A numerical algorithm for solving robot inverse kinematics

Robotica ◽  
1989 ◽  
Vol 7 (2) ◽  
pp. 159-164 ◽  
Author(s):  
K. C. Gupta ◽  
V. K. Singh
Keyword(s):  
Inverse Kinematics ◽  
Computational Time ◽  
Robot Kinematics ◽  
Convergence Criteria ◽  
Euler Parameters ◽  
Rotational Error ◽  
Variable Step ◽  
Zero Reference ◽  
Step Algorithm ◽  
Predictor Corrector

SUMMARYAn extension of the inverse kinematics algorithm by Gupta and Kazerounian is presented. The robot kinematics is formulated by using the Zero Reference Position Method. Euler parameters and the related vector forms of the spatial rotation concatenation have been used to improve the efficiency of the velocity Jacobian computation. The joint rates are formally integrated by using a modified predictor-corrector method particularized to robot inverse kinematics – it is a strict descending, p(1)c(0 – n), variable step algorithm. The definitions of the rotational error and overall error measure have been revised. Depending upon the convergence criteria used, these modifications reduce the overall computational time by 20%.

scholarly journals A Dilated Trigonometrically Equipped Algorithm to Compute Periodic Vibrations through Block Milne’s Implementation

2018 ◽  
Vol 8 (4) ◽  
pp. 3126-3129
Author(s):  
J. G. Oghonyon ◽  
S. A. Bishop ◽  
K. S. Eke
Keyword(s):  
Error Control ◽  
Variable Step Size ◽  
Operational Mode ◽  
Convergence Criteria ◽  
Step Size ◽  
Variable Step ◽  
Predictor Corrector

This paper intends to investigate the use of a dilated trigonometrically equipped algorithm to compute periodic vibrations in block Milne's implementation. The block-Milne implementation is established by developing a block variable-step-size predictor-corrector method of Adam’s family using a dilated trigonometrically equipped algorithm. The execution is carried out using a block variable-step-size predictor-corrector method. This system has significant advantages that include the varying step-size and finding out the convergence-criteria and error control. Convergence-criteria and operational mode are discussed to showcase the accuracy and effectuality of the proposed approach.

Symmetric Multistep Methods Revisited: II. Numerical Experiments

1999 ◽  
Vol 173 ◽  
pp. 309-314 ◽  
Author(s):  
T. Fukushima
Keyword(s):  
Multistep Methods ◽  
Computational Time ◽  
Integration Time ◽  
Implicit Methods ◽  
Symmetric Methods ◽  
Celestial Bodies ◽  
The Stability ◽  
Predictor Corrector ◽  
Symmetric Multistep Methods ◽  
Integration Errors

AbstractBy using the stability condition and general formulas developed by Fukushima (1998 = Paper I) we discovered that, just as in the case of the explicit symmetric multistep methods (Quinlan and Tremaine, 1990), when integrating orbital motions of celestial bodies, the implicit symmetric multistep methods used in the predictor-corrector manner lead to integration errors in position which grow linearly with the integration time if the stepsizes adopted are sufficiently small and if the number of corrections is sufficiently large, say two or three. We confirmed also that the symmetric methods (explicit or implicit) would produce the stepsize-dependent instabilities/resonances, which was discovered by A. Toomre in 1991 and confirmed by G.D. Quinlan for some high order explicit methods. Although the implicit methods require twice or more computational time for the same stepsize than the explicit symmetric ones do, they seem to be preferable since they reduce these undesirable features significantly.

scholarly journals Finite-Horizon Kinetic Energy Optimization of a Redundant Space Manipulator

2021 ◽  
Vol 11 (5) ◽  
pp. 2346
Author(s):  
Alessandro Tringali ◽  
Silvio Cocuzza
Keyword(s):  
Kinetic Energy ◽  
Real Time ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Computational Time ◽  
Redundant Manipulators ◽  
Space Robotics ◽  
Optimal Method ◽  
End Effector ◽  
Global Optimal

The minimization of energy consumption is of the utmost importance in space robotics. For redundant manipulators tracking a desired end-effector trajectory, most of the proposed solutions are based on locally optimal inverse kinematics methods. On the one hand, these methods are suitable for real-time implementation; nevertheless, on the other hand, they often provide solutions quite far from the globally optimal one and, moreover, are prone to singularities. In this paper, a novel inverse kinematics method for redundant manipulators is presented, which overcomes the above mentioned issues and is suitable for real-time implementation. The proposed method is based on the optimization of the kinetic energy integral on a limited subset of future end-effector path points, making the manipulator joints to move in the direction of minimum kinetic energy. The proposed method is tested by simulation of a three degrees of freedom (DOF) planar manipulator in a number of test cases, and its performance is compared to the classical pseudoinverse solution and to a global optimal method. The proposed method outperforms the pseudoinverse-based one and proves to be able to avoid singularities. Furthermore, it provides a solution very close to the global optimal one with a much lower computational time, which is compatible for real-time implementation.

Robust and efficient forward, differential, and inverse kinematics using dual quaternions

2020 ◽  
pp. 027836492093194
Author(s):  
Neil T Dantam
Keyword(s):  
Inverse Kinematics ◽  
Forward Kinematics ◽  
Robot Kinematics ◽  
Dual Numbers ◽  
Dual Quaternion ◽  
Implicit Representation ◽  
Alternative Representation ◽  
Transformation Matrices ◽  
Dual Quaternions ◽  
Efficient Representation

Modern approaches for robot kinematics employ the product of exponentials formulation, represented using homogeneous transformation matrices. Quaternions over dual numbers are an established alternative representation; however, their use presents certain challenges: the dual quaternion exponential and logarithm contain a zero-angle singularity, and many common operations are less efficient using dual quaternions than with matrices. We present a new derivation of the dual quaternion exponential and logarithm that removes the singularity, we show an implicit representation of dual quaternions offers analytical and empirical efficiency advantages compared with both matrices and explicit dual quaternions, and we derive efficient dual quaternion forms of differential and inverse position kinematics. Analytically, implicit dual quaternions are more compact and require fewer arithmetic instructions for common operations, including chaining and exponentials. Empirically, we demonstrate a 30–40% speedup on forward kinematics and a 300–500% speedup on inverse position kinematics. This work relates dual quaternions with modern exponential coordinates and demonstrates that dual quaternions are a robust and efficient representation for robot kinematics.

A Comparative Study for an Inverse Kinematics Solution of an Aerial Manipulator Based on the Differential Evolution Method and the Modifi ed Shuffl ed Frog-Leaping Algorithm

2018 ◽  
Vol 19 (11) ◽  
pp. 714-724
Author(s):  
I. N. Ibrahim
Keyword(s):  
Differential Evolution ◽  
Trajectory Planning ◽  
Inverse Kinematics ◽  
Population Based ◽  
Computing Methods ◽  
Robot Kinematics ◽  
Aerial Manipulator ◽  
Specific Objective ◽  
Inverse Kinematics Problem ◽  
Aerial Vehicle

This paper focuses on the real-time kinematics solution of an aerial manipulator mounted on an aerial vehicle, the vehicle’s motion isn’t considered in this study. Robot kinematics using Denavit-Hartenberg model  was presented. The fundamental scope of this paper is to obtain a global online solution of design configurations with a weighted specific objective function and imposed constraints are fulfilled. Acknowledging the forward kinematics equations of the manipulator; the trajectory planning issue is consequently assigned to on an optimization issue. Several types of computing methods are documented in the literature and are well-known for solving complicated nonlinear functions. Accordingly, this study suggests two kinds of artificial intelligent techniques which are regarded as search methods; they are differential evolution (DE) method and modified shuffled frog-leaping algorithm (MSFLA). These algorithms are constrained metaheuristic and population-based approaches. moreover, they are able to solve the inverse kinematics problem taking into account the mobile platform additionally avoiding singularities since it doesn’t demand the inversion of a Jacobian matrix. Simulation results are carried out for trajectory planning of 6 degree-of-freedom (DOF) kinematically aerial manipulator and confirmed the feasibility and effectiveness of the supposed methods.

scholarly journals Inverse kinematics solution for robotic manipulator based on extreme learning machine and sequential mutation genetic algorithm

2018 ◽  
Vol 15 (4) ◽  
pp. 172988141879299 ◽  
Author(s):  
Zhiyu Zhou ◽  
Hanxuan Guo ◽  
Yaming Wang ◽  
Zefei Zhu ◽  
Jiang Wu ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Extreme Learning Machine ◽  
Inverse Kinematics ◽  
Robotic Manipulator ◽  
Computational Time ◽  
Improved Genetic Algorithm ◽  
Intelligent Algorithm ◽  
End Effector ◽  
Training Time ◽  
Learning Machine

This article presents an intelligent algorithm based on extreme learning machine and sequential mutation genetic algorithm to determine the inverse kinematics solutions of a robotic manipulator with six degrees of freedom. This algorithm is developed to minimize the computational time without compromising the accuracy of the end effector. In the proposed algorithm, the preliminary inverse kinematics solution is first computed by extreme learning machine and the solution is then optimized by an improved genetic algorithm based on sequential mutation. Extreme learning machine randomly initializes the weights of the input layer and biases of the hidden layer, which greatly improves the training speed. Unlike classical genetic algorithms, sequential mutation genetic algorithm changes the order of the genetic codes from high to low, which reduces the randomness of mutation operation and improves the local search capability. Consequently, the convergence speed at the end of evolution is improved. The performance of the extreme learning machine and sequential mutation genetic algorithm is also compared with that of a hybrid intelligent algorithm, and the results showed that there is significant reduction in the training time and computational time while the solution accuracy is retained. Based on the experimental results, the proposed extreme learning machine and sequential mutation genetic algorithm can greatly improve the time efficiency while ensuring high accuracy of the end effector.

Time-Dependent, Three Dimensional Nodal Transport Code Development Based on Unstructured Mesh

2014 ◽  
Author(s):  
Mingtao He ◽  
Hongchun Wu ◽  
Liangzhi Cao ◽  
Youqi Zheng ◽  
ShengCheng Zhou
Keyword(s):  
Direct Method ◽  
Three Dimensional ◽  
Computational Time ◽  
Neutron Kinetics ◽  
Nodal Method ◽  
Transport Code ◽  
Geometry Configuration ◽  
Nodal Transport ◽  
Complicated Geometry ◽  
Predictor Corrector

A space-time nodal transport code, DAISY, was developed to evaluate dynamic neutron behavior in innovative nuclear system. The steady transport process is based on an arbitrary triangles-z mesh nodal method which can treat complicated geometry configuration with enough precision and acceptable calculated quantity. This code employs the improved quasi-static method for neutron kinetics with a predictor-corrector scheme to improve computational efficiency. The direct method and the point approximation for neutron kinetics are also implemented into DAISY to evaluate the precision and efficiency of this predictor-corrector scheme. This code was verified by several transient benchmarks. It shows that the predictor-corrector scheme in DAISY can greatly reduce the computational time with enough precision.

Shift-Independent Model Reduction of Large-Scale Second-Order Mechanical Structures

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
Masih Mahmoodi ◽  
Kamran Behdinan
Keyword(s):  
Model Reduction ◽  
Large Scale ◽  
Second Order ◽  
Computational Time ◽  
Original Structure ◽  
Fe Model ◽  
Krylov Methods ◽  
Convergence Criteria ◽  
Large Scale Systems ◽  
Reduction Techniques

Nonmodal model order reduction (MOR) techniques present accurate and efficient ways to approximate input–output behavior of large-scale mechanical structures. In this regard, Krylov-based model reduction techniques for second-order mechanical structures are typically known to require a priori knowledge of the original system parameters, such as expansion points (or eigenfrequencies). The calculation of the eigenfrequencies of the original finite-element (FE) model can be significantly time-consuming for large-scale structures. Existing iterative rational Krylov algorithm (IRKA) addresses this issue by iteratively updating the expansion points for first-order formulations until convergence criteria are achieved. Motivated by preserving the model properties of second-order systems, this paper extends the IRKA method to second-order formulations, typically encountered in mechanical structures. The proposed second-order IRKA method is implemented on a large-scale system as an example and compared with the standard Krylov and Craig-Bampton reduction techniques. The results show that the second-order IRKA method provides tangibly reduced error for a multi-input-multi-output (MIMO) mechanical structure compared to the Craig-Bampton. In addition, unlike the standard Krylov methods, the second-order IRKA does not require the information on expansion points, which eliminates the need to perform a modal analysis on the original structure. This can be especially advantageous for large-scale systems where calculations of the eigenfrequencies of the original structure can be computationally expensive. For such large-scale systems, the proposed MOR technique can lead to significant reductions of the computational time.

Research and Improvement of the Step Tracking Technology in the Vehicle On-the-Move System

2014 ◽  
Vol 577 ◽  
pp. 412-416
Author(s):  
Xiao Dong Zhang ◽  
Yu Wang
Keyword(s):  
Computational Complexity ◽  
System Performance ◽  
Tracking Accuracy ◽  
Uniform Rotation ◽  
Initial Acquisition ◽  
Traditional Algorithm ◽  
Variable Step ◽  
Acquisition Speed ◽  
Step Algorithm ◽  
Tracking Technology

In order to improve the performance of the existing On-The-Move system, this paper studied a kind of step tracking technology based on the traditional algorithm. For the contradictions between the capture speed and precision performance on the initial acquisition, re-acquisition and auto tracking and controlling algorithm, this technology improved the initial acquisition stage. In the initial acquisition stage, the beacon AGC is distinguished. When the beacon AGC is below the specific threshold, there is a uniform rotation in the azimuth direction. When the AGC is above the threshold, the system turns to the step tracking stage based on variable step algorithm. Research showed that this technology has faster acquisition speed and higher tracking accuracy, maintains low computational complexity, and improves the system performance.

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