Inverse Kinematics Of Redundant Manipulators Research Articles

Multi-objective optimization approach for Inverse Kinematics of redundant manipulator for welding applications

This article presents an optimization-based approach for determining the Inverse Kinematics (IK) of redundant robot manipulators for industrial welding applications. Nine degrees of freedom (DOF) kinematic configuration of a robot manipulator with one prismatic and eight revolute joints has been modelled to improve maneuverability in a welding environment. To perform welding operations at desired task space locations (TSLs), the IK are to be determined. The IK problem is solved using a constrained multi-objective optimization technique with the objective of a reachability manipulator with minimal positional and orientational errors. An obstacle avoidance algorithm is also implemented to avoid collisions during welding operations. IK Simulations of the redundant manipulator in different welding applications were performed in a MATLAB environment. The obtained results shows that the welding manipulator reached desired locations successfully and this approach is adaptable for various shapes of weld joints.

Machine learning-based framework for optimally solving the analytical inverse kinematics for redundant manipulators

Solving the analytical inverse kinematics (IK) of redundant manipulators in real time is a difficult problem in robotics since its solution for a given target pose is not unique. Moreover, choosing the optimal IK solution with respect to application-specific demands helps to improve the robustness and to increase the success rate when driving the manipulator from its current configuration towards a desired pose. This is necessary, especially in high-dynamic tasks like catching objects in mid-flights. To compute a suitable target configuration in the joint space for a given target pose in the trajectory planning context, various factors such as travel time or manipulability must be considered. However, these factors increase the complexity of the overall problem which impedes real-time implementation. In this paper, a real-time framework to compute the analytical inverse kinematics of a redundant robot is presented. To this end, the analytical IK of the redundant manipulator is parameterized by so-called redundancy parameters, which are combined with a target pose to yield a unique IK solution. Most existing works in the literature either try to approximate the direct mapping from the desired pose of the manipulator to the solution of the IK or cluster the entire workspace to find IK solutions. In contrast, the proposed framework directly learns these redundancy parameters by using a neural network (NN) that provides the optimal IK solution with respect to the manipulability and the closeness to the current robot configuration. Monte Carlo simulations show the effectiveness of the proposed approach which is accurate and real-time capable ($\approx$ \SI{32}{\micro\second}) on the KUKA LBR iiwa 14 R820.

Collision-free Inverse Kinematics of Redundant Manipulator for Agricultural Applications through Optimization Techniques

This article presents an optimization-based technique for solving the inverse kinematics (IK) of spatially redundant manipulators in agricultural environments (workspaces). A kinematic configuration of 9 degrees of freedom (DOF) manipulator with eight revolute and one prismatic joint has been modelled to improve the accessibility in complex workspaces. The proposed manipulator has been simulated for harvesting fruits and vegetables. To perform the desired task in the working environment, the IK solution of the robot needs to be determined. The IK problem has been formulated as a constrained optimization problem with the objective of minimizing the positional and orientational errors by avoiding obstacles. A 3D CAD environment with different fruits and vegetable plants has been modelled in Solidworks. A target location in this environment has been chosen to pluck the fruit/vegetables. The trunk, branches, and leaves are considered as obstructions. The collision avoidance technique was implemented using a bounding box approach by including a collision detection algorithm. IK simulations of the spatial redundant manipulator in a cluttered environment were performed and results are reported. The joint trajectories of the robot while reaching desired task-space location has been depicted using Simscape Multibody. The results demonstrate that the end-effector of the robot has been reached desired task location successfully with an accurate IK solution. The approach is adaptable in a wide range of working environments based on the simulation results of the IK solution of robots.

Inverse kinematics of redundant manipulators with guaranteed performance

AbstractIn this paper, the inverse kinematics (IK) of redundant manipulators is presented and studied, where the performance of end-effector path planning is guaranteed. A new Jacobian pseudoinverse (JP)-based IK method is proposed and studied using a typical numerical difference rule to discretize the existing IK method based on JP. The proposed method is depicted in a discrete-time form and is theoretically proven to exhibit great performance in the IK of redundant manipulators. A discrete-time repetitive path planning (DTRPP) scheme and a discrete-time obstacle avoidance (DTOA) scheme are developed for redundant manipulators using the proposed method. Comparative simulations are conducted on a universal robot manipulator and a PA10 robot manipulator to validate the effectiveness and superior performance of the DTRPP scheme, the DTOA scheme, and the proposed JP-based IK method.

Obstacle Avoidance and Multitarget Tracking of a Super Redundant Modular Manipulator Based on Bezier Curve and Particle Swarm Optimization

A super redundant serpentine manipulator has slender structure and multiple degrees of freedom. It can travel through narrow spaces and move in complex spaces. This manipulator is composed of many modules that can form different lengths of robot arms for different application sites. The increase in degrees of freedom causes the inverse kinematics of redundant manipulator to be typical and immensely increases the calculation load in the joint space. This paper presents an integrated optimization method to solve the path planning for obstacle avoidance and discrete trajectory tracking of a super redundant manipulator. In this integrated optimization, path planning is established on a Bezier curve, and particle swarm optimization is adopted to adjust the control points of the Bezier curve with the kinematic constraints of manipulator. A feasible obstacle avoidance path is obtained along with a discrete trajectory tracking by using a follow-the-leader strategy. The relative distance between each two discrete path points is limited to reduce the fitting error of the connecting rigid links to the smooth curve. Simulation results show that this integrated optimization method can rapidly search for the appropriate trajectory to guide the manipulator in obtaining the target while achieving obstacle avoidance and meeting joint constraints. The proposed algorithm is suitable for 3D space obstacle avoidance and multitarget path tracking.

Inverse Kinematics of Redundant Manipulators With Dynamic Bounds on Joint Movements

Redundant manipulators are usually required to perform tasks in the operational space, but collision-free path planning is computed in the configuration space. Limiting the deviation with respect to the collision-free configuration-space trajectory may allow the robot to avoid collisions without modifying the primary task. This letter proposes a method to guarantee that the solution of the inverse kinematic problem deviates from the nominal joint-space trajectory less than a desired threshold. The excursion limitation is ensured by means of linear constraints and the automatic regulation of the weights of secondary tasks. Numerical and experimental results prove the validness of the proposed approach.

Hybrid Mutation Fruit Fly Optimization Algorithm for Solving the Inverse Kinematics of a Redundant Robot Manipulator

The inverse kinematics of redundant manipulators is one of the most important and complicated problems in robotics. Simultaneously, it is also the basis for motion control, trajectory planning, and dynamics analysis of redundant manipulators. Taking the minimum pose error of the end-effector as the optimization objective, a fitness function was constructed. Thus, the inverse kinematics problem of the redundant manipulator can be transformed into an equivalent optimization problem, and it can be solved using a swarm intelligence optimization algorithm. Therefore, an improved fruit fly optimization algorithm, namely, the hybrid mutation fruit fly optimization algorithm (HMFOA), was presented in this work for solving the inverse kinematics of a redundant robot manipulator. An olfactory search based on multiple mutation strategies and a visual search based on the dynamic real-time updates were adopted in HMFOA. The former has a good balance between exploration and exploitation, which can effectively solve the premature convergence problem of the fruit fly optimization algorithm (FOA). The latter makes full use of the successful search experience of each fruit fly and can improve the convergence speed of the algorithm. The feasibility and effectiveness of HMFOA were verified by using 8 benchmark functions. Finally, the HMFOA was tested on a 7-degree-of-freedom (7-DOF) manipulator. Then the results were compared with other algorithms such as FOA, LGMS-FOA, AE-LGMS-FOA, IFOA, and SFOA. The pose error of end-effector corresponding to the optimal inverse solution of HMFOA is 10−14 mm, while the pose errors obtained by FOA, LGMS-FOA, AE-LGMS-FOA, IFOA, and SFOA are 102 mm, 10−1 mm, 10−2 mm, 102 mm, and 102 mm, respectively. The experimental results show that HMFOA can be used to solve the inverse kinematics problem of redundant manipulators effectively.

Inverse Kinematics of Redundant Manipulators Formulated as Quadratic Programming Optimization Problem Solved Using Recurrent Neural Networks: A Review

SUMMARYThe Inverse Kinematics (IK) problem of manipulators can be divided into two distinct steps: (1)Problem formulation,where the problem is developed into a form which can then be solved using various methods. (2)Problem solution,where the IK problem is actually solved by producing the values of different joint space variables (joint angles, joint velocities or joint accelerations). The main focus of this paper is concentrated on the discussion of the IK problem of redundant manipulators, formulated as a quadratic programming optimization problem solved by different kinds of recurrent neural networks.

Neural network-based construction of inverse kinematics model for serial redundant manipulators

Solving the inverse kinematics of redundant manipulators is difficult, because knowledge of the manipulators and their evaluation functions is required. To solve this problem, we propose a novel method of enabling a neural network model to learn the inverse kinematics. The method achieves learning independent of the structure of the evaluation function, by combining multiple neural network models. The method can obtain the neural network models of the inverse kinematics via an automatic calculation process using only training data, which consist of the postures, end-points, and evaluation values. In this paper, the algorithm used by the method and its background is explained, and the effectiveness of the method is validated by a numerical simulation.

Predictive Inverse Kinematics for Redundant Manipulators With Task Scaling and Kinematic Constraints

The paper presents a fast online predictive method to solve the task-priority differential inverse kinematics of redundant manipulators under kinematic constraints. It implements a task-scaling technique to preserve the desired geometrical task, when the trajectory is infeasible for the robot capabilities. Simulation results demonstrate the effectiveness of the methodology.

A Fast Evaluation of Initial Configurations in Repeatable Inverse Kinematics for Redundant Manipulators

Abstract A repeatable inverse kinematic task in robot manipulators consists in finding a loop (cyclic trajectory) in a configuration space, which corresponds to a given loop in a task space. In the robotic literature, an entry configuration to the trajectory is fixed and given by a user. In this paper the assumption is released and a new, indirect method is introduced to find entry configurations generating short trajectories. The method avoids a computationally expensive evaluation of (infinite) many entry configurations for redundant manipulators (for each of them, repeatable inverse kinematics should be run). Some fast-to-compute functions are proposed to evaluate entry configurations and their correlations with resulting lengths of trajectories are computed. It appears that only an original function, based on characteristics of a manipulability subellipsoid, properly distinguishes entry configurations that generate short trajectories. This function can be used either to choose one from a few possible entry configurations or as an optimized function to compute the best initial configuration.

A study on avoiding joint limits for inverse kinematics of redundant manipulators using improved clamping weighted least-norm method

A general method is presented for the inverse kinematics resolution of redundant manipulators with joint limits. The success of avoiding joint angular position limits of the original clamping weighted least-norm method is ascribable to the strength of the repulsive potential field function. However, the repulsive potential field function may lead to excessive joint angular velocities that can exceed the corresponding limits. We propose an improved clamping weighted least-norm method that adds an elastic field function into the original method for the sake of sustaining the constraints of joint angular velocity limits. Moreover, for hierarchical task-level construction, the priority of avoiding joint angular velocity limits is lower than that of avoiding joint angular position limits. To adequately illustrate the effectiveness of the proposed method, case studies were performed in comparison with other methods in singular configurations of a redundant manipulator.

A novel closed-form solution for the inverse kinematics of redundant manipulators through workspace analysis

This work addresses the inverse kinematic problem for redundant serial manipulators. Its importance relies on its effect in the programming and control of redundant robots. Besides, no general closed-form techniques have been developed so far. In this paper, redundant manipulators are reduced to non-redundant ones by selecting a set of joints, denoted redundant joints, and parametrizing its joint variables. This selection is made through a workspace analysis which also provides an upper bound for the number of different closed-form solutions for a given pose. Once these joints have been identified several closed-form methods developed for non-redundant manipulators can be applied for obtaining the analytical solutions. Finally, particular instances for the parametrized joints variables are determined depending on the task to be executed. Different criteria and optimization functions can be defined for that purpose.

Dual arm-angle parameterisation and its applications for analytical inverse kinematics of redundant manipulators

SUMMARYAn S-R-S (Spherical-Revolute-Spherical) redundant manipulator is similar to a human arm and is often used to perform dexterous tasks. To solve the inverse kinematics analytically, the arm-angle was usually used to parameterise the self-motion. However, the previous studies have had shortcomings; some methods cannot avoid algorithm singularity and some are unsuitable for configuration control because they use a temporary reference plane. In this paper, we propose a method of analytical inverse kinematics resolution based on dual arm-angle parameterisation. By making use of two orthogonal vectors to define two absolute reference planes, we obtain two arm angles that satisfy a specific condition. The algorithm singularity problem is avoided because there is always at least one arm angle to represent the redundancy. The dual arm angle method overcomes the shortcomings of traditional methods and retains the advantages of the arm angle. Another contribution of this paper is the derivation of the absolute reference attitude matrix, which is the key to the resolution of analytical inverse kinematics but has not been previously addressed. The simulation results for typical cases that include the algorithm singularity condition verified our method.

Real-time inverse kinematics of redundant manipulators using neural networks and quadratic programming: A Lyapunov-based approach

In this paper, an online adaptive strategy based on the Lyapunov stability theory is presented to solve the inverse kinematics of redundant manipulators. In the proposed approach, Radial Basis Function (RBF) Neural Networks (NNs) are employed to obtain the joint angles of the robot using the Cartesian coordinate of the end-effector. Quadratic Programming (QP) method is incorporated in the training algorithm of the NNs to satisfy the constraints of the problem such as the joint angle limits and obstacles in the workspace of the robot. For better initialization of the NNs’ weights, fuzzy logic is employed. In this way, smaller errors for the initial position of the end-effector and feasibility of the joint angles can be obtained. The convergence of the NNs’ weights and satisfaction of the constraints are guaranteed by employing an adaptive scheme that is based on the Lyapunov stability analysis and Kuhn–Tucker conditions, which is part of the QP to update the NNs’ weights. In addition, obstacle avoidance is also considered in the proposed method. The simulations are carried out on the seven degrees-of-freedom PA-10 robot manipulator. The results show the effectiveness of the proposed approach in obtaining successful configurations of the robot while the solutions of the inverse kinematics are feasible. Moreover, a comparison with the recently reported methods in the literature shows advantages of the proposed method.

Second Order Recurrent Neural Network for the Inverse Kinematics of Redundant Manipulators

In this paper, the second order recurrent neural network is adopted to study the inverse kinematics problem of three degree-of-freedom planar redundant manipulators. The Simulation results show that the network can effectively solve the inverse kinematics problem of redundant manipulators, and it reaches to good precision of solution and solving speed.

An Optimization Method for Solving the Inverse Kinematics of Redundant Manipulator

Based on the weighted least-norm(WLN) solution,an optimization method that avoids calculating the pseu-doinverse of Jacobian matrixes is presented.Firstly,the inverse of the nonsingular 6x6 submatrix of the Jacobian is calculated to determine particular and homogeneous solutions of the inverse kinematics.Then,the solution of the inverse kinematics is obtained by subtracting the homogeneous solution's component in the direction of the particular solution from the particular solution.An illustrative example and simulation on a seven degree-of-freedom redundant manipulator are taken to verify the effectiveness of the method in reducing the solving difficulty,ensuring the accuracy of solution,and avoiding the joint limits.

A multi-objective approach for the motion planning of redundant manipulators

Kinematic redundancy occurs when a manipulator possesses more degrees of freedom than those required to execute a given task. Several kinematic techniques for redundant manipulators control the gripper through the pseudo-inverse of the Jacobian, but lead to a kind of chaotic inner motion with unpredictable arm configurations. Such algorithms are not easy to adapt to optimization schemes and, moreover, often there are multiple optimization objectives that can conflict between them. Unlike single optimization, where one attempts to find the best solution, in multi-objective optimization there is no single solution that is optimum with respect to all indices. Therefore, trajectory planning of redundant robots remains an important area of research and more efficient optimization algorithms are needed. This paper presents a new technique to solve the inverse kinematics of redundant manipulators, using a multi-objective genetic algorithm. This scheme combines the closed-loop pseudo-inverse method with a multi-objective genetic algorithm to control the joint positions. Simulations for manipulators with three or four rotational joints, considering the optimization of two objectives in a workspace without and with obstacles are developed. The results reveal that it is possible to choose several solutions from the Pareto optimal front according to the importance of each individual objective.

Redundant manipulators kinematics inversion

A robotic system is kinematically redundant when it possesses more degrees of freedom than those required to execute a given task. This paper reviews the well-known methods used to find the inverse kinematics of redundant manipulators. Because redundant manipulators have infinite solutions for their inverse kinematics, therefore the conventional method that was used to calculate the inverse kinematics of non-redundant manipulators cannot be used. The methods used to calculate the inverse kinematics of redundant manipulators are divided into three main categories in this paper: pseudoinverse, artificial intelligence and geometrical methods. These types have been explained, their advantages and disadvantages are also discussed in this paper. Key words: Redundant manipulator, inverse kinematics, pseudoinverse, artificial intelligence, geometrical method.

Inverse kinematics of manipulator using weighted fuzzy clustering method for fuzzy training data

The inverse kinematics of redundant manipulator is considered. A model-free regression approach based on weighted fuzzy clustering method is formulated. For the adopted technique, the observed or training data pair is fuzzy instead of crisp for known value of joint variables to enhance the practicability of inverse kinematics solutions, since the real-time data collected by the sensors is generally fuzzy or vague instead of crisp. Simulation results indicate that this method has higher identifying precision and better real-time ability. Therefore, a new way for solving the inverse kinematics of manipulator for fuzzy data is proposed.