple picking robot was developed by analyzing the parameters of apple cultivation and picking methods, in order to replace the manual harvesting operation. Then, the D-H method was used to establish the kinematic Equations of the apple-picking robot, the forward and inverse kinematic calculations were carried out, and the Monte Carlo method was used to analyze the workspace of the robot. Through the robot picking task planning and the simulation of the trajectory of the robotic arm, the scheme of the robot's picking strategy was given, and MATLAB software was applied to simulate the motion trajectory as well as to verify the feasibility of the trajectory planning scheme and the picking strategy. Finally, an apple-picking test bed was set up, the corresponding picking control system program was designed, and 45 apples were selected for picking tests. The results showed that during the robot's picking process, the average time for picking each fruit was 7.59 seconds, the fruit recognition success rate was 86.67%, and the picking damage rate was 5.13%.

Analysis of Positioning Accuracy in Case of Design Errors in the Installation of Mecanum Wheels of the Mobile Platform

Introduction. Mobile robots capable of omnidirectional movement are widely used in various fields of human activity. To provide high accuracy of positioning of omnidirectional platforms with mecanum wheels, it is required to develop their detailed mathematical models used in the construction of a motion control system. Due to the complicated design of the mecanum wheels, various errors may occur during the construction of omnidirectional platforms, including the error of installing such wheels on the platform. Its effect on the accuracy of the platform movement has not been studied before. This work aims at assessing the positioning errors that arise due to the presence of design errors in the installation of mecanum wheels, and analyzing the effect of these errors on the accuracy of program motion testing when using control at the kinematic level.Materials and Methods. The analysis of positioning accuracy was based on mathematical modeling of the platform kinematics, taking into account structural errors in the installation of mecanum wheels. To describe the relationship between the angular speeds of rotation of the wheels and the speeds of the platform, the conditions of nonslip of the contact points on the support surface were used. Numerical calculations were carried out in the Wolfram Mathematica package.Results. A formula was obtained for estimating errors in platform pseudovelocities under program control formed at the kinematic level. The estimation of the errors of the platform speeds for simple movements was carried out. According to the calculation results, it has been shown that the speed errors are significant for robots with mecanum wheels operating autonomously.Discussion and Conclusion. The calculation results demonstrated the significant impact of wheel installation errors on the positioning accuracy of the mecanum-platform, and confirmed the need to take into account these design errors when creating autonomous mecanum-platforms. The constructed model of the robot's kinematics makes it possible to predict errors in platform speeds that arise under program control, as well as deviations of the coordinates of the geometric center of the platform from the program motion. The proposed kinematic model can be used to improve the positioning accuracy through forming a platform motion control that compensates for the influence of wheel installation errors.

A novel saturated PID‐type observer‐based controller for wheeled mobile robots with a guaranteed performance considering path curvature

AbstractThis article proposes a novel saturated PID‐type formation controller for a class of nonholonomic wheeled mobile robots (WMRs) of type (m, s) with mobility m and steerability s. Since the path curvature causes a severe deviation of the followers from the leaders' trajectory in the corners, a new definition of output equations is suggested to construct the coordinates of a virtual reference point in the front of each follower based on the concept of the extended look‐ahead control that utilizes a corrective angle to compensate the trajectory curvature efficiently. A nonlinear transformation and the robot's kinematic and dynamic equations are heuristically combined to develop a novel second‐order Euler–Lagrange formulation of unconstrained errors from constrained errors. Then, a novel saturated PID‐type controller is proposed for WMRs to build a desirable formation with a prescribed performance. An innovative nonlinear observer is presented to estimate followers' velocities. An efficient mixture of a radial basis function neural network (RBFNN) and an adaptive mechanism is proposed to compensate for model uncertainties, external disturbances, and network approximation errors. Lyapunov's direct method verifies semi‐global uniform ultimate boundedness stability by estimating a gain‐dependent region of attraction. Numerical simulations finally show the efficiency of the proposed controller.

Mechanical intelligence simplifies control in terrestrial limbless locomotion.

Limbless locomotors, from microscopic worms to macroscopic snakes, traverse complex, heterogeneous natural environments typically using undulatory body wave propagation. Theoretical and robophysical models typically emphasize body kinematics and active neural/electronic control. However, we contend that because such approaches often neglect the role of passive, mechanically controlled processes (those involving "mechanical intelligence"), they fail to reproduce the performance of even the simplest organisms. To uncover principles of how mechanical intelligence aids limbless locomotion in heterogeneous terradynamic regimes, here we conduct a comparative study of locomotion in a model of heterogeneous terrain (lattices of rigid posts). We used a model biological system, the highly studied nematode worm Caenorhabditis elegans, and a robophysical device whose bilateral actuator morphology models that of limbless organisms across scales. The robot's kinematics quantitatively reproduced the performance of the nematodes with purely open-loop control; mechanical intelligence simplified control of obstacle navigation and exploitation by reducing the need for active sensing and feedback. An active behavior observed in C. elegans, undulatory wave reversal upon head collisions, robustified locomotion via exploitation of the systems' mechanical intelligence. Our study provides insights into how neurally simple limbless organisms like nematodes can leverage mechanical intelligence via appropriately tuned bilateral actuation to locomote in complex environments. These principles likely apply to neurally more sophisticated organisms and also provide a design and control paradigm for limbless robots for applications like search and rescue and planetary exploration.

Configuration Design and Kinematic Performance Analysis of a Novel 4-DOF Parallel Ankle Rehabilitation Mechanism with Two Virtual Motion Centers

Aiming at the problem that the existing ankle rehabilitation robot is difficult to fully fit the complex motion of human ankle joint and has poor human-machine motion compatibility, an equivalent series mechanism model that is highly matched with the actual bone structure of the human ankle joint is proposed and mapped into a parallel rehabilitation mechanism. The parallel rehabilitation mechanism has two virtual motion centers (VMCs), which can simulate the complex motion of the ankle joint, adapt to the individual differences of various patients, and can meet the rehabilitation needs of both left and right feet of patients. Firstly, based on the motion properties and physiological structure of the human ankle joint, the mapping relationship between the rehabilitation mechanism and ankle joint is determined, and the series equivalent model of the ankle joint is established. According to the kinematic and constraint properties of the ankle equivalent model, the configuration design of the parallel ankle rehabilitation robot is carried out. Secondly, according to the intersecting motion planes theory, the full-cycle mobility of the mechanism is proved, and the continuous axis of the mechanism is judged based on the constraint power and its derivative. Then, the kinematics of the parallel ankle rehabilitation robot is analyzed. Finally, based on the OpenSim biomechanical software, a human-machine coupling rehabilitation simulation model is established to evaluate the rehabilitation effect, which lays the foundation for the formulation of a rehabilitation strategy for the later prototype.

Dual quaternion operations for rigid body motion and their application to the hand–eye calibration

The dual quaternion plays an advantageous role in the field of robotic kinematics and dynamics due to its compact expression. It is well known that quaternion can be easily implemented as algebraic operations on vectors through matrix operators. Similarly, the dual matrix operators can convert dual quaternion operations to matrix operations. However, it has not received adequate attention, and thus there are very few applications at present. With the dual matrix operators of dual quaternion, this paper re-verifies the equivalency between the conjugate formula of unit dual quaternion and dual Euler–Rodrigues formula. To combine this equivalence with the homomorphic mapping of Lie groups, a theoretical correlation of the current hand-eye calibration methods is established. Motivated by the attempt to establish a more complete scheme for hand-eye calibration, a new simultaneous method based on the conjugate formula of dual quaternion is proposed. The method verifies that the rotation problem can be extended to the rigid-body transformation problem via the dual algebra. Finally, the simulation and experimental validations for the hand–eye calibration method are given.

ROMI: Design and Experimental Evaluation of a Linear Delta Robotic System for High-Precision Applications

In this paper, the design and experimental evaluation of a parallel robotic system based on a linear delta geometry is presented. The design considers the requirements for high-precision applications including workspace, motion resolution, and payload. The entire design process includes robot kinematics, control, and optimization, resulting in the demonstration of a working device. The robot structure offers a versatile and simplified design when compared with state-of-the-art devices being able to be adapted to perform different tasks while keeping the advantages of high precision with reduced complexity. The presented robot prototype was constructed and evaluated experimentally through three proof-of-concept experiments mimicking tasks requiring high motion precision such as microsurgery, semiconductor testing, and optical device alignment. The obtained results in the three experimental scenarios validate that the here-proposed design can achieve an average motion precision of ~3.3 ± 0.3 μm with varying load conditions, thus confirming its potential to be used for high-precision tasks in industrial and medical settings.

Optimal Design of Robotic Character Kinematics

The kinematic motion of a robotic character is defined by its mechanical joints and actuators that restrict the relative motion of its rigid components. Designing robots that perform a given target motion as closely as possible with a fixed number of actuated degrees of freedom is challenging, especially for robots that form kinematic loops. In this paper, we propose a technique that simultaneously solves for optimal design and control parameters for a robotic character whose design is parameterized with configurable joints. At the technical core of our technique is an efficient solution strategy that uses dynamic programming to solve for optimal state, control, and design parameters, together with a strategy to remove redundant constraints that commonly exist in general robot assemblies with kinematic loops. We demonstrate the efficacy of our approach by either editing the design of an existing robotic character, or by optimizing the design of a new character to perform a desired motion.

Virtual environment for assistant mobile robot

This paper shows the development of a virtual environment for a mobile robotic system with the ability to recognize basic voice commands, which are oriented to the recognition of a valid command of bring or take an object from a specific destination in residential spaces. The recognition of the voice command and the objects with which the robot will assist the user, is performed by a machine vision system based on the capture of the scene, where the robot is located. In relation to each captured image, a convolutional network based on regions is used with transfer learning, to identify the objects of interest. For human-robot interaction through voice, a convolutional neural network (CNN) of 6 convolution layers is used, oriented to recognize the commands to carry and bring specific objects inside the residential virtual environment. The use of convolutional networks allowed the adequate recognition of words and objects, which by means of the associated robot kinematics give rise to the execution of carry/bring commands, obtaining a navigation algorithm that operates successfully, where the manipulation of the objects exceeded 90%. Allowing the robot to move in the virtual environment even with the obstruction of objects in the navigation path.<

A Precise Calibration Method for the Robot-Assisted Percutaneous Puncture System

The precision and stability of the Robot-Assisted Percutaneous Puncture (RAPP) system have become increasingly crucial with the widespread integration of robotic technology in the field of medicine. The accurate calibration of the RAPP system prior to surgery significantly influences target positioning performance. This study proposes a novel system calibration method that simultaneously addresses system hand–eye calibration and robot kinematic parameters calibration, thereby enhancing the surgery success rate and ensuring patient safety. Initially, a Closed-loop Hand–eye Calibration (CHC) method is employed to rapidly establish transformation relationships among system components. These CHC results are then integrated with nominal robot kinematic parameters to preliminarily determine the system calibration parameters. Subsequently, a hybrid algorithm, combining the regularized Levenberg–Marquardt (LM) algorithm and a particle filtering algorithm, is utilized to accurately estimate the system calibration parameters in stages. Numerical simulations and puncture experiments were conducted using the proposed system calibration method and other comparative methods. The experimental results revealed that, among several comparative methods, the approach presented in this paper yields the greatest improvement in the puncture accuracy of the RAPP system, demonstrating the accuracy and effectiveness of this method. In conclusion, this calibration method significantly contributes to enhancing the precision, operational capability, and safety of the RAPP system in practical applications.

Agile robotic inspection of steel structures: A bicycle‐like approach with multisensor integration

AbstractThis paper introduces an innovative and streamlined design of a robot, resembling a bicycle, created to effectively inspect a wide range of ferromagnetic structures, even those with intricate shapes. The key highlight of this robot lies in its mechanical simplicity coupled with remarkable agility. The locomotion strategy hinges on the arrangement of two magnetic wheels in a configuration akin to a bicycle, augmented by two independent steering actuators. This configuration grants the robot the exceptional ability to move in multiple directions. Moreover, the robot employs a reciprocating mechanism that allows it to alter its shape, thereby surmounting obstacles effortlessly. An inherent trait of the robot is its innate adaptability to uneven and intricate surfaces on steel structures, facilitated by a dynamic joint. To underscore its practicality, the robot's application is demonstrated through the utilization of an ultrasonic sensor for gauging steel thickness, coupled with a pragmatic deployment mechanism. By integrating a defect detection model based on deep learning, the robot showcases its proficiency in automatically identifying and pinpointing areas of rust on steel surfaces. The paper undertakes a thorough analysis, encompassing robot kinematics, adhesive force, potential sliding and turn‐over scenarios, and motor power requirements. These analyses collectively validate the stability and robustness of the proposed design. Notably, the theoretical calculations established in this study serve as a valuable blueprint for developing future robots tailored for climbing steel structures. To enhance its inspection capabilities, the robot is equipped with a camera that employs deep learning algorithms to detect rust visually. The paper substantiates its claims with empirical evidence, sharing results from extensive experiments and real‐world deployments on diverse steel bridges, situated in both Nevada and Georgia. These tests comprehensively affirm the robot's proficiency in adhering to surfaces, navigating challenging terrains, and executing thorough inspections. A comprehensive visual representation of the robot's trials and field deployments is presented in videos accessible at the following links: https://youtu.be/Qdh1oz_oxiQ and https://youtu.be/vFFq79O49dM.

A Yaw tracking algorithm for head movement from inertial sensors data

Monitoring head movements is important in many aspects of life from medicine and rehabilitation to sports, and VR entertainment. In this study, we used recordings from two sensors, i.e. an accelerometer and a gyroscope, to calculate the angles of movement of the gesturing person’s head. For the yaw motion, we proposed an original algorithm using only these two inertial sensors and the detected motion type obtained from a pre-trained SVM classifier. The combination of the gyroscope data and the detected motion type allowed us to calculate the yaw angle without the need for other sensors, such as a magnetometer or a video camera. To verify the accuracy of our algorithm, we used a robotic arm that simulated head gestures where the angle values were read out from the robot kinematics. The calculated yaw angles differed from the robot’s readings with a mean absolute error of approx. 1 degree and the rate of differences between these values exceeding 5 degrees was significantly below 1 percent except for one outlier at 1.12%. This level of accuracy is sufficient for many applications, such as VR systems, human-system interfaces, or rehabilitation.

The design and kinematic representation of a soft robot in a simulation environment

AbstractThe increase of human presence in the subsea and seabed environments necessitates the development of more capable and highly dexterous, innovative underwater manipulators. Biomimetic soft-robot arms represent a promising candidate for such manipulation systems. However, the well-known modeling techniques and control theories of traditional rigid robots do not apply to soft robots. The challenges of kinematic and dynamic modeling of soft robots with infinite degrees of freedom require the development of dedicated modeling methods. A novel procedure for representing soft-robotic arms and their motion in a rigid-body simulation environment is proposed in this paper. The proposed procedure relies on the piecewise constant curvature approach to simplify the very complex model of hyper-redundant soft-robotic arms, making it suitable for real-time applications. The proposed method is implemented and verified to be used in model-mediated teleoperation of the soft arms of a biomimetic robotic squid designed for underwater manipulation as a case study.

Shape-controllable inverse kinematics of hyper-redundant robots based on the improved FABRIK method

AbstractHyper-redundant robots have good prospects for applications in confined space due to their high flexibility and slim body size. However, the super-redundant structure brings great challenges for its inverse kinematics with shape constraints. Unfortunately, traditional Jacobian pseudo-inverse-based inverse kinematics method and forward and backward reaching inverse kinematics (FABRIK) method are difficult to constrain the arm shape and realize trajectory tracking in confined spaces. To solve this problem, we propose a shape-controllable FABRIK method to satisfy the given path and shape constraints. Firstly, the kinematic model of the hyper-redundant robot is established, and the canonical FABRIK method is introduced. Based on the preliminary works, the single-layer improved FABRIK method is developed to solve the position and pointing inverse kinematics considering path environment and joint angle constraints instead of two-layer geometric iterations. For tracking the desired end roll angles, the polygonal virtual arm is designed. The real arm roll angle is achieved by controlling its winding on the virtual arm. In this way, the shape can be controlled. Finally, we compare the proposed method with other three approaches by simulations. Results show that the proposed method is more efficient and the arm shape is controllable.

Mobile Robot Path Planning Based on Kinematically Constrained A-Star Algorithm and DWA Fusion Algorithm

Path-planning research has been the key to mobile-robot-navigation technology. However, traditional path-planning algorithms have some shortcomings. To solve these problems, this paper proposes a fusion algorithm that combines the kinematical constrained A* algorithm with the Dynamic Window Approach (DWA) algorithm. The kinematical constrained A* algorithm can plan the global path, and then the DWA algorithm can plan the local path under the global path’s guidance. Firstly, combined with robot kinematics, we improve the node-expansion method and heuristic-function model of the A* algorithm, which improves the search efficiency, reduces the number of path bends and lowers the computational cost so that the path generated by the A* algorithm better meets the needs of robot motion. Secondly, we optimize the trajectory-evaluation function of the DWA algorithm so that the local paths planned by the DWA algorithm are smoother and more coherent, which is easier for robot-motion execution. Finally, we extract the key nodes from the global path planned by the A* algorithm to guide the DWA algorithm for local path planning and dynamic-obstacle avoidance and to make the local path closer to the global path. Through simulation and practical experiments, the effectiveness of the fusion algorithm proposed in this paper is verified.

The Parallel Solving Method of Robot Kinematic Equations Based on FPGA

In the implementation of robot motion control, complex kinematic computations consume too much central processing unit (CPU) time and affect the responsiveness of robot motion. To solve this problem, this paper proposes a parallel method for solving kinematic equations of articulated robots based on the coordinate rotation digital computer (CORDIC) algorithm. The method completes the fast calculation of the transcendental function based on the CORDIC algorithm, adopts the tree structure method to optimize the key computational paths of forward and inverse solutions, and designs a parallel pipeline to realize the low latency and high throughput of the kinematic equations. The experiments of the proposed method are validated based on the field-programmable gate array (FPGA) hardware experimental platform, and the experimental results demonstrate that the computational time to complete the entire kinematic equations is 4.68 μs, of which the computational time for the kinematic positive solution is 0.52 μs and the computational time for the kinematic inverse solution is 4.16 μs.