Kinematics Problem Of Redundant Manipulators Research Articles

T-IK: An Efficient Multi-Objective Evolutionary Algorithm for Analytical Inverse Kinematics of Redundant Manipulator

This letter proposes a new method combined by the parameterization method and T-IK to solve the inverse kinematics problem of redundant manipulators in the position domain. T-IK is an improved multi-objective optimization algorithm based on NSGA-II. By adding population migration strategy and adaptive interval search operator in algorithm, we can maintain the global search ability of T-IK and greatly strengthen its local search ability. This method was applied to an 8-DOF tunnel shotcrete robot whose inverse kinematics algorithm needed to meet the accuracy, continuity and real-time requirement and avoid joint limits. We compared T-IK with Bio-IK, TRAC-IK, NSGA-II, MOEA/D, and ISGABT algorithms on tunnel trajectory, polyline trajectory, and arc trajectory to test its performance. Although T-IK is slightly inferior to MOEA/D in running time, it is much better than other algorithms in almost all indexes.

A novel algorithm by combining nonlinear workspace partition with neural networks for solving the inverse kinematics problem of redundant manipulators

Abstract. Redundant manipulators (RMs) have been gaining more attention thanks to their excellent merits of operating flexibility and precision. Inverse kinematics (IK) study is critical to the design, trajectory planning, and control of RMs, while it is usually more complicated to solve IK problems which may inherently have innumerable solutions. In this work, a novel approach for solving the IK problems for RMs while retaining the redundancy characteristics has been proposed. By employing a constraint function, the method delicately reduces the infinite IK solutions of a RM to a finite set. Furthermore, the workspace of RMs is divided into nonlinear partitions through diverse joint angle intervals, which have further simplified the mapping correlations between the desired point and manipulators' joint angles. For each partition, a pre-trained neural network (NN) model is established to acquire its IK solutions with high efficiency and precision. After combing all nonlinear partitions, multiple reasonable IK solutions are available. The presented method offers a possible selection of the most appropriate solution for trajectory planning and energy consumption and therefore has the potential for facilitating novel robot development.

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.

プレコンディションを行ったヤコビ行列を用いた超冗長マニピュレータの逆運動学計算法

Redundant manipulators avail to make use of various task in complicated work environment because of the wide variety of poses to be taken for a task demand. An agile inverse kinematics calculation, however, is required for obtaining a desired manipulator poses. This paper proposes a simple method of inverse kinematics resolution for redundant manipulators. The method transforms an original inverse kinematics problem of redundant manipulator to regular and small problem, that is a simultaneous equation on a dimension of task space, by preconditions of Jacobian matrix. The result obtained by solving the simple problem is transposed again into the solution of original problem finding out the joint angle of redundant manipulator. Numerical experiences have showed that the result obtained by the proposed method is equivalence to the results solved by using of the pseudo-inverse matrix of Jacobian matrix.

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.

CAM-Rob postprocessor based on a fuzzified redundancy resolution scheme

This work highlights the applicability of different redundancy resolution schemes to the postprocessing stage from a computer-aided manufacturing (CAM) system to an industrial redundant workcell. The inverse kinematic problem for redundant manipulators is not straightforward and, therefore, it is commonly solved using an iteratively approach based on redundant resolution schemes at the velocity level. In this work, two conceptions of redundancy resolution schemes are evaluated and a novel fuzzy inference system is developed to improve the performance during the toolpath tracking in order to avoid singularities and to maintain a preferred reference posture. For this purpose, the fuzzy inference engine properly adjusts the weight of each joint in the calculation of the performance criterion vectors. The proposed approach is validated in the real prototyping of a windmill blade mold using a KUKA KR15/2 manipulator mounted on a linear track and synchronized with a rotary table. To the authors’ knowledge, the proposed method and the results shown are novel in the context of postprocessing techniques from CAM systems to industrial robots devoted to milling works. With the same guidelines, the postprocessor programmed inside the CAM system is expected to be easily applicable not only to other industrial robots, but also for different applications such as welding or painting labors.

A fractional approach for the motion planning of redundant and hyper-redundant manipulators

The trajectory planning of redundant robots through the pseudoinverse control leads to undesirable drift in the joint space. This paper presents a new technique to solve the inverse kinematics problem of redundant manipulators, which uses a fractional differential of order α to control the joint positions. Two performance measures are defined to examine the strength and weakness of the proposed method. The positional error index measures the precision of the manipulator's end-effector at the target position. The repeatability performance index is adopted to evaluate if the joint positions are repetitive when the manipulator execute repetitive trajectories in the operational workspace. Redundant and hyper-redundant planar manipulators reveal that it is possible to choose in a large range of possible values of α in order to get repetitive trajectories in the joint space.

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.

Trial mountain climbing algorithm for solving the inverse kinematics of redundant manipulator

Trial mountain climbing algorithm to solve the inverse kinematics problem of redundant manipulator is introduced, and a method of describing a numeral with a special numeration system is given to define the changed step of the trial mountain climbing algorithm. The results show that a likelihood solution can be found quickly in the infinite groups of likelihood solutions within the limited search times, and need not calculate the anti-trigonometric function and the inverse matrix. In addition, this algorithm has many good qualities such as concise algorithm, tiny computation, fast convergence velocity, good stability and extensive adaptability.

Error-back-propagation solution to the inverse kinematic problem of redundant manipulators

In this paper, the inverse kinematics problem of the generalized n-degrees-of-freedom robot is solved using the error-back-propagation algorithm. The efficiency of the proposed solution has been mewed for redundant manipulators using 5000 randomly chosen Cartesian coordinates within the robot's workspace. Comparison with two other methods, the well-known pseudoinverse method and a technique based on genetic algorithms, shows that the accuracy of the present method is substantially better.

A Generalized Practical Method for Analytic Solution of the Constrained Inverse Kinematics Problem of Redundant Manipulators

This article addresses four important issues relating to practical solutions of the inverse kinematics problem of redundant manipulators. First, a generalized recursive method for systematic derivation of analytic expressions for all possible solutions of any redundant manipulator is presented. The method possesses the advantage of identi fying the linear dependence among joint axes and hence allows all singular configurations to be determined. Sec ond, a joint constraint mapping approach for the inte grated consideration of all joint constraints in the solution procedure of the inverse kinematics problem is presented. The result leads to practical real-time procedures. Map ping of the joint position and actuation constraints onto joint rate space is described. Third, simplification of end- effector velocity equations is shown to be possible for most practical manipulator structures by decomposing the end-effector work space into two orthogonal complement sub-work spaces. The decomposed velocity equations have smaller dimensions and, hence, are easier to solve. In manipulator design, structures can be selected for effi cient kinematics manipulation and simplified end-effector velocity equations. To achieve this purpose, type-synthesis design guidelines are given for efficient decomposition or decoupling of the work space. Fourth, two general approaches are described for optimally resolving the kine matics redundancy. The first approach maximizes the end- effector speed in a prescribed direction, while the second approach minimizes a quadratic objective function defined by the user. Examples on work space decomposition and optimal solution of kinematic redundancy are given. In both cases, expressions for the general analytic solution are derived.

A closed solution to the inverse kinematics of redundant manipulators

In the paper a solution of the inverse kinematics problem for redundant manipulators is presented. The method of solving the problem is based on employing a Frechet differential of a certain criterion function introduced to resolve the redundancy. The fully specified system of non-linear equations was determined by making use of the necessary condition of the extreme criterion function both for non-singular and singular configuration of manipulator.

A solution algorithm to the inverse kinematic problem for redundant manipulators

Based on a recently proposed algorithmic solution technique, the inverse kinematic problem for redundant manipulators is solved. The kinematics of the manipulator is appropriately augmented to include mentioned constraints; the result is an efficient, fast, closed-loop algorithm which only makes use of the direct kinematics of the manipulator. Simulation results illustrate the tracking performance for a given trajectory in the Cartesian space, while guaranteeing a collision-free trajectory and/or not violating a mechanical joint limit.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>