text: The manipulator workspace mapping is an important problem in robotics and has attracted significant attention in the community. However, most of the pre-existing algorithms have expensive time complexity due to the reliance on sophisticated kinematic equations. To solve this problem, this paper introduces subspace learning (SL), a variant of subspace embedding, where a set of robot and scope parameters is mapped to the corresponding workspace by a deep neural network (DNN). Trained on a large dataset of around 6 × 104 samples obtained from a MATLAB®implementation of a classical method and sampling of designed uniform distributions, the experiments demonstrate that the embedding significantly reduces run-time from 5.23 × 103 s of traditional discretization method to 0.224 s, with high accuracies (average F-measure is 0.9665 with batch gradient descent and resilient backpropagation).1MATLAB® Scripts are available at https: github.com liaopeiyuan Subspace-Learning
  @cite_24: Neural networks with their inherent learning ability have been widely applied to solve the robot manipulator inverse kinematics problems. However, there are still two open problems: (1) without knowing inverse kinematic expressions, these solutions have the difficulty of how to collect training sets, and (2) the gradient-based learning algorithms can cause a very slow training process, especially for a complex configuration, or a large set of training data. Unlike these traditional implementations, the proposed metho trains neural network in joint subspace which can be easily calculated with electromagnetism-like method. The kinematics equation and its inverse are one-to-one mapping within the subspace. Thus the constrained training sets can be easily collected by forward kinematics relations. For issue 2, this paper uses a novel learning algorithm called extreme learning machine (ELM) which randomly choose the input weights and analytically determines the output weights of the single hidden layer feedforward neural networks (SLFNs). In theory, this algorithm tends to provide the best generalization performance at extremely fast learning speed. The results show that the proposed approach has not only greatly reduced the computation time but also improved the precision.
  @cite_19: Purpose – This paper aims to combine and further develop different mathematical models of the workspace representation of 6 degrees of freedom parallel mechanisms and to bring a new point of view to existing workspace analysis methods through using neural networks (NN).Design methodology approach – For the orientation workspace of the 6‐3 SPM, discretization method is used which is based on Euler angles and the NN algorithm is applied.Findings – The workspace analysis is carried out in the direction perpendicular to the moving platform which is the most workable direction of 6‐3 Stewart platform mechanisms and NN algorithm has decreased processing time.Originality value – The determination of the point, on that direction, at which the workspace is maximum, is outlined. It is the first time that the NN is used for classification of workspace of a parallel manipulator.
  @cite_21: The main purpose of the paper is to develop a neural network application destined to the workspace generation of a parallel mechanism, as an performant alternative to the workspace representation based on inverse kinematic model. The paper describes both algorithms. The initial testing was made for a parallel mechanism with two degrees of freedom that could be applied for the orientation of different systems like a TV satellite dish antennas, sun trackers, telescopes, cameras, radars etc.
  @cite_20: 
summary: In the literature, the development of a neural network for workspace generation has been already tested on both serial-link and parallel mechanisms, utilizing several model architectures and optimization methods @cite_20 @cite_24 . The feasibility of using an artificial neural network for workspace analysis is first proposed and investigated by @cite_19 , where a two-layer perceptron learns to generate the orientation workspace of a 6-3 SPM parallel mechanism based on a 3-tuple input. In a similar approach, @cite_21 constructs a three-layer deep network that takes the input joint angles of a 2-DOF parallel manipulator and gives the workspace of the mechanism in a particular Cartesian plane. Levenberg-Marquardt method is used for optimization, and the lowest mean squared error obtained by the algorithm is 0.026.