Robot Kinematics Research Articles

An Optimization Method for Multi-Robot Automatic Welding Control Based on Particle Swarm Genetic Algorithm

This paper introduces an optimization method for multi-robot automated control welding based on a Particle Swarm Genetic Algorithm (PSGA), aiming to address issues such as high costs, large footprint, and excessive production cycles in multi-robot welding production lines. The method first constructs a multi-axis robotic kinematic model to provide constraint conditions. Then, the PSO (particle swarm optimization) algorithm, which integrates penalty functions into the fitness evaluation, is used to determine the optimal welding path by simulating collective behavior within a group. The GA (genetic algorithm) encodes the position of the welding robot bases into chromosomes to find the optimal layout for coordinated control of multiple robots. The entire process is optimized according to welding standards and requirements. Additionally, a comprehensive production line performance estimation model was used to quantitatively analyze the new scheme. The results show that the optimized production line’s balance rate increased by 10%, the balance loss rate decreased by 10%, the smoothness index increased by 37.8%, the space costs reduced by 44.4%, the equipment demand reduced by 41.1%, the labor demand reduced by 50%, the total costs reduced by 10%, and the average product cycle time was reduced by 5.07 s. Finally, we tested the algorithm in various complex scenarios and compared its performance against mainstream algorithms within the context of this study. The results demonstrated that the optimized production line significantly improved efficiency while maintaining safety standards.

Region-Based Approach for Machining Time Improvement in Robot Surface Finishing

Traditionally, in robotic surface finishing, the entire workpiece is processed at a uniform speed, predetermined by the operator, which does not account for variations in the machinability across different regions of the workpiece. This conventional approach often leads to inefficiencies, especially given the diverse geometrical characteristics of workpieces that could potentially allow for different machining speeds. Our study introduces a region-based approach, which improves surface finishing machining time by allowing variable speeds and directions tailored to each region’s specific characteristics. This method leverages a task-oriented strategy integrating robot kinematics and workpiece surface geometry, subdivided by the clustering algorithm. Subsequently, methods for optimization algorithms were developed to calculate each region’s optimal machining speeds and directions. The efficacy of this approach was validated through numerical results on two distinct workpieces, demonstrating significant improvements in machining times. The region-based approach yielded up to a 37% reduction in machining time compared to traditional single-direction machining. Further enhancements were achieved by optimizing the workpiece positioning, which, in our case, added up to an additional 16% improvement from the initial position. Validation processes were conducted to ensure the collaborative robot’s joint velocities remained within safe operational limits while executing the region-based surface finishing strategy.

Upper limb exoskeleton rehabilitation robot inverse kinematics modeling and solution method based on multi-objective optimization

The inverse kinematics problem of exoskeleton rehabilitation robots is challenging due to the lack of a standard analytical model, resulting in a complex and varied solution process. This complexity is especially pronounced in redundant upper limb exoskeleton robots, where inefficient solutions hinder the robot’s ability to adapt to the kinematic shape of the upper limb. This paper proposes a modeling and solution method based on multi-objective optimization to address the inverse kinematics of upper limb exoskeleton robots. We analyzed and validated this method using a redundant upper limb exoskeleton rehabilitation robot system developed by ourselves. First, we established a multi-objective inverse kinematics solution model by defining the end-position function, joint motion comfort function, system energy consumption function, motion safety, and human-like constraints. Then, the solution was designed based on the Improved Equilibrium Optimization (IEO) algorithm and validated its computational performance in terms of optimization ability, accuracy, and robustness. Finally, we experimentally tested the inverse kinematics solution model with the IEO algorithm on discrete objectives and continuous training trajectories using a redundant upper limb exoskeleton rehabilitation robot system. The results show that by incorporating the joint comfort function, system energy consumption function, and human-like constraints into the inverse kinematics model, we can not only quickly solve the inverse kinematics of redundant upper limb exoskeleton robots but also significantly improve the robot’s motion shape. Furthermore, it has better solution accuracy and stronger robustness than other algorithms when solving this inverse kinematics model based on the IEO algorithm.

Trajectory error compensation method for grinding robots based on kinematic calibration and joint variable prediction

Trajectory accuracy, a crucial metric in assessing the dynamic performance of grinding robots, is influenced by the uncertain movement of the tool center point, directly impacting the surface quality of processed workpieces. This article introduces an innovative method for compensating trajectory errors. Initially, a strategy for error compensation is derived using differential kinematics theory. Subsequently, a robot kinematic calibration method utilizing ring particle swarm optimization (RPSO) is proposed to address static errors in the grinding robot. Simultaneously, a method for predicting robot joint variables based on a dual-channel feedforward neural network (DCFNN) is designed to mitigate dynamic errors. Finally, a simulation platform is developed to validate the proposed method. Simulation analysis using extensive data demonstrates an 89.3% improvement in absolute position accuracy and a 74.2% reduction in error fluctuation range, outperforming sparrow search algorithm (SSA), improved mayfly algorithm (IMA), multi-representation integrated predictive neural network (MRIPNN), etc. Algorithmic comparison reveals that kinematic calibration significantly reduces the average trajectory error, while joint variable prediction notably minimizes error fluctuation. Validation through trajectory straightness testing and a 3D printing propeller grinding experiment achieves a trajectory straightness of 0.2425 mm. Implementing this method enables achieving 86.1% surface machining allowance within tolerance, making it an optimal solution for grinding robots.

Automatic differential kinematics of serial manipulator robots through dual numbers

Dual Numbers are an extension of real numbers known for its capability of performing exact automatic differentiation of one-valued functions theoretically without error approximation. Also, Differential Kinematics of robots involves the computation of the Jacobian, which is a matrix of partial derivatives of the Forward Kinematic equations with respect to the robot’s joints. Thus, to perform the automatic calculation of the Jacobian matrix, this paper presents an extension of dual numbers composed of a scalar real part and a vector dual part, where the real part represents the angular value of the robot joint, and the dual part represents the direction of the corresponding partial derivative for each joint. The presented method was implemented in Matlab through Object Orientes Programming (OOP), and the results for calculating the Jacobian of the KUKA KR 500 robot model for 1000 random postures were subsequently compared in terms of execution time and Mean Squared Error (MSE) with other conventional methods: the geometric method, the symbolic method, and the finite difference method. The results showed a significant improvement in the computing time for calculating the Jacobian of the robotic model compared to the other methods, as well as a minimum MSE having as reference the numerical value of the symbolic calculations.

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.

Image‐based backbone reconstruction for non‐slender soft robots

AbstractOne advantage of soft robots to conventional robots is their continuous deformation, which makes them highly adaptable to their surroundings. To describe the kinematics of soft robots it is not sufficient to only know the position of the end‐effector. Instead, the steady state of a soft robot can be described by its backbone curvature. An image‐based backbone reconstruction method is used and adopted for a non‐slender soft robot to reconstruct the backbone curve using polynomials to describe an arc length‐dependent curvature. A constant curvature and cubic curvature polynomial have been tested to reconstruct the backbone curve. In the case of a pressurized soft robot without externally applied loads, the constant curvature polynomial can be used to reconstruct the backbone of the soft robot using an image‐based approach, yielding good agreement with the captured images. However, some care has to be put into the consideration of the soft robot geometry in this method, to guide the optimization procedure. From our findings, we can conclude that it is not necessary to apply markers to the soft robot to reconstruct the backbone, nor is it necessary to have a detailed geometric model of the soft robot to be used in a differential rendering process. An image‐based iterative‐closest‐point optimization method, with some carefully placed estimate points, to integrate the volumetric structure of the soft robot can yield good results for the reconstructed backbones.

Energy optimal path planning for wheeled mobile robots with circular obstacle

AbstractThe energy optimal motion planning algorithm for a differential drive robot with a circular obstacle in the maneuver space is introduced in this article. Rather than the traditional unicycle model, a non‐canonical state space model of the kinematics of a wheeled mobile robot is used to formulate the optimal control problem. The necessary conditions for optimality are formally derived using calculus of variations, resulting in constraints for the costates when the inequality constraint become active, revealing that the controls are required to be continuous. The optimality conditions permit decomposing the motion planning problem in two independent segments: prior to and after activation of the inequality constraints. Analytical expressions for the evolving states and control are found to be a function of Jacobi elliptic functions, permitting reducing the optimal control problem to a root‐finding problem. A comprehensive parametric study is included to demonstrate the impact on the optimal trajectories by varying the radius of the obstacle. The study shows that there are three distinct maneuver strategies with respect to the size of the obstacle. Furthermore, by including entering and exit time as optimization variables, a methodology for generalizing the development to any given motion scenario is developed and numerically illustrated.

Vision-guided robot calibration using photogrammetric methods

We propose novel photogrammetry-based robot calibration methods for industrial robots that are guided by cameras or 3D sensors. Compared to state-of-the-art methods, our methods are capable of calibrating the robot kinematics, the hand–eye transformations, and, for camera-guided robots, the interior orientation of the camera simultaneously. Our approach uses a minimal parameterization of the robot kinematics and hand–eye transformations. Furthermore, it uses a camera model that is capable of handling a large range of complex lens distortions that can occur in cameras that are typically used in machine vision applications. To determine the model parameters, geometrically meaningful photogrammetric error measures are used. They are independent of the parameterization of the model and typically result in a higher accuracy. We apply a stochastic model for all parameters (observations and unknowns), which allows us to assess the precision and significance of the calibrated model parameters. To evaluate our methods, we propose novel procedures that are relevant in real-world applications and do not require ground truth values. Experiments on synthetic and real data show that our approach improves the absolute positioning accuracy of industrial robots significantly. By applying our approach to two different uncalibrated UR3e robots, one guided by a camera and one by a 3D sensor, we were able to reduce the RMS evaluation error by approximately 85% for each robot.

Fusion IK: Solving inverse kinematics using a hybridized deep learning and evolutionary approach

Inverse kinematics is a core aspect of robot manipulation. This paper presents an approach to solving Inverse Kinematics (IK) for robots, including articulated industrial ones, combining deep learning with an evolutionary algorithm. Fusion IK passes the manipulator’s target and current joint values into a neural network, the results of which are then used to seed an evolutionary algorithm, Bio IK, to complete the solution of the inverse kinematics problem. Fusion IK allows for solving the position and orientation of the robot while attempting to minimize joint movement times. Comparisons between Fusion IK and its underlying algorithm Bio IK are tested on a six-degree-of-freedom articulated industrial robot as well as a 20-degree-of-freedom robot to explore the move times that Fusion IK produces. The comparisons show that the variations of the Fusion IK algorithm show comparable results to its underlying evolutionary Bio IK algorithm on a six-degrees-of-freedom articulated robot and improvements on a 20-degree-of-freedom robot without any additional hyperparameter tuning. The results show that Fusion IK could be of real value regarding the movement time and the quality of the obtained solutions upon further research, especially with higher degree-of-freedom robots.

Method for robot kinematic parameters identification based on position and orientation data obtained with laser tracker.

How to quickly and accurately identify the kinematic parameter errors is an important prerequisite for robot accuracy compensation. The laser tracker is used to measure and identify the kinematic parameters of the robot. The influence of laser tracker layout in robot pose measurement is analyzed, and the evaluation function of laser tracker layout is constructed to determine the optimal layout position. Then, the mapping relationship between the position and orientation deviation of the robot end and the deviation of each kinematic parameter is established, and the kinematic parameter identification model integrating the position and orientation information is constructed. The identification model is compared to the identification model based on position information to clarify the intrinsic reason of high accuracy. Next, aiming at the problem that the genetic algorithm is easy to prematurely converge to the local optimal solution, a hybrid genetic algorithm is constructed by introducing the simplex method to determine the optimal calibration pose set of the robot. On this basis, the results of robot kinematics parameter identification based on position measurement data, pose measurement data, and optimal calibration pose set are compared and analyzed through experiments, which verifies the effectiveness of the robot kinematics parameter identification model based on pose measurement data and optimization strategy.

Robot Calibration Sampling Data Optimization Method Based on Improved Robot Observability Metrics and Binary Simulated Annealing Algorithm

As the societal demand for precision in industrial robot operations increases, calibration can enhance the end-effector positioning accuracy of robots. Sampling data optimization plays an important role in improving the calibration effect. In this study, a robot calibration sampling point optimization method based on improved robot observability metrics and a Binary Simulated Annealing Algorithm is proposed. Initially, a robot kinematic model based on the Product of Exponentials (POE) model and a generalized error model is established. By utilizing the least squares method, the ideal pose transformation relationship between the robot’s base coordinate system and the laser tracker measurement coordinate system is derived, resulting in an error calibration model based on spatial single points. An improved robot observability metric combined with the Binary Simulated Annealing Algorithm (BSAA) is introduced to optimize the selection of calibration sampling data. Finally, the robot’s parameter errors are obtained using a nonlinear least squares method. Experimental results demonstrate that the average end-effector positioning error of the robot after calibration can be reduced from 0.356 mm to 0.254 mm using this method.

Introduction of a Framework for the Integration of a Kinematic Robot Arm Model in an Artificial Neural Network - Extended Kalman Filter Approach

The aim of this paper is to introduce a model in which systematic effects can be assigned according to their origin or mode of action. The approach intends to improve the positional accuracy of a robot arm. We show the impact of unaccounted model biases on estimated parameters when applying sequential approaches and conclude the necessity of jointly determining all influencing variables. Therefore, we propose a simultaneous estimation of transformation parameters, robot’s kinematic parameters and non-geometric parameters modelled by an artificial neural network (ANN) in further consequence. Thus, the main contribution of this paper is a new approach of the simultaneous estimation of the geometric and non-geometric components of a robot arm model. The integration of the geometric model (transformations, kinematic robot model) with the non-geometric one (ANN) is realised in the extended Kalman filter. The functionality of the algorithm has been proven on simulated data. The adaptive behaviour of machine learning approaches is made possible by an additional iteration of the ANN. The initialisation of the ANN parameters must not deviate from the nominal parameters by more than 10% so that the ANN can learn the non-geometric part. In this setup, the robot arm position corrections are reduced by 32.5%. A final sensitivity analysis proves the estimability of most kinematic parameters in the course of a future adaptive extension of the approach.

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.

Advances in the Kinematics of Hexapod Robots: An Innovative Approach to Inverse Kinematics and Omnidirectional Movement

Advances in the Kinematics of Hexapod Robots: An Innovative Approach to Inverse Kinematics and Omnidirectional Movement

A passive convex optimal control algorithm for teleoperating a redundant robotic arm in minimally invasive surgery

AbstractIn recent years, the remote center of motion (RCM) constraint has moved from purely mechanical to software implementation, enabling the use of serial manipulators in robotic‐assisted minimal invasive surgery. However, ensuring safety with software‐based RCM presents challenges. This article addresses this issue by introducing a novel control algorithm for a 7‐DOF redundant robotic arm, taking into account a software RCM while considering system passivity and kinematic constraints. The algorithm is both a control optimizer and a robot kinematics inversion, enabling precise and dexterous control for various surgical tasks and other control applications. By formulating a quadratic optimization problem under linear constraints, the algorithm guarantees the robotic arm's performance, safety, and stability under communication delay. Experimental validation demonstrates the effectiveness and accuracy of the control algorithm in executing a surgical training task (peg‐and‐ring) during bilateral teleoperation. The results highlight the successful implementation of the RCM constraint, ensuring patient safety and optimizing the manipulation capabilities of the robotic arm.

Objective performance indicators differ in obese and nonobese patients during robotic proctectomy

BackgroundRobotic surgery is perceived to be more complex in obese patients. Objective performance indicators, machine learning–enabled metrics, can provide objective data regarding surgeon movements and robotic arm kinematics. In this feasibility study, we identified differences in objective performance indicators during robotic proctectomy in obese and nonobese patients. MethodsEndoscopic videos were annotated to delineate individual surgical steps across 39 robotic proctectomies (1880 total steps). Thirteen patients were obese and 26 were nonobese. Objective performance indicators during the following steps were analyzed: splenic flexure mobilization, left colon mobilization, pelvic dissection, and rectal transection. ResultsThe following differences were noted during robotic proctectomy in obese patients: during splenic flexure mobilization, more arm swaps, longer camera path length and velocity; during left colon mobilization, longer step time, more arm swaps, higher camera-related metrics (movement, path length, velocity, acceleration, and jerk), greater dominant arm path length, moving time, and wrist articulation; during anterior pelvic dissection, longer energy activation time, camera path length, and moving time; during posterior pelvic dissection, lower nondominant arm velocity, jerk, and acceleration; during left pelvic dissection, longer energy activation time; during right pelvic dissection, greater camera-related metrics (movement, path length, moving time, and velocity); and during rectal transection, longer step time, more arm swaps, master clutch use and camera movements, greater dominant wrist articulation, and longer dominant arm path length. ConclusionWe report step-specific objective performance indicators that differ during robotic proctectomy for obese and nonobese patients. This is the first study to use objective performance indicators to correlate a patient attribute with surgeon movements and robotic arm kinematics during robotic colorectal surgery.

Research on designing dynamic model of TITAN-VIII quadruped robot based on the robot structure

Quadruped robots have many advantages over wheeled robots in that they have high mobility and can move on any terrain. However, the control problem of four-legged robots will be more complicated because the robot's kinematic model has a high order and the dynamic process is complicated, so it is necessary to implement order reduction methods when constructing kinematic equations for four-legged robots. The article proposes a simplified method to determine the kinematic equations for four-legged robots called TITAN-VIII. The Denavit-Hartenberg (D-H) rule is used to analyze the forward kinematics. The inverse kinematic equations are determined on the basis of mathematics and the structure of the robot's legs. The research results are simulated on MATLAB Simulink software.

Multi-Level Behavioral Mechanisms and Kinematic Modeling Research of Cellular Space Robot

The cellular space robot (CSR) is a new type of self-reconfigurable robot. It can adapt the variety of on-orbit service tasks with large space spans through multi-level reconfiguration mechanisms. As the CSR has a large configuration space, kinematic solving becomes a key problem affecting on-orbit operation capability, and kinematic automatic solving research must be conducted. In order to solve this problem, firstly, the cellular space robot system capable of realizing multi-level self-reconfiguration is proposed for the demand of space on-orbit service, and the kinematic equations of modules are constructed by considering a single module function using screw theory. Secondly, the kinematics of the cellular space robot are encapsulated and divided into multiple levels, and the multilevel-assembly relationship-description method for robotic systems is proposed based on graph theory. On this basis, the pathway-solving algorithm is proposed to express the robot organization reachability information. Finally, the module–organ–robot multilevel kinematics solving algorithm is proposed in combination with screw theory. In order to verify the effectiveness of the algorithm in this paper, numerical simulation is used to compare with the proposed algorithm. The results show that compared with the traditional algorithm, the method in this paper only needs to update part of the assembly relations after organ migration, which simplifies the kinematic modeling operation and improves the efficiency of kinematic computation.

Optimizing Redundant Robot Kinematics and Motion Planning via Advanced D-H Analysis and Enhanced Artificial Potential Fields

Optimizing Redundant Robot Kinematics and Motion Planning via Advanced D-H Analysis and Enhanced Artificial Potential Fields