Forward Kinematic Model Research Articles

Integrated Intelligent Control of Redundant Degrees-of-Freedom Manipulators via the Fusion of Deep Reinforcement Learning and Forward Kinematics Models

Redundant degree-of-freedom (DOF) manipulators offer increased flexibility and are better suited for obstacle avoidance, yet precise control of these systems remains a significant challenge. This paper addresses the issues of slow training convergence and suboptimal stability that plague current deep reinforcement learning (DRL)-based control strategies for redundant DOF manipulators. We propose a novel DRL-based intelligent control strategy, FK-DRL, which integrates the manipulator’s forward kinematics (FK) model into the control framework. Initially, we conceptualize the control task as a Markov decision process (MDP) and construct the FK model for the manipulator. Subsequently, we expound on the integration principles and training procedures for amalgamating the FK model with existing DRL algorithms. Our experimental analysis, applied to 7-DOF and 4-DOF manipulators in simulated and real-world environments, evaluates the FK-DRL strategy’s performance. The results indicate that compared to classical DRL algorithms, the FK-DDPG, FK-TD3, and FK-SAC algorithms improved the success rates of intelligent control tasks for the 7-DOF manipulator by 21%, 87%, and 64%, respectively, and the training convergence speeds increased by 21%, 18%, and 68%, respectively. These outcomes validate the proposed algorithm’s effectiveness and advantages in redundant manipulator control using DRL and FK models.

The SG‐Climbot: An Adaptable, Efficient, Inspection and Repair Robot for Steam Generator Heat Transfer Tube Sheet

ABSTRACTThe steam generator plays a crucial role as a safety component and protective barrier in nuclear power plants. Regular inspection and repair of heat transfer tubes, which operate in high‐temperature, high‐pressure, corrosive, and abrasive environments for extended periods, are essential. Inspection and repair robots move inside the steam generator to conduct comprehensive inspections and evaluations of the heat transfer tubes. However, existing robots have relatively simple execution devices and fixed movement methods, resulting in poor adaptability to different specifications of tube sheets and limited flexibility in handling maintenance tasks. In response to these limitations, the SG‐Climbot, a quadruped crawling tube sheet inspection and repair robot, has been proposed. This robot is designed to adapt to full‐specification tube sheets and operate efficiently by conducting inspections while moving. By comparing different motion modes, a robot configuration with a quadruped parallel structure was suggested. Kinematic and static analyses were conducted, resulting in the development of both forward and inverse kinematic models, along with the identification of conditions leading to tipping. Using parametric modeling and optimization design, optimized design parameters were obtained. Finite element simulation analysis was performed on the overall structure and main components, leading to an optimized structural model. Finally, based on the design model and computational analysis, a prototype was developed and tested. The experimental results indicate that the robot has achieved the expected functionality and performance targets. Its efficient maintenance operation mode of conducting inspections while moving provides a basis for the autonomous and intelligent development of steam generators.

Trajectory planning and automatic docking of LNG five-axis loading arm

PurposeIn response to the challenges posed by the conventional manual flange docking method in the LNG (Liquefied Natural Gas) loading process, such as low positioning accuracy, constraints on production efficiency and safety hazards, this study analyzed the LNG five-axis loading arm’s main functions and structural characteristics.Design/methodology/approachAn automated solution for the joints of the LNG loading arm was designed. The forward kinematic model of the LNG loading arm was established using the Denavit–Hartenberg (D-H) parameter method, and its workspace was analyzed. The Newton–Raphson iteration method was employed to solve the inverse kinematics of the LNG loading arm, facilitating trajectory planning. The relationship between the target position and the joint variables was established to verify the stability of the arm’s motion. Flange center identification was achieved using the Hough transform function. Based on the ROS platform, combined with Gazebo and Rviz, an experimental simulation of automatic docking of the LNG loading arm was conducted.FindingsThe docking errors in the XYZ directions were all less than 0.8 mm, meeting the required docking accuracy. Moreover, the motion performance of the loading arm during docking was smooth and free of abrupt changes, validating its capability to accomplish the automatic docking task.Originality/valueThe proposed trajectory planning and automatic docking scheme can be used for the rapid filling of LNG filling arms and LNG tankers to improve the efficiency of LNG transportation. In guiding the docking, the proposed automatic docking scheme is an accurate and efficient way to improve safety.

Industrial Robot Trajectory Optimization Based on Improved Sparrow Search Algorithm

This paper proposes an enhanced multi-strategy sparrow search algorithm to optimize the trajectory of a six-axis industrial robot, addressing issues of low efficiency and high vibration impact on joints during operation. Initially, the improved D-H parametric method is employed to establish both forward and inverse kinematic models of the robot. Subsequently, a 3-5-3 mixed polynomial interpolation trajectory planning approach is applied to the robot. Building upon the conventional sparrow algorithm, a two-dimensional Logistic chaotic system initializes the population. Additionally, a Levy flight strategy and nonlinear adaptive weighting are introduced to refine the discoverer position update operator, while an inverse learning strategy enhances the vigilante position update operator. These modifications boost both the local and global search capabilities of the algorithm. The improved sparrow algorithm, based on 3-5-3 hybrid polynomial trajectory planning, is then used for the time-optimal trajectory planning of the robot. This is compared with traditional sparrow search algorithm and particle swarm algorithm optimization results. The findings indicate that the proposed enhanced sparrow search algorithm outperforms both the standard sparrow algorithm and the particle swarm algorithm in terms of convergence speed and accuracy for robot trajectory optimization. This can lead to the increased work efficiency and performance of the robot.

Trajectory planning for AGV based on the improved artificial potential field- A* algorithm

Abstract There are many redundant nodes and inflection points in the path planned by the traditional A* algorithm, leading to the inefficient trajectory planning of the Automatic Guided Vehicle(AGV) in the multi-static obstacles environment. The artificial potential field algorithm suffers from the problem of unreachable objectives and falling into optimal local value. This article studies the trajectory optimization of AGVs to improve the trajectory planning algorithm's iteration efficiency and shorten the trajectory's total length. This article establishes the forward kinematic and Unified Robot Description Format(URDF) model of the AGV and proposes the Artificial Potential Field-A*(APF-A*) algorithm for trajectory planning. The search cost and the number of turns are effectively optimized. The article simulates the APF-A* algorithm, the results are compared with the trajectory before optimization, and the optimized time is 60% less than that before optimization. The experimental platform of AGV trajectory planning is built, and the algorithm verification experiment of AGV trajectory planning is carried out. The experimental results show that the algorithm studied in this article achieves path smoothing and trajectory length optimization.

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.

Digital mapping of machine tool's volumetric and tracking errors left on the five axis tool paths

Five-axis contouring errors left on the parts contributed by feed drive servos, and intra- and inter-axis geometric errors are predicted along the five-axis tool paths. Quasi-static geometric errors are measured and modeled in the machine's workspace. Servo tracking errors of the three translational and two rotary drives are measured during machining or predicted from the CNC model. All errors are projected to the tooltip using a generalized screw theory-based forward kinematic model. The proposed model is validated experimentally on a CNC machining center for two test parts.

A logistic-tent chaotic mapping Levenberg Marquardt algorithm for improving positioning accuracy of grinding robot

The precision of workpiece machining is critically influenced by the geometric errors in the kinematics of grind robots, which directly affect their absolute positioning accuracy. To tackle this challenge, this paper introduces a logistic-tent chaotic mapping Levenberg Marquardt algorithm designed to accurately identify and compensate for this geometric error. the approach begins with the construction of a forward kinematic model and an error model specific to the robot. Then the algorithm is adopted to identify and compensate for the geometric error. The method establishes a mapping interval around the initial candidate solutions derived from iterative applications of the Levenberg Marquardt algorithm. Within this interval, the logistic-tent chaotic mapping method generates a diverse set of candidate solutions. These candidates are evaluated based on their fitness values, with the optimal solution selected for subsequent iterations. Empirical compensation experiments have validated the proposed method's precision and effectiveness, demonstrating a 6% increase in compensation accuracy and a 47.68% improvement in efficiency compared to existing state-of-the-art approaches. This process not only minimizes the truncation error inherent in the Levenberg Marquardt algorithm but also significantly enhances solution efficiency. Moreover, simulation experiments on grind processes further validate the method's ability to significantly improve the quality of workpiece machining.

Modeling and Control of a Novel Variable Stiffness Three DoFs Wrist

This study introduces an innovative design for a Variable Stiffness 3 Degrees of Freedom actuated wrist capable of actively and continuously adjusting its overall stiffness by modulating the active length of non-linear elastic elements. This modulation is akin to human muscular cocontraction and is achieved using only four motors. The mechanical configuration employed results in a compact and lightweight device with anthropomorphic characteristics, making it potentially suitable for applications such as prosthetics and humanoid robotics. This design aims to enhance performance in dynamic tasks, improve task adaptability, and ensure safety during interactions with both people and objects. The paper details the first hardware implementation of the proposed design, providing insights into the theoretical model, mechanical and electronic components, as well as the control architecture. System performance is assessed using a motion capture system. The results demonstrate that the prototype offers a broad range of motion ([55, −45]° for flexion/extension, ±48° for radial/ulnar deviation, and ±180° for pronation/supination) while having the capability to triple its stiffness. Furthermore, following proper calibration, the wrist posture can be reconstructed through multivariate linear regression using rotational encoders and the forward kinematic model. This reconstruction achieves an average Root Mean Square Error of 6.6°, with an R2 value of 0.93.

Construction and forward kinematics of a novel reconfigurable parallel mechanism

In this paper, a kind of hybrid kinematics chain with variable constraints is constructed by using a 6R spatial bifurcated chain and 4-DOF serial limbs, by using them, a 3-DOF Reconfigurable Parallel Mechanisms (RPM) was constructed, which has four motion modes: 3T, 2T1R, 2R1T, and 3R motion modes. Using screw theory, the change of wrench system in the hybrid kinematics chain caused by the reconfiguration of the 6R bifurcated chain is analyzed, which affects the wrench system of the moving platform (MP), and thus causes the reconfiguration of the parallel mechanism (PM). The triangular pyramid fixed to the MP was found as auxiliary geometry and used to intuitively describe the constraint relationship between joint axes in limbs. The latter was used to establish a unified forward kinematics model of the RPM in four motion modes. The general forward kinematics solution procedure for this type of RPM is given. The overall Jacobian matrix was obtained by screw theory for singularity analysis. The condition number of the Jacobian matrix measures the degree to which the mechanism is close to the singular configuration. Based on the Monte Carlo simulation, point cloud images representing the workspace of RPM were obtained.

Experimental Use Validation of the Master Hybrid Haptic Device Dedicated to Remote Center-of-Motion Tasks

The main objective of this paper is to discuss the experimental validation of a tele-operation system for remote center-of-motion tasks, such as laparoscopic surgery. This validation is based on the use of an extra sensor placed on the master manipulator. The tele-operation system is composed of a new hybrid haptic device (nHH) intended to be used as a master manipulator controlling a collaborative robot, used as a slave surgical robot. The resolution of the forward kinematic model (FKM) of the master device is performed experimentally thanks to the use of an extra sensor. The IMU, as the extra sensor, is installed on the serial part of the nHH device to measure the orientation and is enabled to solve the FKM of the parallel part of the nHH device. The use of an extra sensor reduces the calculation time, improves the accuracy of the KFM, and makes it suitable for real-time applications. The preliminary validation of the force feedback in the nHH workspace is validated. Experiments were conducted on the master–slave platform to validate the proposed approach. The results are promising, which proves that the nHH device presents a suitable performance for the desired task.

Influence of rotary axis angular positioning error motions on robotic probing

The accuracy of touch-trigger probing by a six-axis robotic manipulator is determined by the accuracy of the robot forward kinematic model to estimate the stylus sphere position from angular positions of rotary axes. Many conventional studies have employed the Denavit–Hartenberg (DH) model, containing position and orientation errors of the rotary axis average lines as error sources. This paper proposes the application of a new kinematic model, containing the angular positioning deviations of all the rotary axes, to the robotic probing. The probing accuracy is experimentally investigated in profile probing of a straightedge over the robot's workspace.

NU-Biped-4.5: A Lightweight and Low-Prototyping-Cost Full-Size Bipedal Robot

This paper presents the design of a new lightweight, full-size bipedal robot developed in the Humanoid Robotics Laboratory at Nazarbayev University. The robot, equipped with 12 degrees of freedom (DOFs), stands at 1.1 m tall and weighs only 15 kg (excluding the battery). Through the implementation of a simple mechanical design and the utilization of off-the-shelf components, the overall prototype cost remained under USD 5000. The incorporation of high-performance in-house-developed servomotors enables the robot’s actuation system to generate up to 2400 W of mechanical power, resulting in a power-to-weight ratio of 160 W/kg. The details of the mechanical and electrical design are presented alongside the formalization of the forward kinematic model using the successive screw displacement method and the solution of the inverse kinematics. Tests conducted in both a simulation environment and on the real prototype demonstrate that the robot is capable of accurately following the reference joint trajectories to execute a quasi-static gait, achieving an average power consumption of 496 W.

Programming 2DoF Robot Arm Based on Forward Kinematics using Arduino

This project's main goal is to use Arduino to program a 2-degree-of-freedom (2Dof) robot arm based on forward kinematics. The suggested system is made to precisely regulate the robot arm's motion for a variety of activities, such as pickand-place duties and assembly procedures. The robot arm can be precisely positioned and controlled thanks to the forward kinematics model, which determines the end effector's position based on the joint angles. The system is put into practice and put through its paces in a real-world setting, and the results demonstrate its ability to conduct precise movements with decent accuracy. The 2DoF Robot Arm can be utilized to automate complex processes and boost productivity in a variety of industries, including manufacturing, healthcare, and robotics research.

A Reinforcement Learning Approach for Continuum Robot Control

Rigid joint manipulators are limited in their movement and degrees of freedom (DOF), while continuum robots possess a continuous backbone that allows for free movement and multiple DOF. Continuum robots move by bending over a section, taking inspiration from biological manipulators such as tentacles and trunks. This paper presents an implementation of a forward kinematics and velocity kinematics model to describe the planar continuum robot, along with the application of reinforcement learning (RL) as a control algorithm. In this paper, we have adopted the planar constant curvature representation for the forward kinematic modeling. This choice was made due to its straightforward implementation and its potential to fill the literature gap in the field RL-based control for planar continuum robots. The intended control mechanism is achieved through the use of Deep Deterministic Policy Gradient (DDPG), a RL algorithm that is suited for learning controls in continuous action spaces. After simulating the algorithm, it was observed that the planar continuum robot can autonomously move from any initial point to any desired goal point within the task space of the robot. By analyzing the results, we wanted to recommend a future direction for research in the field of continuum robot control, specifically in the application of RL algorithms. One potential area of focus could be the integration of sensory feedback, such as vision or force sensing, to improve the robot’s ability to navigate complex environments. Additionally, exploring the use of different RL algorithms, such as Proximal Policy Optimization (PPO) or Trust Region Policy Optimization (TRPO), could lead to further advancements in the field. Overall, this paper demonstrates the potential for RL-based control of continuum robots and highlights the importance of continued research in this area.

Development of an automatic control system for a hydraulic pruning robot

Automatic pruning is capable of trimming trees into complex shapes efficiently and continuously. However, this technology faces more challenges under unstructured agricultural environments. In the present paper, we describe the development of a hydraulic disc-saw mounted pruning robot with a relatively low cost for automated geometric pruning of fruit trees based on a new automatic pruning scenario. A pruning control strategy based on rolling observations and continuous prediction algorithm was designed to precisely control the motion of hydraulic cylinders. A forward kinematic model was described using modified Denavit–Hartenberg (D-H) notation, and the accessible workspace for the end-effector was analyzed in the simulation. The inverse kinematics model based on geometry was established, which provided the foundation for the development of a control system together with the forward kinematics model. Performance tests showed a sufficient control accuracy within ± 1.8° of all cylinders. The results of the waypoint tracking tests suggest that an increase in the step-size from 20 mm to 60 mm not only increases the moving speed and improves tracking accuracy, but also increases the fluctuation of the end-effector in the Z-axis direction. The movement of the chassis can introduce new errors and results in a larger average absolute positional error along the X-axis. The average startup and stop lag of the control system was 0.55 s and 0.15 s, respectively. This study provides guidance for pruning robot path planning and lays the foundation for future iterations of autonomous pruning robots.

A Forward Solution Algorithm of 6RUS Parallel Mechanism Based on Dual Quaternion Method

The 6RUS parallel manipulator is a highly versatile and widely used robotic mechanism with six degrees of freedom. Its intricate kinematic structure and its capability to perform complex motion tasks have garnered significant research interest in recent years. The kinematic analysis of the 6RUS mechanism plays a crucial role in understanding its operational characteristics and optimizing its performance for various applications. In this paper, we present a state-of-the-art kinematic algorithm for the 6RUS parallel manipulator. Our algorithm is aimed at addressing the challenges associated with accurately determining the pose and motion of the end-effector relative to the base, considering the complexity of the mechanism’s architecture. By leveraging advanced mathematical modeling techniques and utilizing efficient computational algorithms, our proposed algorithm offers improved accuracy, efficiency, and robustness in determining the kinematic parameters of the 6RUS mechanism. The key contributions of this work include the development of a comprehensive forward and inverse kinematic model for the 6RUS parallel manipulator, incorporating the effects of joint constraints, singularities, and workspace limitations. We also present a detailed analysis of the algorithm’s performance in comparison to existing approaches, demonstrating its superiority in terms of computational efficiency and accuracy. The proposed kinematic algorithm holds significant potential for enhancing the design, control, and trajectory planning of 6RUS parallel manipulators. It provides a solid foundation for advanced applications such as robotic surgery, industrial automation, and virtual reality systems. The results presented in this paper contribute to the growing body of knowledge in parallel manipulator research and pave the way for future developments in the field.

Interpretation and analysis of seismic and analog modeling data of triangle zone: a case study from the frontal part of western Kura foreland fold-and-thrust belt, Georgia

2D seismic reflection profiles revealed the presence of a triangle zone at the frontal part of the western Kura foreland fold-and-thrust belt of the pro-wedge of the Greater Caucasus. To understand the triangle zone geometry, seismic interpretations should be substantiated by forward kinematic modeling, supported by analog experiments. This study presents a new structural model for the region by integrating field observations, well data, and seismic reflection data. East-West directed along-strike structural variation of the frontal thrust is observed on the interpreted seismic profiles which affected the fold geometry. The Bitsmendi breakthrough fault-propagation fold gradually transits into a wedge structure in the W-E direction and is represented by the triangle zone. The seismic profiles interpretation results completely match with analog models of similar triangle zones. The analysis of the experimental results helps us to further understand the kinematic evolution of natural systems and improve seismic interpretation. The triangle zone developed in the western part of the Bitsmendi breakthrough fault-propagation fold is related to double fault-bend fold structural wedges and is characterized by the presence of passive, and active wedges, and passive-backthrust and passive-forethrust.

Multi-objective trajectory optimization of the 2-redundancy planar feeding manipulator based on pseudo-attractor and radial basis function neural network

The establishment and solution of the inverse kinematic model is the key to improve the efficiency of trajectory optimization. To improve the trajectory smoothness and reduce energy consumption of multi-degree-of-freedom (MDOF) robots, this article presents the time-, jitter-, and energy-optimal trajectory optimization method based on pseudo-attractor and radial basis function neural network. Based on the geometric method, the forward kinematic model of MDOF robots is firstly established. The diversity of inverse kinematic solutions is reduced by determining redundant joints. Combined with the attractor theory, the time-adaptive allocation strategy can automatically endow time information with path points. On this basis, the 7-time polynomial interpolation method is used to fit discrete trajectory points and generate the initial trajectory without singularity points. Affected by the pseudo-attractor, radial basis function neural network is transformed into the improved radial basis function neural network (I-RBFNN) to optimize the initial trajectory. The 2-redundancy planar feeding manipulator (2-RPFM) is introduced to verify the effectiveness of the proposed method. Experiment and simulation results show that the proposed method is available in generating high-performance trajectories, which is beneficial to improve the production efficiency of the auto-body-out-panel stamping line.

Motion capture based calibration for industrial robots

Path accuracy of industrial robotic systems is of paramount importance for manufacturing applications. Many robot vendors provide guarantees of locational repeatability for robot arms down to 0.01 mm, however, this level of precision is meaningless if the system is not well calibrated. In many cases, where an offline programming environment is used, the physical system needs to match the behavior of the digital twin with minimal error. Calibration is thus required to ensure that the position and motion of the robot matches that of what was programmed. One approach is to use relative coordinate systems to offset the programmed path to account for any consistent deviations across the path. These offset coordinate systems can be created using techniques such as touch-based, laser-based, and/or vision-based systems. The offset coordinate system approach is used by major robot manufacturers and NC machines to arrive at a well-defined path. However, this approach assumes that the workspace is uniformly shifted, which is not always the case for industrial robots. Such systems can suffer from distortion in their coordinate space due to mechanical flexure, gearing backlash, and other factors that distort their workspace. To correct this distortion, we propose the use of a commercially available motion capture system that precisely monitors and reports the location of a Yaskawa industrial robotic arm. The positional and rotational information of the robot end-effector can be captured using this motion capture system and compared with that of the expected TCP (Tool Center Point) location derived from the forward kinematics model. The difference between these coordinates can then be used to determine and correct offsets from paths created using the digital twin. With motion capture driven path corrections, the accuracy of offline programed robots can be greatly improved without the need for exhaustively complex calibration processes.