Kinematic analysis of a novel 3-DOF actuation redundant parallel manipulator using artificial intelligence approach

Abstract

Kinematic analysis is one of the key issues in the research domain of parallel kinematic manipulators. It includes inverse kinematics and forward kinematics. Contrary to a serial manipulator, the inverse kinematics of a parallel manipulator is usually simple and straightforward. However, forward kinematic mapping of a parallel manipulator involves highly coupled nonlinear equations. Therefore, it is more difficult to solve the forward kinematics problem of parallel robots. In this paper, a novel three degrees-of-freedom (DOFs) actuation redundant parallel manipulator is introduced. Different intelligent approaches, which include the Multilayer Perceptron (MLP) neural network, Radial Basis Functions (RBF) neural network, and Support Vector Machine (SVM), are applied to investigate the forward kinematic problem of the robot. Simulation is conducted and the accuracy of the models set up by the different methods is compared in detail. The advantages and the disadvantages of each method are analyzed. It is concluded that ν-SVM with a linear kernel function has the best performance to estimate the forward kinematic mapping of a parallel manipulator.

Introduction

A parallel kinematic manipulator is a closed-loop mechanism, in which the end-effector is connected to the base by at least two independent kinematic chains. Generally, it comprises two platforms, which are connected by joints and legs acting in parallel [1]. Nowadays, many applications of parallel robots can be found in various industrial fields, such as manufacturing production configurations [2], micro-motion parallel robot for medical applications [3], assembly robot in automotive applications [4], deep sea exploration [5], and so on. More recently, they have been used in the development of high precision machine tools [6].

Redundancy in parallel manipulators is divided into kinematic redundancy and actuation redundancy [7]. This paper introduces a novel 3-DOF parallel manipulator with actuation redundancy, which can be used as a micro-motion platform. Because the design and analysis of a parallel manipulator with actuation redundancy is very complex, therefore, only the kinematic analysis is given, the issues regarding dynamic, stiffness analysis, and workspace optimization will be presented in other sources.

Kinematic analysis includes inverse kinematics and forward kinematics. Forward kinematic problem (FKP) is to compute the position and orientation of the end-effector of the manipulator based on a set of joint angles. In most cases, joint angles can be computed independently. However, the forward kinematics problem of parallel manipulators is generally complicated.

Different efforts have been made in solving FKP either in general cases or in special cases. Generally, there are four different methods to solve this problem: analytical approaches; use of additional sensors or transducers; numerical methods; and neural network based approaches [8]. Some scholars applied Newton–Raphson method [9], [10], [11] or other analytical approaches for solving the FKP [12], [13], [14], [15], [16], [17]. However, most of these analytical approaches were devised for special configurations of parallel manipulators [8]. To address this issue of generalization, numerical approaches, e.g., Newton–Raphson method, have been proposed [18], [19], [20], [21], [22]. Recently, artificial neural network methodology has received considerable attention for solving the FKP of parallel robots, and some meaningful results have been achieved [8], [23], [24].

Although artificial neural network (ANN) is a useful tool for solving the FKP of parallel robot, it still has some intrinsic disadvantages: (1) the multi-layer neural networks cannot be adapted for on-line application, while the control system of a parallel robot requires real-time processing. (2) The ability of the artificial neural network to map the input and output relation is completely dependent on the accurate training of the system, the sample size is large and the training method is crucial. A very large amount of data is required in order to ensure that the results are statistically accurate. (3) It has the problems such as slow convergence speed, local minima, and poor generalization. Therefore, it is necessary to investigate other methods in order to solve the FKP of parallel robots.

Unlike empirical risk minimization used in other methods, Support Vector Machine (SVM) introduced by Vapnik [26], is based on the principle of structural risk minimization. It is originated in modern statistical learning theory, and has found a wide range of real-world applications recently. In good generalization, the absence of local minima and the sparse representation of solution are the advantages of considering SVM as one of the powerful tools for classification and regression. Zha [27] used SVM for solving the FKP of a 6-SPS Stewart platform, some basic results were obtained.

In this paper, we plan to investigate an SVM regression for solving the FKP of the novel 3-DOF parallel manipulator with actuation redundancy. The results show that SVM is more powerful for FKP of robots compared with other intelligent methods, such as MLP and RBF neural networks.

In the following sections, first, geometric modeling and kinematic analysis of the parallel robot are developed, and then an overview of an SVM is presented. The results from the applications of the SVM and neural networks to solve the FKP of the parallel manipulator are presented and the results are compared. Finally, the conclusion and future work are given.