Obtaining the joint variables that result in a desired position of the robot end-effector called as inverse kinematics is one of the most important problems in robot kinematics and control. As the complexity of robot increases, obtaining the inverse kinematics solution requires the solution of non linear equations having transcendental functions are difficult and computationally expensive. In this paper, using the ability of ANFIS (Adaptive Neuro-Fuzzy Inference System) to learn from training data, it is possible to create ANFIS, an implementation of a representative fuzzy inference system using a BP neural network-like structure, with limited mathematical representation of the system. Computer simulations conducted on 2 DOF and 3DOF robot manipulator shows the effectiveness of the approach.

/pdf/neuro-fuzzy-based-approach-for-inverse-kinematics-solution-176vr8sc4c.pdf

Neuro-Fuzzy based Approach for Inverse Kinematics Solution of Industrial Robot Manipulators

The work reported in this thesis aims to design and develop a new neuro-fuzzy control system for robotic manipulators using Machine Learning Techniques, Fuzzy Logic Controllers, and Fuzzy Neural Networks. The main idea is to integrate these intelligent techniques to develop an adaptive position controller for robotic manipulators. This will finally lead to utilising one or two coordinated manipulators to perform upper-limb rehabilitation. The main target is to benefit from these intelligent techniques in a systematic way that leads to an efficient control and coordination system. The suggested control system possesses self-learning features so that it can maintain acceptable performance in the presence of uncertain loads. Simulation and modelling stages were performed using dynamical virtual reality programs to demonstrate the ideas of the control and coordination techniques. The first part of the thesis focuses on the development of neuro-fuzzy models that meet the above requirement of mimicking both kinematics and dynamics behaviour of the manipulator. For this purpose, an initial stage for data collection from the motion of the manipulator along random trajectories was performed. These data were then compacted with the help of inductive learning techniques into two sets of if-then rules that form approximation for both of the inverse kinematics and inverse dynamics of the manipulator. These rules were then used in fuzzy neural networks with differentiation characteristics to achieve online tuning of the network adjustable parameters. The second part of the thesis introduces the proposed adaptive neuro-fuzzy joint-based controller. To achieve this target, a feedback Fuzzy-Proportional-Integral-Derivative incremental controller was developed. This controller was then applied as a joint servo-controller for each robot link in addition to the main neuro-fuzzy feedforward controller used to compensate for the dynamics interactions between robot links. A feedback error learning scheme was applied to tune the feedforward neuro-fuzzy controller online using the error back-propagation algorithm. The third part of the thesis presents a neuro-fuzzy Cartesian internal model control system for robotic manipulators. The neuro-fuzzy inverse kinematics model of the manipulator was used in addition to the joint-based controller proposed and the forward mathematical model of the manipulator in an adaptive internal model controller structure. Feedback-error learning scheme was extended to tune both of the joint-based neuro-fuzzy controller and the neuro-fuzzy internal model controller online. The fourth part of the thesis suggests a simple fuzzy hysteresis coordination scheme for two position-controlled robot manipulators. The coordination scheme is based on maintaining certain kinematic relationships between the two manipulators using reference motion synchronisation without explicitly involving the hybrid position/force control or modifying the existing controller structure for either of the manipulators. The key to the success of the new method is to ensure that each manipulator is capable of tracking its own desired trajectory using its own position controller, while synchronizing its motion with the other manipulator motion so that the differential position error between the two manipulators is reduced to zero or kept within acceptable limits. A simplified test-bench emulating upper-limb rehabilitation was used to test the proposed coordination technique experimentally.

Neuro-fuzzy modelling and control of robotic manipulators

Kinematics is the study of motion without regard to the forces that create it. Generally, kinematics for robot manipulators includes two problems, forward kinematics problem and inverse kinematics problem. Because of the complexity of inverse kinematics, it is difficult to find the solutions for it. This paper applies a self-configuration fuzzy system to finding the solutions for inverse kinematics of robot manipulators. In this paper, the problem of fuzzy approach for inverse kinematics is described first. Then a self-configuration fuzzy system is introduced. Based on a small group of given input-output pairs selected by covering its workspace, an initially simple fuzzy model for inverse kinematics is built, including some basic rules, the number and the parameters of membership functions. Then, by applying given input-output data pairs to this simple fuzzy model, approximating error can be calculated. Consequently, the optimum rule conclusion, optimized membership functions, and new structure can be obtained. Furthermore, an overall analysis in the domain of the whole function is carried out instead of concentrating on the subspace. After optimization problems are solved, a fuzzy system is well defined to solve the inverse kinematics. Finally, the simulation verifies this self-configuration fuzzy system for inverse kinematics of robot manipulators.

Self-Configuration Fuzzy System for Inverse Kinematics of Robot Manipulators

A robot task can be represented as a set of trajectories conformed by a sequence of poses. In this way it is possible to teach a mobile robot to accomplish a manipulation task, and also to reproduce it. Nevertheless robot navigation may normally introduce inaccuracies in localization due to natural events as wheel-slides, causing a mismatch between the end-effector and the objects or tools the robot is supposed to interact with. We propose an algorithm for adapting manipulation trajectories for different locations. The adaptation is achieved by optimizing in position, orientation and energy consumption. The approach is built over the basis of Evolution Strategies, and only uses forward kinematics permitting to avoid all the inconveniences that inverse kinematics imply, as well as convergence problems in singular kinematic configurations. Manipulation paths generated with this algorithm can achieve optimal performance, sometimes even improving original path smoothness. Experimental results are presented to verify the algorithm.

/pdf/adaptive-evolving-strategy-for-dextrous-robotic-manipulation-2p4lum72e1.pdf

Adaptive evolving strategy for dextrous robotic manipulation

Usually, the pseudo-inverse of the Jacobian matrix needs to be calculated in the conventional laws for the Single Gimbal Control Moment Gyroscopes (SGCMGs). However, the steering law can not work when the Jacobian matrix is singular and its pseudo-inverse is indefinite. To avoid the conditions stated above, a new steering law is designed using radial basis function(RBF) neural networks. This algorithm can output the desired gimbal angles directly according to the momentum command. And also, this algorithm can deal with the singular conditions since the pseudo-inverse of the Jacobian matrix is not needed. Simulation results demonstrate the effectiveness of the steering law.

Steering law design for single gimbal control moment gyroscopes based on RBF neural networks

This article presents an inverse kinematics solution for manipulators based on fuzzy logic. This algorithm has been implemented on a simple two-DOF robot manipulator. It has been shown that this algorithm can realize the manipulator's inverse kinematics of continuous motion trajectory with high computational accuracy.

https://ieeexplore.ieee.org/iel5/7719/21162/00983851.pdf

An inverse kinematics solution for manipulators based on fuzzy logic

This paper presents an inverse kinematics control algorithm based on RBF neural networks for manipulators. First, the initial RBF neural networks are trained off-line. The steepest descend method is used to on-line adjust conjunctive weights. A momentum term is used in the learning process. The learning rates are local adjusted for each term of conjunctive weight matrix in terms of variety of errors. The speed of learning has accelerated. The simulation experiments show this method has rapid convergence speed and high control accuracy.

The inverse kinematics control algorithm based on RBF neural networks for manipulators

The robustness of a schedule is an important problem in practice. In this paper it is studied in the angle that the optimal schedules do not change. Firstly, the interval perturbation robustness of an optimal schedule is defined, that is the property that an optimal schedule keeps the same when some of the parameters in the scheduling problem vary in some intervals. Then the interval perturbation robustness of an optimal schedule for single machine discounted total weighted completion time is studied. Form a lemma that gives the relationship between the order of r parameters and the overlaps between each two of the intervals in which these parameters vary, the results in this paper are proved. The results are three if and only if conditions under which an optimal schedule is of interval perturbation robustness. These results relate to the optimality of a schedule at some of the vertices of a hyperrectangle of r dimension consisting of the varying parameters. Some examples that show how to use these results are given.

The interval perturbation robustness of an optimal schedule for single machine discounted total weighted completion time problem

Dynamic scheduling of vehicles is studied in this paper. A new framework for dynamic scheduling of delivery vehicles is proposed. It is a hybrid one that incorporates elements of the hierarchical and heterarchical framework. The scheduling systems based on it can produce both robust and globally optimized solutions in complex and dynamic environments. It can be implemented using intelligent agent technology. Details of each agent and the interaction are described. The flow of information in the dynamic scheduling system is given.

A new framework for dynamic scheduling of delivery vehicles

In the paper the interval perturbation robustness of an optimal schedule is defined. In Li Jiangeng and Tu Fengsheng (2001) some methods are given by which the interval perturbation robustness of an optimal schedule can be determined for some scheduling problems. In this paper some new methods to judge the interval perturbation robustness of an optimal schedule are given. These are: two if and only if conditions for a single machine total weighted completion time problem, some if conditions for a single machine total weighted completion time problem with precedence constraints which take the form of chains, some if conditions for a single machine maximum lateness problem with precedence constraints which take any form, some if conditions for a single machine tardy jobs problem, and some if conditions for a two machine job shop problem with the objective of maximum completion time.

Judging methods for interval perturbation robustness of optimal schedules

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