Solution Of Inverse Kinematics Problem Research Articles

Towards accuracy improvement in solution of inverse kinematic problem in redundant robot: A comparative analysis

AbstractThe redundant manipulators have more DOFs (degree of freedoms) than it requires to perform specified task. The inverse kinematic (IK) of such robots are complex and high nonlinear with multiple solutions and singularities. As such, modern Artificial Intelligence (AI) techniques have been used to address these problems. This study proposed two AI techniques based on Neural Network Genetic Algorithm (NNGA) and Particle Swarm Optimization (PSO) algorithm to solve the inverse kinematics (IK) problem of 3DOF redundant robot arm. Firstly, the forward kinematics for 3 DOF redundant manipulator has been established. Secondly, the proposed schemes based on NNGA and PSO algorithm have been presented and discussed for solving the inverse kinematics of the suggested robot. Thirdly, numerical simulations have been implemented to verify the effectiveness of the proposed methods. Three scenarios based on triangle, circular, and sine-wave trajectories have been used to evaluate the performances of the proposed techniques in terms of accuracy measure. A comparison study in performance has been conducted and the simulated results showed that the PSO algorithm gives 7% improvement compared to NNGA technique for triangle trajectory, while 2% improvement has been achieved by the PSO algorithm for circular and sine-wave trajectories.

Self-Collision Avoidance Control of Dual-Arm Multi-Link Robot Using Neural Network Approach

The problem of mutual collisions of manipulators of a dual-arm multi-link robot (so-called self-collisions) arises during the performance of a cooperative technological operation. Self-collisions can lead to non-fulfillment of the technological operation or even to the failure of the manipulators. In this regard, it is necessary to develop a method for online detection and avoidance of self-collisions of manipulators. The article presents a method for detecting and avoiding self-collisions of multi-link manipulators using an artificial neural network by the example of the dual-arm robot SAR-401. A comparative analysis is carried out and the architecture of an artificial neural network for self-collisions avoidance control of dual-arm robot manipulators is proposed. The novelty of the proposed approach lies in the fact that it is an alternative to the generally accepted methods of detecting self-collisions based on the numerical solution of inverse kinematics problems for manipulators in the form of nonlinear optimization problems. Experimental results performed based on MATLAB model, the simulator of the robot SAR-401 and on the real robot itself confirmed the applicability and effectiveness of the proposed approach. It is shown that the detection of possible self-collisions using the proposed method based on an artificial neural network is performed approximately 10 times faster than approaches based on the numerical solution of the inverse kinematics problem while maintaining the specified accuracy.

Mathematical Modeling of Human Gait in a Rehabilitation Exoskeleton Using Gait Video Analysis Method

Purpose of research One of the ways to increase effectiveness of rehabilitation systems for patients with musculoskeletal disorders is the use of exoskeletons, which make it possible to ensure lower limbs movement according to the laws close to natural gait set by the rehabilitation therapist. The article considers a method based on construction of ankle joint motion trajectories (AJ) followed by synchronous determination of rotation angles of lower limb links based on numerical solution of inverse kinematics problem. It is known that the use of simplified laws of ancle joint movement and feet without taking into account anthropometric parameters of a patient leads to the formation of an incorrect gait and, as a result, a significant increase in rehabilitation time of a patient. Therefore, when constructing mathematical model of ankle motion patterns, it is proposed to use the method of video capture of marker points selected on AJ and foot, followed by processing and approximation of received signals using polynomials, which provides high accuracy of reproducing motion patterns. Purpose of research is to build motion laws of exoskeleton links along the trajectory of AJ motion based on a numerical solution of inverse kinematics problem.Methods. Experimental walking studies with the construction of AJ motion trajectory based on video fragment, smoothing and approximation of this trajectory and solving reverse kinematics problem are used to achive this goal.Results. Method for construction and processing of foot motion trajectory and finding kinematic characteristics of links motion for creation of exoskeleton motion patterns in gait is introduced.Conclusion. Simulation results shows that proposed methods of constructing motion trajectory and gait modeling of the exoskeleton make it possible to copy the gait of a person with high accuracy in rehabilitation process.

DESIGN OF OPTIMAL INVERSE KINEMATIC SOLUTION FOR HUMANOID ROBOTIC ARMS

One of the main problems in robotics is the Inverse Kinematics (IK) problem. In this paper, three optimization algorithms are proposed to solve the IK of Humanoid Robotic Arms (HRAs). A Particle Swarm Optimization (PSO), Social Spider Optimization (SSO), and Black Hole Optimization (BHO) algorithms are proposed in order to optimize the parameters of the proposed IK. Also, in this paper, each optimization method is applied on both right and left arms to find the desired positions and required angles with a minimum error. Denavit-Hartenberg (D-H) method is used to design and simulate the mathematical model of HRAs for both arms in which each arm has five Degree Of Freedom (DOF). The HRAs model is tested for performance by several positions to be reached by both arms in the same time to find which optimization algorithm is better. Optimal solution obtained by SSO, PSO and BHO algorithms are evaluated and listed in comparison table between them. These optimization algorithms are assessed by calculating the Computational Time (CT) and Root Mean Squared Error (RMSE) for the absolute error vector of the positions. Calculation and simulation results showed that BHO algorithm is better than the other optimization algorithms from point of view of CT and RMSE. The worst RMSE is 0.0864 was calculated using PSO algorithm. But longer CT is 7.6521 second, which was calculated using SSO. While the best RMSE and shorter CT.are and 3.0156 second respectively were calculated by BHO algorithm. Moreover, in this paper, the Graphical User Interface (GUI) is designed and built for motional characteristics of the HRAs model in the Forward Kinematics (FK) and IK. The optimization algorithms are designed using MATLAB package facilities to simulate the HRAs model and the solution of IK problem.

Analysis of computational efficiency for the solution of inverse kinematics problem of anthropomorphic robots using Gröbner bases theory

This article presents an analysis of computational efficiency to solve the inverse kinematics problem of anthropomorphic robots. Two approaches are investigated: the first approach uses Paul’s method applied to the matrix obtained by the Denavit–Hartenberg algorithm and the second approach uses Gröbner bases theory. With each approach, the problem of inverse kinematics for an anthropomorphic robot will be solved. When comparing each method, this article will demonstrate that the method using Gröbner bases theory is more computationally efficient.

Motion specification algorithms for both platform and arms of a mobile robot for planetary research

This article describes some aspects of the control system design for a four-wheel mobile platform with individual wheel-steering equipped with two redundant robotic arms. The considered control issues include different ways of platform maneuvering as well as a solution of inverse kinematics problem for a redundant arm with an original approach to redundancy resolution depending on operator’s intention.

Generalized solution for inverse kinematics problem of a robot using hybrid genetic algorithms

The robot control consists of kinematic control and dynamic control. Control methods of the robot involve forward kinematics and inverse kinematics (IK). In Inverse kinematics the joint angles are found for a given position and orientation of the end effector. Inverse kinematics is a nonlinear problem and has multiple solutions. This computation is required to control the robot arms. A Genetic Algorithm (GA) and Hybrid genetic algorithm (HGA) (Genetic Algorithm in conjunction with Nelder-Mead technique) are proposed for solving the inverse kinematics of a robotic arm. HGA introduces two concepts exploration, exploitation. In an exploration phase, the GA identifies the good areas in entire search space and then exploitation phase is performed inside these areas by using Nelder- mead technique Binary Simulated Crossover and niching strategy for binary tournament selection operator is used. Proposed algorithms can be used on any type of manipulator and the only requirement is the forward kinematic equations, which are easily obtained. As a case study inverse kinematics of a Two Link Elbow Manipulator and PUMA manipulator are solved using GA and HGA in MATLAB. The algorithm is able to find all solutions without any error

Algorithmic approach to geometric solution of generalized Paden–Kahan subproblem and its extension

Kinematics as a science of geometry of motion describes motion by means of position, orientation, and their time derivatives. The focus of this article aims screw theory approach for the solution of inverse kinematics problem. The kinematic elements are mathematically assembled through screw theory by using only the base, tool, and workpiece coordinate systems—opposite to conventional Denavit–Hartenberg approach, where at least n + 1 coordinate frames are needed for a robot manipulator with n joints. The inverse kinematics solution in Denavit–Hartenberg convention is implicit. Instead, explicit solutions to inverse kinematics using the Paden–Kahan subproblems could be expressed. This article gives step-by-step application of geometric algorithm for the solution of all the cases of Paden–Kahan subproblem 2 and some extension of that subproblem based on subproblem 2. The algorithm described here covers all of the cases that can appear in the generalized subproblem 2 definition, which makes it applicable for multiple movement configurations. The extended subproblem is used to solve inverse kinematics of a manipulator that cannot be solved using only three basic Paden–Kahan subproblems, as they are originally formulated. Instead, here is provided solution for the case of three subsequent rotations, where last two axes are parallel and the first one does not lie in the same plane with neither of the other axes. Since the inverse kinematics problem may have no solution, unique solution, or many solutions, this article gives a thorough discussion about the necessary conditions for the existence and number of solutions.

Trajectory generation for a walking in-pipe robot moving through spatially curved pipes

In this paper, a walking in-pipe robot is studied. The robot has six legs, each consisting of 3 links connected via rotary joints. The legs are attached to the robot’s body. The work is focused on the problem of generating desired position and orientation for the robot’s body, using a given footstep sequence. An iterative geometric algorithm for generating orientation sequence is proposed. The problem of finding the desired position of the center of mass of the robot’s body is formulated as a problem of minimizing stretching of the robot’s legs during steps. Also, an analytical solution for inverse kinematics problem has been given. All proposed algorithms do not require extensive calculation and use basic algebraic operations.

Position model computational complexity of walking robot with different parallel leg mechanism topology patterns

This article studies computational complexity of kinematic models for 2 patterns of 1UP-2UPS parallel mechanisms. These mechanisms are designed for hexapod walking robots applying real time control systems, which require the computing speed of kinematic models to be as swift as possible. The difference of these 2 patterns is that rotational axes of universal joints on limb 1 are reversed. In this paper, both forward and inverse kinematic models are formulated and it will be shown that both pattern I and II have analytical solutions for inverse kinematic problems. However, the forward models can be derived to univariate polynomial equations with different orders: 8th for pattern I and 4th for pattern II. It is known that the highest degree of polynomials can be solved analytically is 4, thus the computational complexity of pattern I is much higher than pattern II. In our prototypes, the forward kinematic model of pattern I costs 10 times more time than pattern II, hence pattern II is preferred for mobile robots.

Rigid Dynamics Solution Methodology for3-PSU Parallel Kinematic Manipulators

In the world of robotics, the parallel kinematic manipulators have proved their unique potentials like rigid structural capacities, better dynamic behaviours, and excellent spatial positional accuracy for many applications. One of the prime focus areas of the paper is to test and to establish a simplified novel approach for the Inverse Kinematics problem solution for a 3-PSU Parallel Kinematic Manipulator platform. Additionally, the methodology for simulation of Inverse Kinematics has been checked and verified. The obtained solution is further used for positional simulation of virtual prototype of 3-PSU PKM using Pro/Mechanism module. Further, these derived data is used for simulation of the Rigid Dynamics Solution for PKM (considering inertial forces acting on actuator) is also simulated in case of circular contouring.

The Inverse Kinematic Problem Solution for the Slider-crank Mechanism-based Parallel Structure Manipulator with Three Degrees of Freedom

The Inverse Kinematic Problem Solution for the Slider-crank Mechanism-based Parallel Structure Manipulator with Three Degrees of Freedom

Neural-Networks-Based Inverse Kinematics for a Robotic Manipulator

The solution of inverse kinematics problem of robotic manipulator is a fundamental problem in robot control. This paper involves the study of forward and inverse kinematics of a robotic manipulator platform with revolute joints. The (Denavit-Hartenberg) kinematic model of the prescribed manipulator is presented to robot links and joints. In addition inverse kinematics solution has been provided using geometric approach. This solution is used to develop a dataset used to train three artificial feed forward neural networks (ANN). Each network is used to calculate one joint variable using position and orientation of the end effector as an input. Experimental results have shown a good mapping over the working area of the robot with smaller RMS error than that reported in the cited literature.

A neural-network committee machine approach to the inverse kinematics problem solution of robotic manipulators

In robotics, inverse kinematics problem solution is a fundamental problem in robotics. Many traditional inverse kinematics problem solutions, such as the geometric, iterative, and algebraic approaches, are inadequate for redundant robots. Recently, much attention has been focused on a neural-network-based inverse kinematics problem solution in robotics. However, the result obtained from the neural network requires to be improved for some sensitive tasks. In this paper, a neural-network committee machine (NNCM) was designed to solve the inverse kinematics of a 6-DOF redundant robotic manipulator to improve the precision of the solution. Ten neural networks (NN) were designed to obtain a committee machine to solve the inverse kinematics problem using separately prepared data set since a neural network can give better result than other ones. The data sets for the neural-network training were prepared using prepared simulation software including robot kinematics model. The solution of each neural network was evaluated using direct kinematics equation of the robot to select the best one. As a result, the committee machine implementation increased the performance of the learning.

A neuro-simulated annealing approach to the inverse kinematics solution of redundant robotic manipulators

The neural-network-based inverse kinematics solution is one of the recent topics in the robotics because of the fact that many traditional inverse kinematics problem solutions such as geometric, iterative and algebraic are inadequate for redundant robots. However, since the neural networks work with an acceptable error, the error at the end of inverse kinematics learning should be minimized. In this study, simulated annealing (SA) algorithm was used together with the neural-network-based inverse kinematics problem solution robots to minimize the error at the end effector. The solution method is applied to Stanford and Puma 560 six-joint robot models to show the efficiency. The proposed algorithm combines the characteristics of neural network and an optimization technique to obtain the best solution for the critical robotic applications. Three Elman neural networks were trained using separate training sets and different parameters, since one of them can give better results than the others can. The best result is selected within three neural network results by computing the end effector error via direct kinematics equation of the robotic manipulator. The decimal part of the neural network result was improved up to 10 digits using simulated annealing algorithm. The obtained best solution is given to the simulated annealing algorithm to find the best-fitting 10 digits for the decimal part of the solution. The end effector error was reduced significantly.

Exact solution of inverse kinematic problem of 6R serial manipulators using Clifford Algebra

SUMMARYIn this paper, Clifford Algebra is used to model and facilitate solving the inverse kinematic problem for robots with only two consecutive parallel axes. It is shown that when a solution exists, it is usually the case that one of the angles of rotation can be arbitrarily chosen from a union of intervals. The remaining angles are then uniquely determined. Of course, there are cases when no solution exists, such as when the object is out of reach. But typically, when solutions exist, there are infinitely many sets of solutions.

A genetic algorithm approach to a neural-network-based inverse kinematics solution of robotic manipulators based on error minimization

The solution of the inverse kinematics problem is fundamental in robot control. Many traditional inverse kinematics problem solutions, such as the geometric, iterative, and algebraic approaches, are inadequate for redundant robots. Recently, much attention has been focused on a neural-network-based inverse kinematics problem solution in robotics. However, the precision of the result obtained from a neural network requires improvement for certain sensitive tasks. In this paper, neural network and genetic algorithms are used together to solve the inverse kinematics problem of a six-joint Stanford robotic manipulator to minimize the error at the end effector. The proposed hybrid approach combines the characteristics of neural networks and evolutionary techniques to obtain more precise solutions. Three Elman neural networks were trained using separate training sets because one of the sets yields better results than the other two. The floating-point portions of each network were placed in the initial population of the genetic algorithm with the floating-point portions from randomly generated solutions. The end-effector position error was defined as the fitness function, and the genetic algorithm was implemented. Using this approach, the floating-point portion of the neural-network result was improved by up to ten significant digits using a genetic algorithm, and the error was reduced to micrometer levels. These results were compared with those from studies in the literature and found to be significantly better.

A neuro-genetic approach to the inverse kinematics solution of robotic manipulators

In this paper, a neuro-genetic approach is proposed for the inverse kinematics problem solution of robotic manipulators. The proposed solution method is based on using neural networks and genetic algorithms in a hybrid system. Neural networks have been used by many researchers in the inverse kinematics solution. Since the neural networks work with an acceptable error, the error at the end of learning has to be minimized for sensitive applications. This study is based on using genetic algorithms to minimize this error. A case study is presented for a 6 degree of freedom robot. In the neural network part, three Elman networks are separately trained and then used in parallel since one Elman network may give better result than the other two ones. These three results are placed in the initial population of the genetic algorithm. The end effector position error is defined as the fitness function and genetic algorithm is implemented. Thus, the error is reduced in micrometer levels. Key words: Elman neural networks, error minimization, six-degree-of-freedom robot, genetic algorithms, robotics.

Reliability-based approach to the inverse kinematics solution of robots using Elman's networks

The solution of inverse kinematics problem of redundant manipulators is a fundamental problem in robot control. The inverse kinematics problem in robotics is the determination of joint angles for a desired cartesian position of the end effector. For the solution of this problem, many traditional solutions such as geometric, iterative and algebraic are inadequate if the joint structure of the manipulator is more complex. Furthermore, many neural network approaches have been done to this problem. But the neural network-based solutions are not much reliable due to the error at the end of learning. Therefore, a reliability-based neural network inverse kinematics solution approach has been presented, and applied to a six-degrees of freedom (dof) robot manipulator in this paper. The structure of the proposed method is based on using three networks designed parallel to minimize the error of the whole system. Elman network, which has a profound impact on the learning capability and performance of the network, is chosen and designed according to the proposed solution method. At the end of parallel implementation, the results of each network are evaluated using direct kinematics equations to obtain the network with best result.

High accuracy spline interpolation for 5-axis machining

This article presents a new algorithm for simultaneous 5-axis spline interpolation. The algorithm basically merges two concepts: (1) the interpolation of the toolpath with Pythagorean Hodograph (PH) curves and (2) the analytic solution of the inverse kinematic problem using the template equation method. The first method allows one to obtain a analytic relation between the arclength and the parameter of the toolpath curve. This one enables one to control the velocity of the tool on the workpiece. The second method allows one to determine the analytic solution of the parameterized inverse kinematic problem that permits us to introduce arbitrary number of geometric parameters. A natural selection of the possible parameters can be the parameters of tool geometry and the workpiece placement. This way, the off-line generated inverse solutions—that transform the cutter contact curve into axis values—can be online compensated, as soon as the exact parameter values are become known. Based on these two approaches, a robust and fast method for the simultaneous 5-axis spline interpolation is developed. The result of this new algorithm is time-dependent axis splines which represent the given toolpath with high accuracy.