Approximation of the inverse kinematics of a robotic manipulator using a neural network

A fundamental property of a robotic manipulator system is that it is capable of accurately following complex position trajectories in three-dimensional space. An essential component of the robotic control system is the solution of the inverse kinematics problem which allows determination of the joint angle trajectories from the desired trajectory in the Cartesian space. There are several traditional methods based on the known geometry of robotic manipulators to solve the inverse kinematics problem. These methods can become impractical in a robot-vision control system where the environmental parameters can alter. Artificial neural networks with their inherent learning ability can approximate the inverse kinematics function and do not require any knowledge of the manipulator geometry. This thesis concentrates on developing a practical solution using a radial basis function network to approximate the inverse kinematics of a robot manipulator. This approach is distinct from existing approaches as the centres of the hidden-layer units are regularly distributed in the workspace, constrained training data is used and the training phase is performed using either the strict interpolation or the least mean square algorithms. An online retraining approach is also proposed to modify the network function approximation to cope with the situation where the initial training and application environments are different. Simulation results for two and three-link manipulators verify the approach. A novel real-time visual measurement system, based on a video camera and image processing software, has been developed to measure the position of the robotic manipulator in the three-dimensional workspace. Practical experiments have been performed with a Mitsubishi PA10-6CE manipulator and this visual measurement system. The performance of the radial basis function network is analysed for the manipulator operating in two and three-dimensional space and the practical results are compared to the simulation results. Advantages and disadvantages of the proposed approach are discussed

Forward and Inverse Kinematics Solution of A 3-DOF Articulated Robotic Manipulator Using Artificial Neural Network

In this research paper, the multilayer feedforward neural network (MLFFNN) is architected and described for solving the forward and inverse kinematics of the 3-DOF articulated robot. When designing the MLFFNN network for forward kinematics, the joints' variables are used as inputs to the network, and the positions and orientations of the robot end-effector are used as outputs. In the case of inverse kinematics, the MLFFNN network is designed using only the positions of the robot end-effector as the inputs, whereas the joints’ variables are the outputs. For both cases, the training of the proposed multilayer network is accomplished by Levenberg Marquardt (LM) method. A sinusoidal type of motion using variable frequencies is commanded to the three joints of the articulated manipulator, and then the data is collected for the training, testing, and validation processes. The experimental simulation results demonstrate that the proposed artificial neural network that is inspired by biological processes is trained very effectively, as indicated by the calculated mean squared error (MSE), which is approximately equal to zero. The resulted in smallest MSE in the case of the forward kinematics is 4.592×10^(-8) in the case of the inverse kinematics, is 9.071×10^(-7). This proves that the proposed MLFFNN artificial network is highly reliable and robust in minimizing error. The proposed method is applied to a 3-DOF manipulator and could be used in more complex types of robots like 6-DOF or 7-DOF robots

The control of a manipulator using cerebellar model articulation controllers

Thesis (Master)--Izmir Institute of Technology, Mechanical Engineering, Izmir, 2003Includes bibliographical references (leaves: 72-74)Text in English; Abstract: Turkish and Englishviii, 91 leavesThe emergence of the theory of artificial neural networks has made it possible to develop neural learning schemes that can be used to obtain alternative solutions to complex problems such as inverse kinematic control for robotic systems. The cerebellar model articulation controller (CMAC) is a neural network topology commonly used in the field of robotic control which was formulated in the 1970s by Albus. In this thesis, CMAC neural networks are analyzed in detail. Optimum network parameters and training techniques are discussed. The relationship between CMAC network parameters and training techniques are presented. An appropriate CMAC network is designed for the inverse kinematic control of a two-link robot manipulator

IK-FA, a new heuristic inverse kinematics solver using firefly algorithm

In this paper, a heuristic method based on Firefly Algorithm is proposed for inverse kinematics problems in articulated robotics. The proposal is called, IK-FA. Solving inverse kinematics, IK, consists in finding a set of joint-positions allowing a specific point of the system to achieve a target position. In IK-FA, the Fireflies positions are assumed to be a possible solution for joints elementary motions. For a robotic system with a known forward kinematic model, IK-Fireflies, is used to generate iteratively a set of joint motions, then the forward kinematic model of the system is used to compute the relative Cartesian positions of a specific end-segment, and to compare it to the needed target position. This is a heuristic approach for solving inverse kinematics without computing the inverse model. IK-FA tends to minimize the distance to a target position, the fitness function could be established as the distance between the obtained forward positions and the desired one, it is subject to minimization. In this paper IK-FA is tested over a 3 links articulated planar system, the evaluation is based on statistical analysis of the convergence and the solution quality for 100 tests. The impact of key FA parameters is also investigated with a focus on the impact of the number of fireflies, the impact of the maximum iteration number and also the impact of (a, ß, ¿, d) parameters. For a given set of valuable parameters, the heuristic converges to a static fitness value within a fix maximum number of iterations. IK-FA has a fair convergence time, for the tested configuration, the average was about 2.3394 × 10-3 seconds with a position error fitness around 3.116 × 10-8 for 100 tests. The algorithm showed also evidence of robustness over the target position, since for all conducted tests with a random target position IK-FA achieved a solution with a position error lower or equal to 5.4722 × 10-9.Peer ReviewedPostprint (author's final draft

Compliance error compensation technique for parallel robots composed of non-perfect serial chains

The paper presents the compliance errors compensation technique for over-constrained parallel manipulators under external and internal loadings. This technique is based on the non-linear stiffness modeling which is able to take into account the influence of non-perfect geometry of serial chains caused by manufacturing errors. Within the developed technique, the deviation compensation reduces to an adjustment of a target trajectory that is modified in the off-line mode. The advantages and practical significance of the proposed technique are illustrated by an example that deals with groove milling by the Orthoglide manipulator that considers different locations of the workpiece. It is also demonstrated that the impact of the compliance errors and the errors caused by inaccuracy in serial chains cannot be taken into account using the superposition principle.Comment: arXiv admin note: text overlap with arXiv:1204.175

Computational neural learning formalisms for manipulator inverse kinematics

An efficient, adaptive neural learning paradigm for addressing the inverse kinematics of redundant manipulators is presented. The proposed methodology exploits the infinite local stability of terminal attractors - a new class of mathematical constructs which provide unique information processing capabilities to artificial neural systems. For robotic applications, synaptic elements of such networks can rapidly acquire the kinematic invariances embedded within the presented samples. Subsequently, joint-space configurations, required to follow arbitrary end-effector trajectories, can readily be computed. In a significant departure from prior neuromorphic learning algorithms, this methodology provides mechanisms for incorporating an in-training skew to handle kinematics and environmental constraints

Design of a Parallel Robotic Manipulator using Evolutionary Computing

In this paper the kinematic design of a 6‐dof parallel robotic manipulator is analysed. Firstly, the condition number of the inverse kinematic jacobian is considered as the objective function, measuring the manipulator’s dexterity and a genetic algorithm is used to solve the optimization problem. In a second approach, a neural network model of the analytical objective function is developed and subsequently used as the objective function in the genetic algorithm optimization search process. It is shown that the neuro‐genetic algorithm can find close to optimal solutions for maximum dexterity, significantly reducing the computational burden. The sensitivity of the condition number in the robot’s workspace is analysed and used to guide the designer in choosing the best structural configuration. Finally, a global optimization problem is also addressed

Kinematically optimal hyper-redundant manipulator configurations

“Hyper-redundant” robots have a very large or infinite degree of kinematic redundancy. This paper develops new methods for determining “optimal” hyper-redundant manipulator configurations based on a continuum formulation of kinematics. This formulation uses a backbone curve model to capture the robot's essential macroscopic geometric features. The calculus of variations is used to develop differential equations, whose solution is the optimal backbone curve shape. We show that this approach is computationally efficient on a single processor, and generates solutions in O(1) time for an N degree-of-freedom manipulator when implemented in parallel on O(N) processors. For this reason, it is better suited to hyper-redundant robots than other redundancy resolution methods. Furthermore, this approach is useful for many hyper-redundant mechanical morphologies which are not handled by known methods