Kinematics Of Robot Manipulators Research Articles

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.

Correction to: A Geometric Algebra Based Higher Dimensional Approximation Method for Statics and Kinematics of Robotic Manipulators

Correction to: A Geometric Algebra Based Higher Dimensional Approximation Method for Statics and Kinematics of Robotic Manipulators

A Geometric Algebra Based Higher Dimensional Approximation Method for Statics and Kinematics of Robotic Manipulators

Evaluation of a robotic (serial or parallel) manipulator’s static and kinematics performance requires the solution of closed and complicated non-closed form systems of equations for both the forward and inverse problem types. In this work, a robotic system or manipulator is represented as a network whose motion generating kinematic pairs are represented as the network’s inter-connected nodes. Within this network theoretic context, we develop a formulation employing higher dimensional multivectors defined in Clifford Algebra that approximates the computational outcomes of such complicated systems of equations, for both inverse and forward problem types. The statics and kinematics performance of these mechanical networks (serial and parallel robots) are rapidly evaluated without the need to solve their respective traditional systems of equations using what we call ‘screw hypervolumes’, which capture the algebro-geometric structures generated by a robot’s physical design parameters and end-effector position in terms of kinematics and statics. These dimensionless hypervolume functions enable the specialist to produce a very computationally efficient function/index that approximates the kinematic and static output spaces of robots. We find that this formulation inadvertently presents a curious mathematical analogue to these systems of equations. A 6R serial robot, the Delta robot and the 3-RRR manipulator are analysed using the hypervolume methods for the case studies. This approach can be adapted and applied to other multi-agent physical systems displaying non-commutative interactions as well.

Solution and validation of inverse kinematics using Deep Artificial neural network

Researchers and roboticists face one of the most complex problems of solving inverse kinematics while designing the robotic manipulator. For the sake of this research, a Deep Artificial neural network (DANN) model is used to solve the inverse kinematics of a 5-axis serial link robotic manipulator. The joints in this robotic manipulator are rotary. MATLAB is used to train the proposed DANN model. Transformation matrix and forward kinematics of the robotic manipulator is used for generation of the training dataset. An experimental robotic model is constructed to authenticate inverse calculations made by this model. A Basler ACA smart camera system is connected with MATLAB. This arrangement calculates deviation at the end needle in real-time. Image processing is used for this purpose. Results of training of DANN showed that there was a deviation of ±0.1 rad in each joint. This result feed-forward satisfactory as it was also validated experimentally. Even with fewer input data, one could achieve the desired target coordinate points with a robotic manipulator using the proposed method.

ROBOT MANIPULATOR KINEMATICS AND ITS WORKING SPACE APPROXIMATION

ROBOT MANIPULATOR KINEMATICS AND ITS WORKING SPACE APPROXIMATION

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.

Efficient FPGA Hardware Implementation for Robot Manipulator Kinematic Modeling Using Rational Trigonometry

A common approach to model kinematics for robot manipulators uses functions such as sin(), cos() and atan(),however, the rational trigonometry allows to exclude the use of these transcendental functions. Most of the computing processing to control a manipulator is dedicated to solving its kinematics, therefore, reduce the complexity of kinematic equations leads to a more compact and efficient model. In this paper, we propose a geometric analysis to solve the kinematics of robot manipulator of up to three degrees of freedom, avoiding the use of transcendental functions in the kinematic equations. We present three kinematic models for the mechanism positions and theirimplementations in an FPGA. The experimental results show that our proposed models: 1) use less logic elements compared with an implementation based on parallel CORDIC and 2) has lower latency respect with iterative CORDIC implementation.

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.

Robot Manipulator Capability in MATLAB: A Tutorial on Using the Robotics System Toolbox [Tutorial

i»?The Robotics System Toolbox for MATLAB provides a wide and growing set of functionalities for creating robotic systems: Robot Operating System (ROS) integration, mobile robotics, and robot manipulator arms. This capability increases with each release and is targeted at industrial developers as well as academic teaching and research. This tutorial is concerned with the robot manipulator kinematic functionality that has been available since MATLAB release 2016b.

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.

Solution of Inverse Kinematics for General Robot Manipulators Based on Multiple Population Genetic Algorithm

Solution of Inverse Kinematics for General Robot Manipulators Based on Multiple Population Genetic Algorithm

A Comparative Study Between the Successive Screw Displacement and Quaternion Based Methods Used in Forward Kinematics of Serial Robot Manipulator

A Comparative Study Between the Successive Screw Displacement and Quaternion Based Methods Used in Forward Kinematics of Serial Robot Manipulator

Inverse kinematics of a 7-DOF redundant robot manipulator using the active set approach under joint physical limits

This paper presents a new approach for an online solution of the inverse kinematics problem based on nonlinear optimization for robots with joint physical constraints. The inverse kinematics problem is stated as a constrained nonlinear optimization problem and is solved using Kuhn--Tucker conditions analysis. The nonlinear multivariable optimization problem is locally converted into independent local linear constrained subproblems and each subproblem is analytically solved. For each joint, position limits and velocity limits are considered as physical constraints. The proposed structure benefits from a very low complexity design. The proposed method is fast and requires few calculations. The convergence of the proposed algorithm is proven based on the Lyapunov function. While keeping the algorithm stable, it can navigate the manipulator to a desired position under joint physical limits. The algorithm is simulated on a 7-DOF PA-10 manipulator. Results indicate good efficiency for the proposed structure in constrained path planning of joint space.

A New Approach to the Solution of Robot Kinematics Based on Relative Transformation Matrices

In analyzing robot manipulator kinematics, we need to describe relative movement of adjacent linkages or joints in order to obtain the pose of end effector (both position and orientation) in reference coordinate frame. Denavit-Hartenberg established a method based on a 4×4 homogenous matrix so called “A” matrix. This method used by most of the authors for kinematics and dynamic analysis of the robot manipulators. Although it has many advantages, however, finding the elements of this matrix and link/joint’s parameters is sometimes complicated and confusing. By considering these difficulties, the authors proposed a new approach called ‘convenient approach’ that is developed based on “Relative Transformations Principle”. It provides a very simple and convenient way for the solution of robot kinematics compared to the conventional D-H representation. In order to clarify this point, the kinematics of the world known Stanford manipulator has been solved through D-H representation as well as convenient approach and the results are compared.

Inverse kinematics of 3-DOF robotic manipulator using analytical method, ANFIS method and experiments

Inverse kinematics of industrial robotic manipulators is a very complex task. This paper involves the kinematic analysis of robotic manipulator with industrial importance. Forward kinematic analysis has been performed by analytical method using Denavit-Hartenberg convention. Inverse kinematics solutions have been obtained by geometrical method. A hybrid combination of neural networks and fuzzy logic intelligent techniques using two different membership functions has also been used to perform inverse kinematic analysis. Experimental validation has been attempted on robotic manipulator to trace different desired trajectories. Comparative analysis of joint angle errors using two different membership functions shows the importance of selection of a particular membership function. A comparison drawn on all the applied techniques, namely analytical method, adaptive neuro-fuzzy inference system method with experiments for desired trajectories shows the results for inverse kinematics to be in reasonable agreement with each other.

Inverse kinematics of 3-DOF robotic manipulator using analytical method, ANFIS method and experiments

Inverse kinematics of 3-DOF robotic manipulator using analytical method, ANFIS method and experiments

Comparative Analysis For Kinematics Of 5-DOF Industrial Robotic Manipulator

Abstract This paper gives the kinematic analysis of a 5-DOF industrial robotic manipulator while considering wrist in motion. Analytical solutions have been obtained for forward kinematics and inverse kinematics to accurately position the end-effector of robotic manipulator in three dimensional spaces. For the first time, a hybrid neuro-fuzzy intelligent technique with two different membership functions has been studied and their performances are comparatively evaluated with analytical solutions. An experiment has been performed for a desired trajectory. It is seen that the results for the intelligent technique are reasonably in agreement with experiment. Also, the results obtained highlight the importance of selection of a particular membership function for robotic manipulators of industrial use.