Inverse Kinematics Of Robot Manipulators Research Articles

Improved Bald Eagle Search Optimization Algorithm for the Inverse Kinematics of Robotic Manipulators.

The inverse kinematics of robotic manipulators involves determining an appropriate joint configuration to achieve a specified end-effector position. This problem is challenging because the inverse kinematics of manipulators are highly nonlinear and complexly coupled. To address this challenge, the bald eagle search optimization algorithm is introduced. This algorithm combines the advantages of evolutionary and swarm techniques, making it more effective at solving nonlinear problems and improving search efficiency. Due to the tendency of the algorithm to fall into local optima, the Lévy flight strategy is introduced to enhance its performance. This strategy adopts a heavy-tailed distribution to generate long-distance jumps, thereby preventing the algorithm from becoming trapped in local optima and enhancing its global search efficiency. The experiments first evaluated the accuracy and robustness of the proposed algorithm based on the inverse kinematics problem of manipulators, achieving a solution accuracy of up to 10-18 m. Subsequently, the proposed algorithm was compared with other algorithms using the CEC2017 test functions. The results showed that the improved algorithm significantly outperformed the original in accuracy, convergence speed, and stability. Specifically, it achieved over 70% improvement in both standard deviation and mean for several test functions, demonstrating the effectiveness of the Lévy flight strategy in enhancing global search capabilities. Furthermore, the practicality of the proposed algorithm was verified through two real engineering optimization problems.

Inverse Kinematics of Robotic Manipulators Based on Hybrid Differential Evolution and Jacobian Pseudoinverse Approach

Robot manipulators play a critical role in several industrial applications by providing high precision and accuracy. To perform these tasks, manipulator robots require the effective computation of inverse kinematics. Conventional methods to solve IK often encounter significant challenges, such as singularities, non-linear equations, and poor generalization across different robotic configurations. In this work, we propose a novel approach to solve the inverse kinematics (IK) problem in robotic manipulators using a metaheuristic algorithm enhanced with a Jacobian step. Our method overcomes those limitations by selectively applying the Jacobian step to the differential evolution (DE) algorithm. The effectiveness and versatility of the proposed approach are demonstrated through simulations and real-world experimentation on a 5 DOF KUKA robotic arm.

Modifications of Fully Resampled PSO in the Inverse Kinematics of Robot Manipulators

Modifications of Fully Resampled PSO in the Inverse Kinematics of Robot Manipulators

A reinforcement learning-based neighborhood search operator for multi-modal optimization and its applications

In this paper, a reinforcement learning-based neighborhood search operator (RLNS) is proposed for multi-modal optimization problems where the main novelties lie in the reinforcement learning-based neighborhood range selection strategy, the neighborhood subpopulation generation strategy and the local vector encirclement model. The reinforcement learning-based neighborhood range selection strategy is proposed to dynamically adjust the subpopulation size to address the issue of too many parameters to be adjusted in the multi-modal optimization algorithm based on the niching methods, while the neighborhood subpopulation generation strategy and the local vector encirclement model are designed with the hope of enhancing the individual’s ability to local exploitation to obtain more accurate solutions. To verify the effectiveness of the proposed RLNS, SSA-RLNS, PSO-RLNS and EO-RLNS are proposed by integrating the proposed RLNS with the existing sparrow search algorithm, particle swarm optimization and equilibrium optimizer. The performances of the proposed SSA-RLNS, PSO-RLNS, EO-RLNS and existing multi-modal optimization algorithms are tested in CEC2015 multi-niche benchmark functions. The experimental results show that the SSA-RLNS, PSO-RLNS and EO-RLNS could locate multiple global optimal solutions with satisfactory accuracy, which illustrate that the proposed RLNS could be successfully used to deal with multi-modal optimization problems by integrating with common population-based optimization algorithms. Finally, the SSA-RLNS is successfully applied in the inverse kinematics of robot manipulator.

A comparison of methods solving repeatable inverse kinematics for robot manipulators

A comparison of methods solving repeatable inverse kinematics for robot manipulators

Inverse Kinematics of Robot Manipulator Based on BODE-CS Algorithm

Differential evolution is a popular algorithm for solving global optimization problems. When tested, it has reportedly outperformed both robotic problems and benchmarks. However, it may have issues with local optima or premature convergence. In this paper, we present a novel BODE-CS (Bidirectional Opposite Differential Evolution–Cuckoo Search) algorithm to solve the inverse kinematics problem of a six-DOF EOD (Explosive Ordnance Disposal) robot manipulator. The hybrid algorithm was based on the differential evolution algorithm and Cuckoo Search algorithm. To avoid any local optimum and accelerate the convergence of the swarm, various strategies were introduced. Firstly, a forward-kinematics model was established, and the objective function was formulated according to the structural characteristics of the robot manipulator. Secondly, a Halton sequence and an opposite search strategy were used to initialize the individuals in the swarm. Thirdly, the optimization algorithms applied to the swarm were dynamically allocated to the Differential Evolution algorithm or the Cuckoo algorithm. Fourthly, a composite differential algorithm, which consisted of a dynamically opposite differential strategy, a bidirectional search strategy, and two other typically used differential strategies were introduced to maintain the diversity of the swarm. Finally, two adaptive parameters were introduced to optimize the amplification factor F and cross-over probability Cr. To verify the performance of the BODE-CS algorithm, two different tasks were tested. The experimental results of the simulation showed that the BODE-CS algorithm had high accuracy and a fast convergence rate, which met the requirements of an inverse solution for the manipulator.

A comparative analysis of metaheuristic algorithms for solving the inverse kinematics of robot manipulators

In this paper, a comparison in the performance of metaheuristic algorithms was performed for solving the inverse kinematics problem of redundant robot manipulators. First, a review of several popular metaheuristic techniques and their variants was made. Then, the forward kinematics for the 6-DOF UR5 universal robot and the 7-DOF Motoman SIA20D were obtained using the DH convention. Two optimization problems were defined to evaluate the performance of the different heuristic approaches in order to identify their weaknesses and strengths. The first one consists in solving the inverse kinematics only for the position of the defined Tool Center Point (TCP) of the manipulators; the second one, which is the major contribution of this work, extends the analysis of the studied algorithms to solve the inverse kinematics for a desired pose of the end-effector of the robot. To validate the robustness of each metaheuristic, 30 trials were performed for each optimization problem. Each trial consisted of finding the joint values for 50 random positions within the robot's workspace and validating how many optimal solutions were obtained during that trial. The results present the best and worst performing metaheuristics based on the optimal solutions obtained, standard deviation of the optimal solution and the execution time.

Iterative inverse kinematics for robot manipulators using quaternion algebra and conformal geometric algebra

Iterative inverse kinematics for robot manipulators using quaternion algebra and conformal geometric algebra

A modified firefly algorithm for the inverse kinematics solutions of robotic manipulators

The inverse kinematics of robotic manipulators consists of finding a joint configuration to reach a desired end-effector pose. Since inverse kinematics is a complex non-linear problem with redundant solutions, sophisticated optimization techniques are often required to solve this problem; a possible solution can be found in metaheuristic algorithms. In this work, a modified version of the firefly algorithm for multimodal optimization is proposed to solve the inverse kinematics. This modified version can provide multiple joint configurations leading to the same end-effector pose, improving the classic firefly algorithm performance. Moreover, the proposed approach avoids singularities because it does not require any Jacobian matrix inversion, which is the main problem of conventional approaches. The proposed approach can be implemented in robotic manipulators composed of revolute or prismatic joints of n degrees of freedom considering joint limits constrains. Simulations with different robotic manipulators show the accuracy and robustness of the proposed approach. Additionally, non-parametric statistical tests are included to show that the proposed method has a statistically significant improvement over other multimodal optimization algorithms. Finally, real-time experiments on five degrees of freedom robotic manipulator illustrate the applicability of this approach.

A parallel learning particle swarm optimizer for inverse kinematics of robotic manipulator

In this study, a novel parallel learning particle swarm optimizer (PLPSO) is proposed. The evolutionary strategy of the algorithm is quite different from that of the existing PSO algorithms. To enhance the global search capability of the particle swarm, the original particle swarm is divided into two parallel evolving independent particle subpopulations to explore the search space simultaneously. In addition, according to the evolutionary factor in each iteration, the poorly performing particles in the two subpopulations are spurred and learned to improve the search speed of the particle swarm. In the process of particle learning, delay information is added to the velocity update item to reduce the occurrence of local capture. Twenty-eight benchmark functions of CEC2013 are used to evaluate the performance of the proposed PLPSO algorithm. Numerous comparisons demonstrate that the performance of the PLPSO algorithm is better than that of other nine PSO algorithms. Afterwards, the PLPSO algorithm is applied to the inverse kinematics (IK) solution of a robotic manipulator. By comparing with other three intelligent algorithms, the PLPSO algorithm shows an excellent performance in solving the IK problem. Finally, tests are carried out on an UR5 manipulator to confirm the practicability of the proposed PLPSO algorithm further. Thus, the feasibility of using the PLPSO algorithm for solving the IK problem of a robotic manipulator is verified.

A General Approach Based on Newton’s Method and Cyclic Coordinate Descent Method for Solving the Inverse Kinematics

The inverse kinematics of robot manipulators is a crucial problem with respect to automatically controlling robots. In this work, a Newton-improved cyclic coordinate descent (NICCD) method is proposed, which is suitable for robots with revolute or prismatic joints with degrees of freedom of any arbitrary number. Firstly, the inverse kinematics problem is transformed into the objective function optimization problem, which is based on the least-squares form of the angle error and the position error expressed by the product-of-exponentials formula. Thereafter, the optimization problem is solved by combining Newton’s method with the improved cyclic coordinate descent (ICCD) method. The difference between the proposed ICCD method and the traditional cyclic coordinate descent method is that consecutive prismatic joints and consecutive parallel revolute joints are treated as a whole in the former for the purposes of optimization. The ICCD algorithm has a convenient iterative formula for these two cases. In order to illustrate the performance of the NICCD method, its simulation results are compared with the well-known Newton–Raphson method using six different robot manipulators. The results suggest that, overall, the NICCD method is effective, accurate, robust, and generalizable. Moreover, it has advantages for the inverse kinematics calculations of continuous trajectories.

A soft computing approach for inverse kinematics of robot manipulators

The solution of the inverse kinematics problem is an essential capability for robotic manipulators. This capability is used to solve tasks such as path planning, control of manipulators, object grasping, etc. In this paper, we present an approach for solving the inverse kinematics of robot arm manipulators using a soft computing approach. Given a desired end effector pose, the proposed approach is able to solve both the position and orientation for the inverse kinematic problem. In addition, the proposed approach avoids singularities configurations, since, it is based on the forward kinematics equations. We present simulations and experiments, where a comparative study among some selected soft computing algorithms is realized. The simulations and experiments illustrate the effectiveness of the proposed approach.

Solving Inverse Kinematics of Robot Manipulators by Means of Meta-Heuristic Optimisation

This paper presents the use of meta-heuristic algorithms (MHs) for solving inverse kinematics of robot manipulators based on using forward kinematic. Design variables are joint angular displacements used to move a robot end-effector to the target in the Cartesian space while the design problem is posed to minimize error between target points and the positions of the robot end-effector. The problem is said to be a dynamic problem as the target points always changed by a robot user. Several well established MHs are used to solve the problem and the results obtained from using different meta-heuristics are compared based on the end-effector error and searching speed of the algorithms. From the study, the best performer will be obtained for setting as the baseline for future development of MH-based inverse kinematic solving.

A Comparison of Damped Least Squares Algorithms for Inverse Kinematics of Robot Manipulators

A critical review of inverse kinematics algorithms for robots in presence of kinematic singularities is addressed in this paper. In particular, with the aim to assess the efficiency in handling joint velocity limits and the possibility that the target value is physically not reachable. Real-time control of redundant robot driven by operator can not guarantee, in fact, that the selected target corresponds to a non-singular configuration. On the other hand, activating the regularization, or damping, factor too far from the singularity corresponds to large tracking errors and severe velocity constraints. In addition, as it will be shown in the paper, reaching a singular configuration with an error different from zero usually affects the efficiency of several algorithms. Various approaches presented in the literature have been tested in different scenarios on the Kinova Jaco2, 7 degrees-of-freedom manipulator. Conclusions show that none of the tested algorithms performs in a satisfactory way.

Suboptimal approximations in repeatable inverse kinematics for robot manipulators

Abstract In this paper a repeatable inverse kinematic task was solved via an approximation of a pseudo-inverse Jacobian matrix of a robot manipulator. An entry configuration to the task was optimized and a task-dependent definition of an approximation region, in a configuration space, was utilized. As a side effect, a relationship between manipulability and optimally augmented forward kinematics was established and independence of approximation task solutions on rotations in augmented components of kinematics was proved. A simulation study was performed on planar pendula manipulators. It was demonstrated that selection of an initial configuration to the repeatable inverse kinematic task heavily impacts solvability of the task and its quality. Some remarks on a formulation of the approximation task and its numerical aspects were also provided.

Inverse Kinematic Solution of Robot Manipulator Using Hybrid Neural Network

Inverse kinematics of robot manipulator is to determine the joint variables for a given Cartesian position and orientation of an end effector. There is no unique solution for the inverse kinematics thus necessitating application of appropriate predictive models from the soft computing domain. Although artificial neural network (ANN) can be gainfully used to yield the desired results but the gradient descent learning algorithm does not have ability to search for global optimum and it gives slow convergence rate. This paper proposes structured ANN with hybridization of Gravitational Search Algorithm to solve inverse kinematics of 6R PUMA robot manipulator. The ANN model used is multi-layered perceptron neural network (MLPNN) with back-propagation (BP) algorithm which is compared with hybrid multi layered perceptron gravitational search algorithm (MLPGSA). An attempt has been made to find the best ANN configuration for the problem. It has been observed that MLPGSA gives faster convergence rate and improves the problem of trapping in local minima. It is found that MLPGSA gives better result and minimum error as compared to MLPBP.

FPGA-based hardware implementation of arctangent and arccosine functions for the inverse kinematics of robot manipulator

Purpose– The inverse kinematics in robot manipulator have to handle the arctangent and arccosine function. However, the two functions are complicated and need much computation time so that it is difficult to be realized in the typical processing system. The purpose of this paper is to solve this problem by using Field Programmable Gate Array (FPGA) to speed up the computation power.Design/methodology/approach– The Taylor series expansion method is firstly applied to transfer arctangent and arccosine function to a polynomial form. And Look-Up Table (LUT) is used to store the parameters of the polynomial form. Then the behavior of the computation algorithm is described by Very high-speed IC Hardware Description Language (VHDL) and a co-simulation using ModelSim and Simulink is applied to evaluate the correctness of the VHDL code.Findings– The computation time of arctangent and arccosine function using by FPGA need only 320 and 420 ns, respectively, and the accuracy is <0.01°.Practical implications– Fast computation in arctangent and arccosine function can speed up the motion response of the real robot system when it needs to perform the inverse kinematics function.Originality/value– This is the first time such to combine the Taylor series method and LUT method in the computation the arctangent and arccosine function as well as to implement it with FPGA.

Solving the Inverse Kinematics for Robot Manipulators using Modified Electromagnetism-like Algorithm with Record to Record Travel

A new modification of Electromagnetism-like (EM) algorithm which incorporating the Record-to-Record Travel (RRT) local search algorithm; namely MEMR has been developed to solve the problem of Inverse Kinematics (IK) for a four Degree-of-Freedom (DOF) manipulator. The proposed method is able to generate multiple robot configurations for the IK test performed at different end effect or positions. In addition, the comparison between the proposed MEMR and Genetic Algorithm (GA) was carried out using two mathematical test functions; De Jong and Rastrigin. The tests results show that the proposed MEMR is comparable in performance to GA in terms of both convergence speed and error rate.

A Fast Convergence Efficiency Method of Inverse kinematics for Robot Manipulators

A Fast Convergence Efficiency Method of Inverse kinematics for Robot Manipulators

2A1-E13 遺伝的アルゴリズムとニューラルネットワークを用いたロボットの運動学問題の解法

A new method for solving inverse kinematics of robot manipulator using genetic algorithm (GA) and neural network (NN) is proposed. This method is divided to three procedures as follows: first, forward kinematics is learned by NN. Second, training data for supervised learning for NN of inverse kinematics are generated by GA. In this calculation, the obtained NN of forward kinematics is used as the estimator for fitness value of chromosome. Third, inverse kinematics is learned by NN using this training data. The effectiveness of proposed method is confirmed by simulation.