Kinematic Model Of Robot Research Articles

Precise motion control for a space mining robot based on improved African vultures optimization

Space mining robots can develop and utilize abundant mineral resources in the outer space to solve the problem of the depletion of earth mineral resources. However, the motion errors of space mining robots in complex environments on the outer space surface of asteroids greatly hinder its applications. To bridge this research gap, a precise motion controller of the space mining robot is proposed in this study. Firstly, the kinematics model of robot’s wheels and the whole vehicle dynamics model in soft soil are established. Then, the optimal PID motion controller is developed based on the improved African vultures optimization algorithm (IAVOA). The Henon chaotic mapping, nonlinear adaptive incremental inertial weight factor and reverse learning competition strategy are introduced to optimize the initial population position, position update method and optimal solution output, respectively. Meanwhile, the excellent optimization performance of IAVOA is also validated by test results of nine benchmark functions. Lastly, the performance of controller is verified by simulations and experiments. The simulation results show that the proposed IAVOA-PID controller is superior to the original PID and AVOA-PID controller with faster response time and smaller overshoot. The experiment results show the space mining robot with the assistance of proposed motion controller can move with a trajectory error of less than 0.2 m and a motion error of less than 0.01 m.

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.

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.

Analysis of the PID Controller Parameters for A Surface Mobility Platform Mobile Robot

Surface mobility control is a fundamental challenge in robotics, and its applications range from autonomous vehicles to industrial automation. The main aim of the paper is to analyze the PID controller parameters for the speed control of a surface mobility platform mobile robot. MATLAB simulation toolbox and mathematical model of the DC motor are used to find the optimal PID controller parameters to complete the DC motor speed control system. For the SMP motion control system, the mobile robot kinematic model is supported as a differential drive system. In this paper, the PID controller parameters for the DC motor control system are analyzed with simulation results using various KP, KI, KD gains. The experimental results of the SMP mobile robot with optimal PID controller parameters are analyzed by driving on the rough, slope and even terrains. According to simulation results and experimental tests, the proposed system effectively controls the speed of the SMP mobile robot, demonstrating satisfactory performance in settling time, rise time, and system overshoot. Among PI and PID controllers, the designed PID controller can quickly control to reach the desired DC motor speed. Using the optimal PID coefficient parameters, all motors reached their desired speed in 0.12 seconds during simulations. In the experimental tests on various terrain (even, slope and rough), all motors achieved their desired speed simultaneously within 25 seconds.Keywords: Differential drive, PID controller, motion trajectory, real-time speed control. skid steering, SMP mobile robot, surface mobility control

Path Planning Algorithm of Orchard Fertilization Robot Based on Multi-Constrained Bessel Curve

Path planning is the core problem of orchard fertilization robots during their operation. The traditional full-coverage job path planning algorithm has problems, such as being not smooth enough and having a large curvature fluctuation, that lead to unsteady running and low working efficiency of robot trajectory tracking. To solve the above problems, an improved A* path planning algorithm based on a multi-constraint Bessel curve is proposed. First, by improving the traditional A* algorithm, the orchard operation path can be fully covered by adding guide points. Second, according to the differential vehicle kinematics model of the orchard fertilization robot, the robot kinematics constraint is combined with a Bessel curve to smooth the turning path of the A* algorithm, and the global path meeting the driving requirements of the orchard fertilization robot is generated by comprehensively considering multiple constraints such as the minimum turning radius and continuous curvature. Finally, the pure tracking algorithm is used to carry out tracking experiments to verify the robot’s driving accuracy. The simulation and experimental results show that the maximum curvature of the planned trajectory is 0.67, which meets the autonomous operation requirements of the orchard fertilization robot. When tracking the linear path in the fertilization area, the average transverse deviation is 0.0157 m, and the maximum transverse deviation is 0.0457 m. When tracking the U-turn path, the average absolute transverse deviation is 0.1081 m, and the maximum transverse deviation is 0.1768 m, which meets the autonomous operation requirements of orchard fertilization robots.

Design and analysis of a lower limb assistive exoskeleton robot.

In recent years, exoskeleton robot technology has developed rapidly. Exoskeleton robots that can be worn on a human body and provide additional strength, speed or other abilities. Exoskeleton robots have a wide range of applications, such as medical rehabilitation, logistics and disaster relief and other fields. The study goal is to propose a lower limb assistive exoskeleton robot to provide extra power for wearers. The mechanical structure of the exoskeleton robot was designed by using bionics principle to imitate human body shape, so as to satisfy the coordination of man-machine movement and the comfort of wearing. Then a gait prediction method based on neural network was designed. In addition, a control strategy according to iterative learning control was designed. The experiment results showed that the proposed exoskeleton robot can produce effective assistance and reduce the wearer's muscle force output. A lower limb assistive exoskeleton robot was introduced in this paper. The kinematics model and dynamic model of the exoskeleton robot were established. Tracking effects of joint angle displacement and velocity were analyzed to verify feasibility of the control strategy. The learning error of joint angle can be improved with increase of the number of iterations. The error of trajectory tracking is acceptable.

Direct and Inverse Kinematics of a 3RRR Symmetric Planar Robot: An Alternative of Active Joints

Existing direct and inverse kinematic models of planar parallel robots assume that the robot’s active joints are all at the bases. However, this approach becomes excessively complex when modeling a planar parallel robot in which the active joints are within one single kinematic chain. To address this problem, our article unveils an alternative for a 3RRR symmetric planar robot modeling technique for the derivation of the robot workspace and the analysis of its direct and inverse kinematics. The workspace was defined using a system of inequalities, and the direct and inverse kinematics models were generated using vectorial analysis and an optimized geometrical approach, respectively. The resulting models are systematically presented and validated. Two final model renditions are delivered supplying a thorough equation analysis and an applicability discussion based on the importance of the robot’s mobile platform orientation. The advantages of this model are discussed in comparison to the traditional modeling approach: whereas conventional techniques require the solution of complex eighth-degree polynomials for the analysis of the active joint configuration of these robots, these models provide an efficient back-of-the-envelope analysis approach that requires the solution of a simple second-degree polynomial.

Modeling and analysis of a parallel robotic system for lower limb rehabilitation with predefined operational workspace

The paper presents the mathematical modeling and analysis of LegUp, a novel parallel robotic system for lower limb rehabilitation of bedridden patients. The operational workspace of the robotic system is defined based on a set of parameters that describe the motion of the lower limb joints, which is natural in the rehabilitation task. To comply with this representation of the operational workspace, the parallel robot kinematic models describe the dependency between the robotic system actuators and the lower limb joints. Furthermore, the singularity analysis is achieved in the joint space, which shows whether the operational workspace is singularity-free. To achieve a feasible mechanical design for the prescribed operational workspace and to ensure safe operation, the design parameters of the parallel robotic system are determined based on a multi-objective optimization problem. Numerical simulations show that the operational workspace is singularity-free for the selected design parameters, which are then used to construct the experimental model of LegUp.

Composite continuum robots: Accurate modeling and model reduction

Models of continuum robots often trade off accuracy and speed. The constant curvature assumption model can perform fast calculations but with poor accuracy. Static models can obtain good calculation accuracy but with slower computation speed. In this paper, a precise and efficient method for establishing a non-constant curvature kinematic model for composite continuum robots is proposed. First, an algorithm based on the Beam Constraint Model is proposed to establish the static model of the continuum robot. The situation in which friction changes gradually in continuum robots is considered in the static model. Then, the Kepler elliptic curve is used to simplify the static model to build a non-constant curvature kinematic model of the continuum robot. Then, complex inverse kinematics solutions are transformed into explicit sets of equations by mathematical transformation. Finally, simulations and experiments are designed to demonstrate the algorithm proposed in this paper. The simulation results show that the proposed algorithm is 1572 times faster than the Levenberg–Marquardt algorithm. The experimental results show that the average error of the static model is 0.065 mm, accounting for 0.13% of its length. The maximum error is 0.309 mm, accounting for 0.618% of its length. The positioning accuracy of the non-constant curvature model proposed in this paper is 2.02 times that of the constant curvature model. The results show that the simplified kinematic model algorithm based on the static model has high accuracy and computational efficiency. This research is crucial for the practical application of continuum robots in engineering.

Comprehensive research and analysis on obstacle–singularity–joint limit avoidance of redundant robot

Redundant robots can complete other tasks while performing main task and have excellent motion performance. Although redundant robots have redundancy characteristics, they may still fall into singular configuration or cannot overcome joint limits due to the limitation of their own structure and motion law. Besides, currently, most of the research mainly focus on obstacle avoidance at the end of the robot. So comprehensive study is conducted on avoidance of obstacle, singularity, and joint limit of redundant robot. Firstly, the kinematics model of robot is obtained by D-H matrix method. Space vector distance method is proposed to calculate the position relationship between robot and obstacle, and potential function is constructed. Based on gradient projection method, using the damped generalized inverse and the weighted norm method, the mathematical models of obstacle avoidance, singularity avoidance, and joint limit avoidance are constructed. The simulation results show that the robot can avoid the obstacle in three-dimensional redundant space. At the same time, manipulability and minimum singular value of the robot are always positive. After adding the function of avoiding joint limit, during the whole control process, the motion range of joint angle is reduced and the angular velocity is relatively small, which ensure the motion stability of robot. Namely, the singular configuration and joint limit of robot are avoided. The research is of great significance for practical application of redundant robot.

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.

Design and Analysis of Bionic Continuum Robot With Helical Winding Grasping Function

Abstract In the field of grasping application, continuum robots are characterized by flexible grasping and high adaptability. Based on research on the physiological structure and winding method of seahorses, a continuum robot with a helical winding grasping function is presented in this paper. The continuum robot is driven by cables and uses a new flexural pivot with large deformation as a rotation joint. Firstly, based on the Serret–Frenet frame of the spatial cylindrical helix, the helical winding continuum robot is modeled and solved. The change rules of parameters such as the rotation angle of the joint and the helix parameters under the helical winding method are derived. Then, the compliance matrix of the joint is solved using the structural matrix method, and a stiffness model is established to analyze the relationship between the load and deformation of the continuum robot. The kinematics model of the continuum robot is established by using the modified Denavit–Hartenberg parameter method. The static model of the continuum robot is solved by vector analysis under the condition of considering gravity, and the relationship between the length change of cables and joint curvature is obtained. Finally, the stiffness model and static model of the continuum robot are verified by simulations and experiments. The test results show that within a certain radial range, the continuum robot has the function of helical winding and grasping for objects. Compared to the previous imitation seahorse tail robot, the helical winding structure not only provides a larger grasping area compared to in-plane form but also achieves a better bionic effect.

Neuro-Integral Sliding Mode Control for the Perturbed Unicycle Mobile Robot

This work proposes the design of a robust controller for the perturbed kinematic model of the unicycle mobile robot. The controller is based on integral sliding modes (ISMs) and the approximation provided by a differential neural network (DNN) for the tracking error dynamics, represented as an uncertain time-varying linear system. The methodology ensures asymptotic stability for the tracking error despite multiplicative disturbances in the control channel. The ISM compensates for the matched dynamics identified with the DNN. Then, a feedback controller minimizes the effect of unmatched dynamics by solving a set of Linear Matrix Inequalities. Simulation results show the feasibility of the proposed strategy against classical controllers.

Robust Control Design for the Unicycle Mobile Robot Based on Composite Lyapunov Functions

This work proposes the design of a robust time-varying controller for the perturbed kinematic model of the unicycle mobile robot. The controller is based on composite Lyapunov functions applied in time-varying linear systems. The methodology ensures the stability of the tracking error despite the presence of multiplicative disturbances in the control channel. The synthesis of the proposed controller requires the solution of a set of off-line Linear Matrix Inequalities and the solution of an optimization process regarding the composite Lyapunov approach. Simulation results show the feasibility of the proposed strategy against classical controllers.

Developing a Static Kinematic Model for Continuum Robots Using Dual Quaternions for Efficient Attitude and Trajectory Planning

Kinematic modeling is essential for planning and controlling continuum robot motion. The traditional Denavit Hartenberg (DH) model involves complex matrix multiplication operations, resulting in computationally intensive inverse solutions and trajectory planning. Solving position and orientation changes in continuum robots using the double quaternion rule can reduce computational complexity. However, existing dual quaternion methods are direct equational transformations of DH rules and do not give a complete modeling process. They usually require more interpretability when applying continuum robot kinematic modeling. This paper uses the dual quaternion method to establish a kinematic model of a continuum robot. It uses a two-section continuum robot model to compare the advantages of dual quaternion and traditional modeling methods. In addition, this paper proposes a five-polynomial interpolation algorithm based on the dual quaternion method for trajectory planning of continuum robots. This method accurately models spatial bending and torsional motions of singularity-free continuum robots.

Kinematic Modelling of a 3RRR Planar Parallel Robot Using Genetic Algorithms and Neural Networks

Kinematic modelling of parallel manipulators poses significant challenges due to the absence of analytical solutions for the Forward Kinematics (FK) problem. This study centres on a specific parallel planar robot, specifically a 3RRR configuration, and addresses the FK problem through two distinct methodologies: Genetic Algorithms (GA) and Neural Networks (NN). Utilising the Inverse Kinematic (IK) model, which is readily obtainable, both GA and NN techniques are implemented without the need for closed-loop formulations or non-systematic mathematical tools, allowing for easy extension to other robot types. A comparative analysis against an existing numerical method demonstrates that the proposed methodologies yield comparable or superior performance in terms of accuracy and time, all while reducing development costs. Despite GA’s time consumption limitations, it excels in path planning, whereas NN delivers precise results unaffected by stochastic elements. These results underscore the feasibility of using neural networks and genetic algorithms as viable alternatives for real-time kinematic modelling of robots when closed-form solutions are unavailable.

Kinematics Model Estimation of 4W Skid-Steering Mobile Robots Using Visual Terrain Classification

Accurate real-time kinematics model is very important for the control of a skid-steering mobile robot. In this study, the kinematics model of the skid-steering mobile robots was first designed based on instantaneous rotation centers (ICRs). Then, the extended Kalman filter (EKF) technique was applied to obtain the parameters of ICRs under the same specific terrain online. To adapt to different terrain environments, the fractal dimension-based SFTA (segmentation-based fractal texture analysis) method was used to extract features of different terrains, and the k-nearest neighbor (KNN) method was used to classify the terrains. In the case of real-time terrain recognition, the filter parameters of the EKF for estimating the ICRs are adjusted adaptively. Experiments on a real skid-steering mobile robot show that this method can quickly estimate the kinematics model of the robot in the case of terrain changes, and can meet the needs of practical applications. The average error of odometer estimation based on visual terrain classification is 0.06 m, while the average error of odometer estimation without terrain classification is 0.14 m.

Design and Implementation of a 3RRR Parallel Planar Robot

Parallel manipulators have a rigid structure and can pick up heavy objects. Therefore, a parallel manipulator has been developed based on the cooperation of three arms of a robotic system to make the whole system suitable for solving many problems such as materials handling and industrial automation. The three revolute joints are used to achieve the mechanism operation of the parallel planar robot. Those revolute joints are geometrically designed using an open-loop spatial robotic platform. In this paper, the geometric structure with three revolute joints is used to drive and analyze the inverse kinematic model for the 3RRR parallel planar robot. In the proposed design, three main variables are considered: the length of links of the 3RRR parallel planar robot, the base positions of the platform, and the joint angles’ geometry. Cayley-Menger determinants and bilateration are proposed to calculate these three variables to determine the final position of the platform and to move specific objects according to given desired trajectories. The proposed structure of the 3RRR parallel planar robot is simulated and different desired trajectories are tested to study the performance of the proposed stricter. Furthermore, the hardware implementation of the proposed structure is accomplished to validate the design in practical terms.