Inverse kinematics solution by using Matlab

In this letter, we present a novel inverse kinematics (IK) solution for a robotic arm-hand system to achieve precision grasp. This problem is kinematically over-constrained and to address the issue and to solve the problem, we propose a new approach with three key insights. First, we propose a human-inspired thumb-first strategy and consider one finger of the robotic hand as the “thumb” to narrow down the search space and increase the success rate of our algorithm. Second, we formulate the arm-thumb serial chain as a closed chain such that the entire arm-hand system is controlled as a hybrid parallel-serial system. The closed-chain formulation simplifies the task hierarchy of the entire arm-hand system. Third, we attach a virtual revolute joint to the thumb's tip with its rotation axis aligning with the thumb's contact normal The virtual joint will embody the thumb's functional redundancy. By selecting the thumb's joints including the added virtual revolute joint as active joints of the arm-thumb closed chain, the arm-thumb system's self-motion (i.e., the palm pose) and the thumb's functional redundancy can be directly controlled without using the null space projection. This provides a new possibility to control the self-motion of arm-hand systems. Simulation results will demonstrate the advantages and superior performance of the proposed approach for achieving precision grasp compared to other classical approaches.

Total differential methods based universal post processing algorithm considering geometric error for multi-axis NC machine tool

In this study, an inverse kinematic solution approach applicable to six degree-of-freedom industrial robotic manipulators is introduced. The approach is based on a previously introduced kinematic classification of industrial robotic manipulators by Balkan et al. (1999), and depending on the kinematic structure, either an analytical or a semi-analytical inverse kinematic solution is obtained. The semi-analytical method is named as the parametrized joint variable (PJV) method. Compact forward kinematic equations obtained by utilizing the properties of exponential rotation matrices. In the inverse kinematic solutions of the industrial robots surveyed in the previous study, most of the simplified compact equations can be solved analytically and the remaining few of them can be solved semi-analytically through a numerical solution of a single univariate equation. In these solutions, the singularities and the multiple configurations of the manipulators can be determined easily. By the method employed in this study, the kinematic and inverse kinematic analysis of any manipulator or designed-to-be manipulator can be performed and using the solutions obtained, the inverse kinematics can also be computerized by means of short and fast algorithms. As an example for the demonstration of the applicability of the presented method to manipulators with closed-chains, ABB IRB2000 industrial robot is selected which has a four-bar mechanism for the actuation of the third link, and its compact forward kinematic equations are given as well as the inverse kinematic solution.

A cuspidal robot can move from one inverse kinematics (IK) solution to another without crossing a singularity. Multiple industrial robots are cuspidal. They tend to have a beautiful mechanical design, but they pose path-planning challenges. A task-space path may have a valid IK solution for each point along the path, but a continuous joint-space path may depend on the choice of the IK solution or even be infeasible. This article presents new analysis, path planning, and optimization methods to enhance the utility of cuspidal robots. We first demonstrate an efficient method to identify cuspidal robots and show, for the first time, that the ABB GoFa and certain robots with three parallel joint axes are cuspidal. We then propose a new path-planning method for cuspidal robots by finding all IK solutions for each point along a task-space path and constructing a graph to connect each vertex corresponding to an IK solution. Graph edges have a weight based on the optimization metric, such as minimizing joint velocity. The optimal feasible path is the shortest path in the graph. This method can find nonsingular paths as well as smooth paths that pass through singularities. Finally, we incorporate this path-planning method into a path optimization algorithm. Given a fixed workspace toolpath, we optimize the offset of the toolpath in the robot base frame while ensuring continuous joint motion. Code examples are available in a publicly accessible repository.

Comparison of RBF and MLP neural networks to solve inverse kinematic problem for 6R serial robot by a fusion approach

Two niching strategies for the tournament selection, along with the simulated binary crossover operator and a parameter-based mutation operator are used to solve the inverse kinematics problem of a robotic manipulator. The niching strategies are compared on the basis of their ability to evaluate the multiple inverse kinematics solutions and maintain an acceptable distribution of individuals around these solutions. The approach requires the use of robot kinematics equations and the limits of joint angles only. It does not require the use of geometric heuristics as suggested by earlier researchers. The proposed approach provides the correct number of inverse kinematics solutions even when some of them may be unachievable due to the limits of the joint angles. In other approaches, all the inverse kinematics solutions are calculated and the unachievable ones are discarded. The total joint displacements associated with the multiple inverse kinematics solutions provide a means for multiplicity resolution.

A concept for a three dimensional, non-contacting metrology system is presented. Both the forward and the inverse kinematics solutions for the system are developed using a line geometry, resulting in an efficient representation that may describe a general assembly of the kinematic system and error parameters determined through calibration. The inverse kinematics solution is a general solution, assuming very little about the assembly of the system. The forward kinematics solution is less general and resorts to making a few assumptions. In the development of the forward and inverse kinematics solutions singularities of the system are identified.

In this study a five Degrees of Freedom (DOF) serial robot manipulator was designed and implemented. The inverse kinematics problem, which has not exact analytical solution (only one inverse kinematic solution for a predefined end effector position in three dimensional space), of the robot mechanism was solved by using the combination of the analytical method and a simple search method. In order to use the proposed method in real-time applications, the method is designed so that it can be used to solve the inverse kinematics problem for the next point of the end-effector while the mechanism is working. Moreover, so that to control the implemented mechanism, a user interface program was written by using Visual Basic programming language. Finally, the proposed inverse kinematic solution method was tested on two different trajectories, an arc shaped trajectory that composed of 58 points and a linear trajectory divided into 29 points. The obtained results revealed that the proposed method can be used successfully in solving the inverse kinematic problem of the designed mechanism.

This paper deals with real-time implementation of visual-motor control of a 7 degree of freedom (DOF) robot manipulator using self-organized map (SOM) based learning approach. The robot manipulator considered here is a 7 DOF PowerCube manipulator from Amtec Robotics. The primary objective is to reach a target point in the task space using only a single step movement from any arbitrary initial configuration of the robot manipulator. A new clustering algorithm using Kohonen SOM lattice has been proposed that maintains the fidelity of training data. Two different approaches have been proposed to find an inverse kinematic solution without using any orientation feedback. In the first approach, the inverse Jacobian matrices are learnt from the training data using function decomposition. It is shown that function decomposition leads to significant improvement in accuracy of inverse kinematic solution. In the second approach, a concept called sub-clustering in configuration space is suggested to provide multiple solutions for the inverse kinematic problem. Redundancy is resolved at position level using several criteria. A redundant manipulator is dexterous owing to the availability of multiple configurations for a given end-effector position. However, existing visual motor coordination schemes provide only one inverse kinematic solution for every target position even when the manipulator is kinematically redundant. Thus, the second approach provides a learning architecture that can capture redundancy from the training data. The training data are generated using explicit kinematic model of the combined robot manipulator and camera configuration. The training is carried out off-line and the trained network is used on-line to compute the joint angle vector to reach a target position in a single step only. The accuracy attained is better than the current state of art.

Inverse kinematics is computationally expensive and can result in significant control delays in real time. For redundant robots, since there is infinite inverse kinematics solutions, additional computations are required through optimization schemes. Based on the fact that humans do not compute exact inverse kinematics, but can do precise positioning from heuristics, we developed an inverse kinematics solving method through fuzzy logic which is optimized for real time applications. As a result, a simple accurate and fast inverse kinematics solution is obtained. The simulation results verify the efficiency of the proposed solution.

In rehabilitation of upper-limb disability, robotic exoskeleton often need to perform task-based exercises. In order for exoskeleton to conduct task-based exercises, using inverse kinematic solution is a must to generate the safe trajectory from staring point to end point. Finding inverse kinematic solution for manipulator or exoskeletons that involve hybrid serial-parallel mechanisms always remains an open problem. This situation is worsened when joints with complex motion are considered, such as the shoulder joint. Therefore, in this research we present the inverse kinematic solution of a hybrid exoskeleton called u-Rob4, which includes two parallel configurations to handle the changes of the shoulder center of rotation.

Positioning 3R manipulators may have two or four inverse kinematic solutions (IKS). This paper derives a necessary and sufficient condition for 3R positioning manipulators with orthogonal joint axes to have four distinct IKS. We show that the transition between manipulators with two and four IKS is defined by the set of manipulators with a quadruple root of their inverse kinematics. The resulting condition is explicit and states that the last link length of the manipulator must be greater than a quantity that depends on three of its remaining DH parameters. This result is of interest for the design of new manipulators.

This paper presents the inverse kinematics solution using the neural network for a robotic arm in 3-dimension. This paper creates neural networks to represent x, y and z position of the end-effector in the forward kinematics equations. The structure of the network has 4 layers; input layer, 2 hidden layers, and output layer. The input and output layers are defined as robotic arm angle and position of the end-effector, respectively. Then, the network updates the weights by the backpropagation with variable learning rate algorithm until reaching criteria that the output of the network is equal to the desired positions. Finally, the inverse kinematics solution is defined by the optimal weights of the network. To evaluate the performance algorithm, the MATLAB Program is used to demonstrate the robotic arm movement in 3-dimension. As a result, the proposed algorithm can help the robotic arm move to the desired position quickly and correctly.

This paper presents an inverse kinematics solution method for a seven-degree-of-freedom (7-DOF) dual-arm robot. After comparing and studying the structural characteristics of other dual-arm robots, a 7-DOF dual-arm robot with shoulder joints was proposed. Firstly, the product-of-exponentials(POE) formula of inverse kinematics is briefly described. Then, according to the structural characteristics of the 7-DOF dual-arm robot, the inverse kinematics solution of the 7-DOF dual-arm robot is calculated by using the POE formula and Paden-Kahan sub-problem solving method. Finally, the inverse kinematic closed solution is verified by the example calculation and MATLAB motion simulation. The results show that this method can simplify the inverse solution calculation, has clear geometric meaning and high reliability. It provides a new method for solving inverse kinematics solutions of a similar high-degree-of-freedom dual-arm robots.

The aim of this paper is to characterize the notion of aspect in the workspace and in the joint space for parallel manipulators. In opposite to the serial manipulators, the parallel manipulators can admit not only multiple inverse kinematic solutions, but also multiple direct kinematic solutions. The notion of aspect introduced for serial manipulators in [Borrel 86], and redefined for parallel manipulators with only one inverse kinematic solution in [Wenger 1997], is redefined for general fully parallel manipulators. Two Jacobian matrices appear in the kinematic relations between the joint-rate and the Cartesian-velocity vectors, which are called the "inverse kinematics" and the "direct kinematics" matrices. The study of these matrices allow to respectively define the parallel and the serial singularities. The notion of working modes is introduced to separate inverse kinematic solutions. Thus, we can find out domains of the workspace and the joint space exempt of singularity. Application of this study is the moveability analysis in the workspace of the manipulator as well as path-planing and control. This study is illustrated in this paper with a RR-RRR planar parallel manipulator.